Principles of Technology



Principles of Technology

Due Fri, 5/26/17

HW 6: Work & Energy in Mechanical Systems

1. a. How much energy is required to pick up a 1kg book off the ground and raise it to a height of 1.2m?

b. How much work was done on the book by the person doing the lifting?

2. In a hydroelectric power plant, suppose that water falls a distance of 110m before reaching the turbine/generator. What is the speed of the water when it reaches the turbine?

3. A 90kg box is stored on a warehouse shelf 8.2 meters above the floor.

a. What is the box’s gravitational potential energy relative to the floor?

b. What is the box’s gravitational potential energy relative to a forklift’s blades 3.5 meters above the floor?

4. A spring compresses 1.25 in from its equilibrium position when a force of 8.4lb is applied.

a. Calculate the spring constant of the spring

b. How much work can the spring do if it is extended 0.85in from equilibrium?

5. A spring with a spring constant of 1800N/m is attached to a wall. A 1.5kg mass is attached to the free end of the spring. The mass can move right and left without friction.

a. The mass is pulled to the right 0.75cm from the equilibrium position. How much potential energy is stored in the spring relative to the equilibrium position?

b. The mass is released. When it reaches the equilibrium position, what is the kinetic energy of the mass? What is its speed?

c. How far to the left will the mass continue past the equilibrium position?

6. A rail gun consists of a U-shaped conductor with a sliding conducting rail lying across it. When a pulse of current is induced into the circuit, the rail will quickly move outward due to the magnetic fields generated in the loop. Suppose a marble with a mass of 0.060 kg is placed on the rail and launched at a speed of 450 m/s.

What is the kinetic energy (J) of the marble at that instant?

7. A 75 gram hailstone has a terminal speed of 180m/s. How much energy does the hailstone impart when it hits a shingle on the roof of a house?

8. A crane lifts a crate 10 feet into the air using a force of 250 pounds. If it takes 5 seconds to perform the lift,

a. How much work was done by the crane?

b. How much energy was used by the crane?

c. How much power was consumed by the crane? (Remember power is energy/time or work/time.)

Report your answer in horsepower (746 watts = 1 HP)

9. A 1250 kg wrecking ball is lifted to a height of 12.7 m above its resting point. When the wrecking ball is released, it swings toward an abandoned building and makes an indentation of 43.7 cm in the wall.

a. What is the potential energy of the wrecking ball at a height of 12.7 m?

b. What is its kinetic energy as it strikes the wall?

c. If the wrecking ball transfers all of its kinetic energy to the wall, how much force does the wrecking

ball apply to the wall?

d. Why should a wrecking ball strike a wall at the lowest point in its swing?

10. A man uses a rope and system of pulleys to lift a 160 lb object to a height of 5 ft. He exerts a force of 45 lb on the rope and pulls a total of 20 ft of rope through the pulleys in the course of lifting the object, which is at rest afterward. a. How much work does the man do in lifting the object and b) what is the percent efficiency of the system?

11. A manual starting system of a chain saw requires a force of 180N to pull the cord. A worker pulls the rope a total of 0.8m when attempting to start the engine. The disk-shaped flywheel around which the rope is wound has a radius of 12 cm and a mass of 7 kg. Find:

a. The moment of inertia of the flywheel

b. The work put into pulling the cord

c. The kinetic energy and angular velocity imparted to the flywheel, assuming no load conditions.

12. A flywheel between an air compressor and its drive motor dampens torque variations. The moment of inertia of the flywheel is 8640 kg•m2.

a. What is the kinetic energy of the flywheel when it rotates at 441 RPM?

b. Calculate the work done by the flywheel if the speed decreases from 441 RPM to 440RPM

in ¼ of a revolution.

13. You are designing the wheels for a solar-powered car competition. You can use solid, annular, or hoop design, approximated by the illustrations shown below. The mass of each wheel is 0.75kg.

Suppose the car starts from rest and 1J of work is transmitted to each wheel, resulting in the rotational motion of the wheel. Calculate the angular speed, in RPM, for each wheel. Which design would you use? EXPLAIN.

Useful equations for this assignment:

Work is the product of force and displacement. [pic] This equation is used for straight line (translational) motion. The units for work are ft•lbs or N•m.

Work is the product of torque and angular displacement. [pic] This is the angular equivalent of the equation above. It is used for rotational motion. To use this equation, make sure that theta θ is in radians, not degrees. The units for work are ft·lbs or N·m.

Recall that to convert between radians, degrees and revolutions use these conversion factors:

1 rev = 360° 1 rev = 2π rad 360° = 2π rad

The equation for efficiency is given by: [pic]. What you get out of a system is always less than you put in. Some energy is lost to heat through friction or other processes. Efficiency is often expressed as a percent so multiply the result of the equation above by 100 to change the decimal to a percentage. Efficiency is a unitless number, that is, the units in the numerator must cancel the units in the denominator.

Translational Kinetic Energy [pic]

Rotational Kinetic Energy [pic]

Work-Energy Theorem [pic]

Gravitational Potential Energy: [pic]

Potential Energy of a spring: [pic]

You will also need to use some of the previously supplied equations, too, such as [pic].

YOUR TEXT COVERS WORK AND ENERGY IN CHAPTER 7 (8th ed.) and CHAPTER 8 (9th ed.) ROTATIONAL MOTION IS COVERED N CHAPTER 8 (8th ed.) and CHAPTER 9 (9th ed.)

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