Newton’s Second Law



In-class examples (part A)

1) An 50 kg object is accelerating at a rate of 5 m/s2 to the right. Find the net force acting on the object.

2) Three forces (50N [S], 60N [W], and 30N [E] ) act simultaneously upon a 30 kg object. Find the object’s acceleration.

3) A man pushes a 60 lb lawnmower across the grass with a constant horizontal force of 30N. If the lawnmower moves with a constant velocity, find the force of friction opposing the lawnmower’s motion.

4) A box is accelerated from rest along a frictionless surface by a net force of 100N. It covers 40 meters in 5 seconds. Find the mass of the box.

5) A father (80 kg) pulls his son (30 kg) in a radio-flyer wagon (10 kg). The handle of the wagon makes an angle of 40o with the horizontal, and the dad pulls with a force of 200N. First, draw an FBD (free-body-diagram) of this situation, showing all the forces acting on the wagon. Then, find the acceleration of the wagon if …

a) the ground is frictionless (which, by the way, is highly unlikely)

b) the ground provides a constant frictional force of 30N.

Homework Problems (part A)

1. A 5 kg box is sitting at rest on a perfectly frictionless surface. Suddenly, a 100 N forces pulls it eastward. Find the acceleration of the box.

2. A 300 kg block is sitting at rest on a perfectly frictionless surface. Two 25N forces act on the block, one directed east and one directed west. Find the acceleration of the block.

3. A block of unknown mass sits on a perfectly frictionless surface. It is pulled by a force of 100 N [S] and pushed by a force of 50 N [N]. The magnitude of its acceleration is 9 m/s2. Find the mass of the block as well as the direction of the acceleration.

4. An object is pulled in two opposite directions along a frictionless surface by forces of 50 kN [E] and 30 kN [W]. If the object is accelerated at 5 m/s2, find the object’s mass.

5. A 40 kg box is pulled from rest at an angle of 30o above the horizontal with a constant force of 500N. If the force of friction opposing the motion is 100N, find the box’s acceleration parallel to the ground. Now use an equation of motion to figure out how far will it move in 7 seconds? What will its velocity be after these 7 seconds?

6. A 100 kg block is sitting on a perfectly frictionless surface. A force of 200 N directed at an angle of 30o above the horizontal pulls the block. Find the acceleration of the block parallel to the ground.

7. A block is pulled along a surface at a constant velocity by a force of 200 N. Find the force of friction opposing the movement.

8. A 60 kg block is being pulled along a surface by a force of 100N. If the magnitude of the block’s acceleration is 1.2 m/s2, find the force of friction opposing the movement. Start off by drawing a full Free-Body-Diagram (FBD) of the block.

9. A 1.0 kg toy car is moving across a smooth floor with a velocity of 5.0 m/s. An unbalanced force of 2.0 N acts on the car for 4.0 s. Determine the velocity of the car at the end of the interval if the force acts in the opposite direction to the motion of the car.

In-class examples (part B)

1) A 30 kg box is pushed along a surface. The person pushing the box pushes with a constant force of 300 Newtons directed at an angle of 30o below the horizontal. If the box starts from rest and reaches a speed of 5 m/s after only 2 seconds of pushing, find the force of friction acting on the box. Make sure to start with a complete FBD of the box, showing all the forces acting upon it.

2) A skydiver of mass 75 kg is falling through the non-physics-land air. Eventually he reaches a terminal velocity and falls at a constant speed. Find the resistive force (from the air) that acts on the skydiver at this time. Make sure to start with a complete FBD, showing all the forces acting upon the skydiver.

3) Explain the relationship between Newton’s 1st Law and his 2nd Law.

Homework Problems (part B)

10. An electron has a mass of 9.1 x 10–31 kg. Between the electrodes of a cathode-ray tube, it moves a distance of 4.0 mm, accelerated by a net electrical force of 5.6 x 10–15 N. Assuming that it started from rest, find its acceleration and its final velocity.

11. A bullet of mass 20 g strikes a fixed block of wood at a speed of 320 m/s. The bullet embeds itself in the block of wood, penetrating to a dept of 6.0 cm. Calculate the average net force acting on the bullet while it is being brought to rest.

12. A 2 kg block is pulled across a frictionless surface by forces of 5N [E], 16 N [SW], and 10 N [S 30 E]. Find the magnitude and direction of the block’s acceleration.

13. A 9 kg ball falls through the air, which resists the ball with a constant force of 9N. Draw a free-body diagram of the ball and then find its acceleration. Why is the acceleration of the ball NOT equal to g? Fully explain.

14. If an object is moving at a constant velocity, explain what Newton’s 2nd law says about the object. Does this agree with or disagree with Newton’s 1st Law.

15. A 3-car train is being pulled on frictionless tracks. The lead car is has a mass of 2000 kg, while the 2nd two cars each have masses of 1500 kg. How much force is required to accelerate the train at 3 m/s2? If the train is being pulled by this force and the last car suddenly detaches, what will its new acceleration be?

16. Two girls pull a sled from rest across a field of snow, as shown in the diagram. A third girl pulls backward with a 2.0 N force. All forces are constant. If the mass of the sled is 10 kg, determine its instantaneous acceleration. Then, determine the time required for the sled to move a distance of 10 m.

(A view from above, or a “bird’s eye view”, is assumed in this problem)

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30°

40°

10 N

10 N

2 N

10 kg

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