- Louise kicks a 10 N soccer ball up a hill. It rolls over the top of the hill, which is elevated 20 m above the ground she is standing on, and comes to a stop halfway down the other side of the hill where there is a wall. That wall’s elevation is 10 m below the top of the hill.
- If she kicks with 400 J of energy, what is the efficiency?
- How can she kick the ball to improve her efficiency?
- If she does so, what is the maximum efficiency she can achieve?
- A set of pulleys has a mechanical advantage of 1.5 and an ideal mechanical advantage of 2. If you wish to lift a 30 N weight by 10 m, how far do you have to pull and how hard?
- Jared lifts a 100 N mass by 10 m. He does so using a wheel and axle, providing an input force of 10 N and turning the wheel for 200 m.
- What is the mechanical advantage?
- What is the ideal mechanical advantage?
- What is the efficiency?
- An engine is attached to a set of gears with a gear ratio of two. Those gears drive an axle, which is connected to wheels. The ratio between the wheels’ radius and the axle’s radius is 10.
- The engine provides 100 N m of torque. How much torque do the wheels provide?
- The engine provides 50 N of force. How much force do the wheels provide?
- Use your answers to a and b to calculate the radius of the wheels.
- Larissa and Kasey built a block-and-tackle assembly to lift a 15 kg box. They had to pull their end of the rope with an input force of 120 N. Furthermore, they moved their end a distance of 3.0 m to lift the box 150 cm. What was the efficiency of the block-and-tackle assembly?
- Gears A, B, and C have 10, 20, and 30 teeth, respectively.
- If A is the input and B is the output, what is the gear ratio?
- If A is the input and C is the output, what is the gear ratio?
- If B is the input and A is the output, what is the mechanical advantage?
- If B is the input and C is the output, what is the mechanical advantage?
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- You place an ErgoBot with a mass of 460 g on a ramp that is 3.4 m long and 0.8 m high.
- What is the mechanical advantage of this ramp?
- Draw a free-body force diagram of the ErgoBot.
- Using your diagram, calculate the force it would take to push the ErgoBot up the ramp it is placed on.
- What direction is the ErgoBot most likely to travel once you let it go? Use your free-body diagram to help you answer.
- A man is pushing his 75 kg dresser into a moving van up a ramp with a force of 175 N. The ramp is 5.7 m long and 1.1 m high.
- Draw a free-body diagram of the dresser.
- Assuming there is no friction, how much force does the man have to apply to keep the dresser from slipping down the ramp?
- What is the acceleration of the dresser when the man pushes with a force of 175 N? Does the dresser move up or down the ramp? Use your free-body diagram to help you answer.
- What is the mechanical advantage of the ramp?
 On your computer, use the interactive simulation of a wind turbine on page 355 to calculate the difference in cost per kWh (ten-year average) between a 120 m high, 80 m diameter turbine in 8 m/s average wind speed that is located in a rural versus urban site. What about the sites makes the costs different?
- The ancient Greek crane shown on page 350 has a block and tackle with a mechanical advantage of three and a winch (wheel-and-axle assembly) with a mechanical advantage of six. Which one of the following changes would most increase the MA of the entire crane?
- Increase the radius of the winch handle from 30 cm (0.3 m) to 45 cm (0.5 m).
- Decrease the radius of the winch axle from 5 cm (0.05 m) to 2.5 cm (0.025 m).
- Replace the block and tackle with one that supports the load with four strands instead of three.
- Replace the block and tackle with one that supports the load with five strands instead of three.
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