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2010 AP Physics Midterm Review Sheet

E Period Exam [Lucia]

D Period Exam [Schemm]

Topics are listed below, followed by unit skills and objectives you should be able to complete for the respective concepts. At the end are a batch of sample problems for your review.

I. Newtonian Mechanics

A.   Kinematics

(including vectors, vector algebra and components,

coordinate systems, displacement, velocity, and acceleration)

[pic][pic]1. Motion in one dimension

[pic][pic]2. Motion in two dimensions, projectile motion

B.   Newton’s laws of motion

[pic][pic]1. Static equilibrium (First law)   [pic][pic]

[pic][pic]2. Dynamics of a single particle  (Second law)[pic]

[pic][pic]3. Systems of two or more bodies (Third law)[pic]

C. Work, energy, power

[pic][pic]1. Work and work-energy theorem[pic][pic]

[pic][pic]2. Conservative forces and potential energy

[pic]3. Conservation of energy

4. Power

D. Systems of particles, linear momentum

1. Center of mass

2. Impulse and momentum

3. Conservation of linear momentum, collisions

E. Circular motion and rotation

1. Uniform circular motion

2. Torque and rotational statics

F. Oscillations and gravitation

1. Simple harmonic motion (dynamics and energy relationships)

2. Mass on a spring

3. Pendulum and other oscillations

4. Newton’s law of gravity

5. Orbits of planets and satellites

a. Circular

II. Fluid Mechanics and Thermal Physics

A.  Fluid Mechanics

1. Hydrostatic pressure

2. Buoyancy 

3. Fluid flow continuity

4. Bernoulli’s equation

B. Thermal Physics

1. PV cycles

2. Laws of Thermodynamics

AP Multiple Choice Questions- Kinematics

You may be given a motion graph to interpret. For example, you may be asked to determine the acceleration of an object from a position vs time graph. You may be asked to determine the position of an object at a specified time on a velocity vs time graph.

1. Be able to calculate average speed and average velocity.

2. Be able to use acceleration formulas for simple calculations in multiple choice questions.

3. Be able to calculate the position of an object either from a graph or from data.

4. Know that all objects fall at the same rate in a vacuum.

5. Be able to predict the appearance of a motion graph (either d vs t or v vs t) from data.

AP Free Response Questions - Kinematics

1. Given a v vs. t graph, be able to create the corresponding a vs. t or d vs. t graph. Given a d vs t graph, be able to create the corresponding v vs t or a vs t graph.

2. Be able to make predictions about the velocity of an object at a certain time from a v vs t graph or predictions about position at a certain time from a d vs t graph.

3. Given a v vs t graph, be able to predict when the magnitude of the velocity is increasing or decreasing. Given a d vs t graph, be able to predict when the object is moving away or toward its starting position.

4. Be able to use acceleration formulas to calculate an object's position, velocity, and/or acceleration.

5. Be able to draw a graph of an object's motion.

6. Be able to describe the motion of an object. Describe its velocity (is it constant or is it accelerating?). State its initial velocity, if known. State its rate of acceleration, if known. If it is moving horizontally as well as vertically, remember to describe both sets of motion. The key words to use -- velocity, acceleration, and position!

AP Multiple Choice Questions on Newton’s Laws of Motion

1. Be able to draw and interpret free body diagrams (FBDs) that represent all forces acting on an object! The following are examples of FBDs you must interpret:

o A weight hangs from two strings which make angles θ1 or θ2 with the horizontal or with the vertical. There are three forces acting: the weight of the object, W, acts down toward the center of the earth, and the upward components of the tensions in each string. You should be able to state which string has the greater tension (judge it by how much of the weight it supports). Or, you might be asked to solve for tension in terms of angle and weight.

o A weight W is on an inclined plane with a rough surface. If W slides down the plane, there are three "real" forces (not components!) acting: W, N (for the normal force), and f (for the frictional force). Be able to draw a FBD showing each of these forces and the directions they act in. Be able to solve for any one of the three forces in terms of the other two. Be able to apply Newton's Second Law to the motion of the block.

o A weight W is on an inclined plane with a rough surface. If W is pushed up the plane, there are four "real" forces (not components!) acting: W, N (for the normal force), F for the applied force (the push!), and f (for the frictional force). Be able to draw a FBD showing each of these forces and the directions they act in. Be able to solve for any one of the four forces in terms of the other three. Be able to apply Newton's Second Law to the motion of the block.

o A weight W is pulled across a rough horizontal surface by a force F applied at angle θ to the horizontal. Draw the FBD for the three "real" forces acting (not components!). Be able to solve for one force (usually normal force) in terms of the other two forces.

o A weight W is pushed across a rough horizontal surface by a force F applied at angle θ to the horizontal. Draw the FBD for the three "real" forces acting (not components!). Be able to solve for one force (usually normal force) in terms of the other two forces.

o A mass m is connected by a weightless cord which passes over a frictionless pulley to mass M which rests on a smooth table. Be able to use Newton's Second Law and your FBDs to write an expression for the acceleration of the system. Be able to do this for a rough surface.

o Two unequal masses are connected by a cord and are pulled by a rope along a smooth surface. Be able to use Newton's Second Law and your FBDs to write and expression for the acceleration of the system. Be able to do this for a rough surface.

o An weight W falls through the air, experiencing a retarding force F due to air friction. Be able to use Newton's Second Law and your FBD to write an expression for the acceleration of the weight.

2. Be able to do simple calculations using Hooke's Law.

3. Be able to recognize the definitions of simple terms such as acceleration and inertia.

4. Be able to recognize when an object is accelerating and be able to determine the unbalanced force causing the acceleration.

5. Be able to determine the direction of the net force (unbalanced force) causing the acceleration.

6. Be able to recognize the conditions for translational equilibrium.

7. Be able to recognize a motion graph that for an object in translational equilibrium or for an object that is accelerating.

AP Free Response Questions on Newton’s Laws of Motion

1. Be able to draw FBDs! In an FBD, only show "real" forces, not components. For example, if you have a force applied at an angle, only show that force at the angle, not its horizontal and vertical components. You must lable the forces and give their signs. Always use the given nomenclature. For example, if they say block 4 M rests on a table, its weight must be shown as 4 Mg. Notice, if a capital letter is given, use the capital letter!

2. Be able to apply Newton's Second Law and interpret your FBD for all the cases listed above. Also, we will study other forces in later units that will be asked on AP Free Response Questions.

AP Multiple Choice Questions -- Motion in Two Dimensions

1. Be prepared to perform simple calculations. For example, an object is rolled off a table a height h above the ground. The object has initial horizontal speed v. Calculate how long the object is in the air. Calculate how far it lands from the edge of the table. Predict how time in the air and distance it lands from the edge of the table would change if the horizontal velocity of the object were increased or decreased.

2. Be prepared to perform simple calculations. For example, and projectile is launched with velocity v from the ground at an angle θ. Points are labeled on its trajectory, one being at its apex. Be able to identify the acceleration vector for each point. Be able to compare the speeds at each point. Be able to compare the velocities at each point. Be able to identify graphs of its vertical velocity, its horizontal velocity, and its acceleration for each point in its trajectory.

3. Important - know that the horizontal velocity is constant for each point in the trajectory. Know that the vertical velocity is accelerating. At the apex of the trajectory, the object has a vertical velocity of zero. It still has acceleration (gravity) and horizontal velocity. The speed of the object at any point is the vector sum of the horizontal and vertical velocities at that point. Remember -- going up, vertical velocity is positive and acceleration is negative; going down, vertical velocity is negative and acceleration is negative.

4. Remember -- acceleration involves a change in speed and/or direction.

AP Free Response Questions -- Motion in Two Dimensions

1. These questions occur over and over in free response questions! They all involve an object that is some height h above the ground. Something has given it horizontal velocity v at this point. Its initial vertical velocity is zero. You will be asked to describe its motion as it falls to the ground. Remember -- describe its horizontal motion (it moves with constant horizontal speed v); describe its vertical motion (it accelerates downward at -9.8 m/s/s); and, describe the trajectory that you see as the vector sum of these two motions.

2. Be able to recognize this type of problem which is asked over and over. They all involve an object that is some height h above the ground. Something has given it horizontal velocity v at this point. Its initial vertical velocity is zero. You have to calculate the time it takes for the object to reach the ground. You have to calculate how far it lands (horizontally). You have to calculate its speed when it hits the floor (remember, it is the vector sum of its final vertical velocity and its horizontal velocity).

3. Be able to recognize an Atwood machine or its variation. Two objects with different masses are hung by a cord across a frictionless pulley (in its variation, one object is on a table and the other hangs off the edge or the object is on an incline and the other object hangs off its edge). Calculate the acceleration of the system. You have to calculate the time it takes for the object to reach the ground. You have to calculate how far it lands (horizontally). You have to calculate its speed when it hits the floor (remember, it is the vector sum of its final vertical velocity and its horizontal velocity).

4. Trajectory problems and their variations (common variation is to launch the object and have it clear a fence, etc.). Be able to calculate how high the object goes and how long it is in the air. Be able to calculate its height at a specific point above the ground.

5. Be able to draw horizontal velocity vs. time, vertical velocity vs. time, and acceleration vs. time graphs for projectile motion.

AP Multiple Choice Questions on Work

1. Be able to recognize situations when work is not done. For example, an object in circular motion does no work in one revolution (the displacement is zero!).

2. Know your that power is the rate of doing work!

3. Important: Power = Force * speed (P=Fv).

4. Be able to perform simple work and power calculations.

5. Know that the work done by the gravitational force corresponds to the change in gravitational potential energy.

AP Free Response Questions on Work

1. Very important - Know the work/energy theorem! The work done is equal to the change in kinetic energy.

2. Remember to find the component doing the work - the one parallel to the displacement.

3. Be able to calculate the work done by different forces. For example, when a box is pushed across the floor. You can calculate the work done by the applied force, the work done by the frictional force, and the net work done.

4. Be able to graphically determine work. You may be given data that involves how force varies with displacement. Work is the area under the curve (W=Fd).

AP Multiple Choice Questions on Energy

1. Be able to recognize the relationship between potential energy and kinetic energy for oscillating objects. The energies are equal, but occur at different times. When is potential energy a maximum? When is kinetic energy a maximum? The total mechanical energy (the sum of the KE and the U at each point) is always a constant value.

2. Be able to graphically show how kinetic energy changes. For example, you roll a ball off the table. If you graph KE vs time, the graph will be parabolic (since the object is accelerating). KE increases with time, but not linearly. Also, in this example, initial KE is not zero. Since the ball is rolling, it already had speed, so it already had KE. Remember, if the object is accelerating, it's KE vs time graph is parabolic, not linear!

3. Know the formula for elastic potential energy.

4. Be able to manipulate other formulas to solve for KE. An example, think of the centripetal force formula (F=mv2/r) and the KE formula (KE=1/2 mv2). See how you can manipulate both to get an expression for KE for an object in circular motion?

5. Be able to perform simple KE and U calculations.

AP Free Response Questions on Energy

1. Know the work/energy theorem. The change in an object's KE is equal to the work done. This can be used to find, for example, the distance that an object slides before coming to rest. Use the work/energy theorem to solve problems that can't be solved by acceleration formulas.

2. Energy isn't usually asked seperately, but is incorporated into problems. For example, an object rolls off a table. You are asked to find its kinetic energy the instant before it hits the floor. Remember, total KE = KE x + KEy. You must include the KE it has before due to its horizontal speed. You must find its vertical velocity the instant before it hits the floor and use that to find its vertical KE.

3. If friction is ignored, KE equals U. For example, a pendulum - you can find its initial potential energy and use that to find its speed at the bottom of its swing.

4. In a pendulum problem, think how you can use trig to find how far the bob is above base level when all you know is the length of the string and the angle relative to the vertical the string is pulled back.

5. Be able to draw total mechanical energy vs time, KE vs time, and U vs time graphs for objects in SHM (pendulums, springs, etc.).

6. Be able to read a graph of experimental data (U vs x, for example) for an object in SHM to determine how to find an object's potential energy at any position.

AP Multiple Choice Questions for Momentum

1. Be prepared to perform simple calculations for linear momentum problems.

2. Remember signs for your velocities! For example, remember sign conventions for problems in which a ball rebounds from a bat, etc. The sign of its incoming velocity is opposite that of its outgoing velocity. This does not give you a net momentum change of zero!

3. Remember that momentum is conserved (the same) in any collision.

4. Be able to identify an elastic collision (objects rebound, do not stick together).

5. Remember that momentum is conserved, but kinetic energy is not, in inelastic collisions (which represent everything in real life).

6. Be able to recognize when momentum is changing from a graph. Momentum changes when speed changes.

7. Be able to predict the speeds and directions of objects after a collision.

AP Free Response Choice Questions for Momentum

1. Be able to perform calculations for ballistic pendulum problems. These are problems where an object is suspended in such a way that it can swing upward. It is hit with a moving object that becomes imbedded in the suspended object. This collision is the conservation of momentum part of the problem. You can use conservation of momentum to predict the speed of the suspended object/moving object (sometimes you work this problem "backwards" and use conservation of momentum to predict the speed of the moving object). The suspended object/moving object now has kinetic energy. It swings upward a height h, converting its kinetic energy into potential energy. You can use conservation of energy to predict how high it will swing upward.

2. Remember that energy lost in an inelastic collision usually results in a thermal energy gain (because of work done against friction).

3. Momentum is usually combined with kinetic energy calculations in free response questions.

4. Be able to perform calculations for objects attached to a spring. A moving object collides with the object on a spring and becomes stuck to it. The spring is compressed a distance d before it comes to rest. You can use conservation of momentum to predict the initial speed of the moving object/object attached to a spring. Its kinetic energy is now converted into elastic potential energy of the spring. Another variation -- collisions like this usually set the object into SHM, so they can ask you about the period of oscillation of the objects on the spring.

5. Use a graph or use data to estimate the average force acting on an object during a collision. Use this to calculate the impulse given to the object and its average acceleration. Remember, impulse better describes a collision where the force is variable.

6. You may be asked to work an inelastic collision problem, writing expressions for velocity. Then, they will ask you to do the same problem for an elastic collision!

7. Another calculation that is given that combines momentum and motion involves collisions occurring on rough surfaces. Remember that the frictional force serves as the unbalanced force that eventually causes the object to stop. You can predict how far it will go before it stops using the work/energy theorem or calculation the frictional force and using acceleration formulas and second law.

8. Not very common, but they have asked you to write velocity expressions before and after the collision for momentum in two dimension problems.

AP Multiple Choice Questions Torque

1. Common questions involve simple torque calculations:

o A plank rests on the edge of a table. How far from the edge can a weight be placed before the plank tips?

o Determine an unknown weight using torque calculations.

o Use torque calculations to determine where an object should be suspended to achieve rotational equilibrium.

AP Free Response Questions-Torque

1. There has never been a torque free response question. I have only seen them asked as multiple choice questions.

AP Multiple Choice Questions- Fluids   Fluid questions were added to the AP B test beginning in 2002.

• Be able to determine the buoyant force acting on an object when given the weight in air and the weight in the fluid.

• Be able to recognize that the pressure acting on the bottom of a container is due to the weight of the fluid above it.

• Recognize that high velocity fluid has low pressure. Predict the consequences of low pressure due to high velocity fluid.

AP Free Response Questions-Fluids   Fluid questions were added to the AP B test beginning in 2002.

• All the ones that have occurred since 2002 have dealt with either a fluid-based laboratory exercise or with fluids at rest. (Caution: Newer ones are now including velocity of a stream of fluid using Bernoulli’s principle)

• Be able to calculate gauge pressure.

• Be able to calculate absolute pressure.

• Be able to calculate pressure.

• Kinematics is frequently integrated into fluid problems.

Velocity Sample Problems

1. A car moves east at 18 m/s for 5 min. What is its displacement?

2. A car goes 25 m, east, in 5 min. What is its speed? Its velocity?

3. A car has a speed of 40 km/h. What is its speed in m/s?

4. A car has a speed of 15 m/s. What is its speed in km/h?

5. A car travels at the rate of 20 m/s, E, for 50 seconds and then travels at the rate of 30 m/s, W, for 40 seconds. What is its average speed for the entire trip? What was its average velocity?

6. A boat has a velocity of 8 m/s, east. It is crossing a river that is 20 m wide. The current in the river flows south at 5 m/s. How long will it take the boat to cross the river? How far downstream does it land from its starting point?

7. Answer the following questions about the object’s motion. You may enter the data into a graphing calculator, setting your StatPlot at connected dots or you may draw a graph, connecting the points. You will connect the points so each time interval is its own unique motion. Ignore any acceleration associated with changes in direction.

time in sec, distance in m)

(0,0)

(1,5)

(2,10)

(3,10)

(4,8)

o What is the object’s speed between 0 and 2 sec?

o When is the object motionless?

o What is the object’s speed between 3 and 4 sec?

o When does the object travel its fastest?

o When is the object moving toward its reference point?

Acceleration Sample Problems

1. A car’s velocity increases from rest to 14 m/s, E, in 3.5 sec. What is its acceleration? What is its acceleration if it next slows down to 7 m/s, E, in 2 sec?

2. A mass is attached to a string and then dropped. What is its velocity after 5 sec?

3. A car accelerates from 6 m/s, W, to 20 m/s, W, over a distance of 50 m. What is its rate of acceleration?

4. A ball rolls off a horizontal roof 5 m above the ground. How long does it take to hit the ground?

5. A car is moving at 16.67 m/s when it begins to slow at the rate of 1.5m/s2. How long does it take for it to go 70 m?

6. At the instant a traffic light turns green, a waiting car takes off with a uniform acceleration rate of 8 m/s2. At exactly the same instant, another car, traveling at a constant rate of 20 m/s, passes the first car in another lane. How long does it take the first car to overtake the second? How far does the first car travel before overtaking the second? How fast is the first car traveling at the moment it overtakes the second car?

7. Using data collected in an experiment, a student determined the speed of his object at each time interval. Ignore any acceleration due to a change in direction. Draw your graph with connected data points (not best-fit line!).

(time in sec, speed in m/s)

(0, 0)

(1, 2)

(2, 2)

(3,5)

(4, 1)

o a) During which time interval did the object move at constant speed?

o b) When was the object’s rate of acceleration the greatest?

o c) What was the object’s rate of acceleration between 3 and 4 seconds?

o d) What was his displacement between 3 and 4 sec?

8. A car initially traveling at 20 m/s puts on its brakes and slows to 10 m/s in 5 s. What distance did it travel over this braking interval?

9. A girl stands 2 m above the ground and throws a ball into the air with an upward velocity of +5 m/s. How long does it take the ball to reach its apex? How high above the ground is the apex? How long does it take the ball to hit the ground?

Newton's Laws & Universal Law of Gravitation Sample Problems

1. What gravitational force exists between two 3 kg balls placed 7.25 m apart?

2. A sphere weighing 9800 N and another sphere weighing 1960 N are separated by 4 m. What gravitational force exists between them?

3. A 20 N force gives a stone an acceleration of 4 m/s2. What is the weight of the stone?

4. A 5 kg rocket is acted upon by an upward force of 59 N due to the thrust produced by its engines. What is the rocket's weight? Draw the free-body diagram representing these forces. What is the net force? What acceleration does it cause?

5. A rope attached to an 80 N wagon pulls it horizontally to the right with an acceleration of 0.5 m/s2. What is the mass of the wagon? What is the net force causing this acceleration?

6. A 65 N boy sits on a sled weighing 52 N on a horizontal surface. The coefficient of friction between the sled and the snow is 0.012. What is the magnitude of the frictional force? The sled is pulled at constant speed by a rope held horizontally. What is the tension (the pull) in the rope?

7. A 100 N force is applied to a 10 kg box to push it across a horizontal surface. A frictional force of 20 N exists. What is the acceleration of the box?

8. An object weighing 40 N rests on a surface. The coefficient of friction between the surface and the object is 0.35. What is the frictional force between the object and the surface? A 20 N force is applied to pull the object horizontally. What is the magnitude of the net force? What is the acceleration of the box?

9. A man pulls a 300 N object across a horizontal surface using a 100 N force applied at a 35° angle. What is the normal force? If the object is pulled with an acceleration of 2 ms-2, what is the coefficient of friction?

10. A man pulls a 80 N object across a horizontal surface using a 50 N force applied at a 25° angle. What is the normal force? If the coefficient of friction is 0.3, what is the acceleration of the object?

11. A man pushes a 80 N object across a horizontal surface using a 50 N force applied at a 25° angle. What is the normal force? If the coefficient of friction is 0.3, what is the acceleration of the object?

12. A 10 N object rests on a 10° incline. What is the normal force? What is the parallel force? A 10 kg object rests on a 10° incline. What are the normal and the parallel forces?

13. A 5 N block slides down a 20° incline at constant speed. What is the frictional force? A 75 kg box slides down a 25° incline at constant speed. What is the fricitonal force?

14. What force is needed to push a 15 N object up a 20° incline at constant speed when the coefficient of friction is 0.30?

15. What is the coefficient of friction if a 50 N force is needed to push a 5 kg object up a 25° incline at constant speed?

16. What is the acceleration of a 20 N object which slides down a 35° incline when the coefficient of friciton is 0.4?

17. What is the coefficient of friction if a 40 N objbect slides down a 20° incline with an acceleration of 2 m/s-2?

18. Find the tensions in the cables shown.

[pic]

19. Find the tensions in the cables shown.

[pic]

20. A man pulls a 300 N object across a horizontal surface using a 100 N force applied at a 35° angle. What is the normal force? If the object is pulled with an acceleration of 2 ms-2, what is the coefficient of friction?

21. A man pulls a 80 N object across a horizontal surface using a 50 N force applied at a 25° angle. What is the normal force? If the coefficient of friction is 0.3, what is the acceleration of the object?

22. A man now pushes a 200 N object across a horizontal surface using a 100 N force applied at a 35° angle. What is the normal force? If the object is pulled with an acceleration of 2 ms-2, what is the coefficient of friction?

23. A man pushes a 80 N object across a horizontal surface using a 50 N force applied at a 25° angle. What is the normal force? If the coefficient of friction is 0.3, what is the acceleration of the object?

Two Dimensional Motion

1. An object is thrown horizontally at 15 m/s from the top of a 44 m building. How long does it take for it to strike? How far from the building's base does it land?

2. A missle is dropped from a bomber, giving it an initial horizontal velocity of 8 m/s. The bomber is 122.5 m above the ground. What is the missile's range?

3. A plane flying horizontally at 220 m/s drops a tank when it is 490 m above the ground. How long does it take to fall? What is its range?

4. A rock is dropped from a cliff 90 m high. What is its velocity the instant before it strikes the ground?

1. A missile is launched at a speed of 25 m/s at an angle of 35° to the ground. What is its range? How high did it go vertically?

2. Another is launched at 39.2 m/s and 30°.

3. Another is launched at 67 m/s and 20°.

4. Another is launched at 60 m/s and 40°.

5. A missile is traveling at 7 m/s horizontally and 9.6 m/s vertically when it leaves the launchpad. What is its range and how long is it in the air?

6. Grease pops onto your hand from a frying pan 1 m away from you (measured horizontally). If it were in the air 0.50 sec, what was the initial velocity (resultant) of the grease? Assume optimum angle.

Centripetal Force and Acceleration

1. A moving ball is spun in a circle with a diameter of 1 m at a speed of 3 m/s. What is its centripetal acceleration?

2. A 250 g mass is spun in a horizontal circle. It is held at the end of a 1 m length of string. If it is spun at 15 m/s, what force is applied?

3. A ball weighing 5 N is attached to a 1 m string and swung in a horizontal circle above one's head at the rate of 5 rev/sec (5 rps). What centripetal force is required?

4. Convert 10 rpm (rev/min) into m/s for a horizontal circle of 50 cm radius.

Pendulums

1. What is the period of a pendulum (located on earth) that is 70 cm long?

2. It takes 230 sec for a pendulum to reach its starting point 100 times after its release. What is its period?

3. A pendulum bob is suspended on a string 75 cm long. It has a frequency of 0.57 sec-1. What would the period of a pendulum be that is located at the same location and is 50 cm long?

4. A pendulum on earth has a length of 35 cm. What is its period?

5. What is the acceleration due to gravity on planet X? A 1 m long pendulum has a period of 2 sec on this planet.

Torque Sample Problems

1. An 8 N weight hangs at the end of a 4 m uniform board weighing 2 N. The board pivots at its center. How far must a 10 N weight be hung from the pivot to achieve equilibrium?

2. A uniform 3 m long board with a mass of 50 kg pivots at its center. A 30 kg mass is hung 1.6 m from one end. Where must a 40 kg mass be hung to achieve rotational equilibrium?

3. A 20 N force is applied at the end of a 4 m long massless pole. It is applied at an angle of 25 degrees. What torque is produced?

4. Now a 35 N force is applied at an angle of 35 degrees at the end of a 3 m long massless pole. What torque does it produce?

5. A tapered log 3 m long weighs 50 N and has its center of gravity 1 m from its thick end. It is supported at its center. Where must a 25 N weight be placed to establish equilibrium?

Linear Momentum Sample Problems

1. A 4 N force acts on a 3 kg object moving at 8 m/s for 10 sec. What is the object's change in momentum? What impulse acts on the object? What is the object's final speed?

2. A 1000 kg car traveling at 9 m/s, east, strikes a stationary 2000 kg truck. They interlock as a result of the collision and move off as one. What is their speed? What is their velocity?

3. A 15,000 kg rocket launcher holds a 5000 kg rocket. The rocket exits the launcher at +450 m/s. What is the recoil velocity of the launcher?

4. A 100 g ball traveling to the right at 2 m/s strikes a 200 g ball traveling to the left at 4 m/s. After the collision, the 100 g ball has a velocity of 8 m/s, left. What is the velocity of the 200 g ball?

5. A 1200 kg car moving at 8m/s, north, strikes a 2000 kg truck moving at 4 m/s, south. The velocity of the car is 6 m/s, south. What is the velocity of the truck?

Momentum in Two Dimensions - Sample Problems

1. A 1325 kg car traveling north at 27 m/s collides with a 2165 kg car moving east at 17 m/s. As a result of the collision, they stick together. What is their velocity after the collision?

2. A sticky ball with a mass of 200 g is moving to the west at 6 m/s. It collides with another sticky ball with a mass of 300 g moving north at 5 m/s. The sticky balls stick together as a result of the collision and move off as one. What is their velocity?

3. A 6 kg object A moving at 3 m/s, right, collides with a 6 kg object B at rest. After the collision, A moves at 1.6 m/s, 30°. What is the velocity of B after the collision?

Work Sample Problems

1. A 1200 N force is applied parallel to a horizontal surface. It pushes an 80 N box 2 m across the surface. What work is done? What power is dissipated in 3 minutes?

2. Now the force is applied at a 30° angle relative to the horizontal. What is the force that does work on the box? What work is done? What power is dissipated 5 minutes?

3. A 500 N weight is pushed up an incline that is 4 m long and 1.2 m high. A 200 N force is applied to push the weight, taking 5 minutes. What is the work output? Work input? IMA? MA? Efficiency? Power dissipated? What work is done to overcome friction?

4. A set of pulleys lift a 1200 N load. A 200 N force is applied over an unknown distance. The pulleys are lifted 2 m. If the pulleys are 80% efficient, what distance is the 200 N force applied over? What work is done to overcome friction?

Energy Sample Problems

1. A 5 kg ball is lifted from the floor to a height of 1.5 m above the floor. What is its increase in potential energy?

2. An 8 kg ball is moving at 4 m/s. Work is done on the ball to give it a speed of 12 m/s. What is the ball’s initial kinetic energy? What is the ball’s final kinetic energy? What work was done on the ball?

3. A 3 kg object falls from a height of 10 m. What is its velocity just before it hits the ground? How would this problem differ if the object falling from a height of 10 m only had a mass "m"?

4. For the drawing shown, find the following at each point: The object's mass is 10 kg.

5. Calculate the speed of the object at the bottom of its swing.

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Fluid Sample Problems

1. What is the pressure exerted by a 3 kg mass on a box top 5 cm x 2 cm?

2. What is the force causing a pressure of 3000 Pa over a 0.50 m2 cross-sectional area?

3. A lake is 30 m deep. What is the pressure at that depth?

4. What is the buoyant force experienced by a box of mass 5 kg with dimensions of 15 cm x 12 cm x 13 cm when it is totally immersed in water? What is the apparent weight of the object?

5. What is the buoyant force exerted on 0.001 m3 of steel (ρ = 9000 kg/m3) immersed in water? What is its apparent weight?

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