Worksheet: Energy Conversion and Conservation

In this worksheet, we will practice converting between different types of mechanical energy and identifying mechanical energy dissipation.

Q1:

An object with a velocity 𝑣 is slowed to rest by a constant force 𝐹 over a distance of 12 m. If the object’s velocity is increased to 5𝑣 and then 𝐹 is again applied to decelerate the object, how far does the object move between the force being applied and the object coming to rest?

Q2:

A ball with an initial velocity of 20 m/s rolls along a curved surface, as shown in the diagram. The mass of the ball is 100 g. Assume that the only energy conversions that take place are between the kinetic energy and the gravitational potential energy of the ball and calculate the height of the ball at different positions, to the nearest meter.

Find .

Find .

Find .

Find .

Q3:

A ball with an initial velocity of 10 m/s rolls along a curved surface, as shown in the diagram. The mass of the ball is 100 g. Assume that the only energy conversions that take place are between the kinetic energy and the gravitational potential energy of the ball and calculate the speed of the ball at different positions to the nearest meter per second.

Find the magnitude of 𝑣.

Find the magnitude of 𝑣.

Find the magnitude of 𝑣.

Find the magnitude of 𝑣.

Q4:

A cell phone with a mass of 120 g is held in the hand of a tourist relaxing on a boat on vacation. The tourist distractedly holds the phone just over the surface of the water and accidentally loses hold of it. The phone sinks through the water, and the instantaneous speed at which it sinks when at a depth of 10 cm is 1.1 m/s. How much work is done moving water out of the phone’s path as it sinks by 10 cm?

Q5:

A child with a mass of 36 kg carries a sled with a mass of 14 kg to the top of an evenly sloping hill, walking 33 m along the hillside and moving vertically upward by 8.8 m. The child puts the sled on the slope where it is just held in place by friction and carefully climbs on board. The added weight of the child is just enough to start the sled moving and it slides down the hill, moving at 10 m/s when it arrives at the base of the slope.

How much energy is dissipated during the sled’s downhill motion?

What average force of friction does the hillside apply to the sled during the sled’s motion? Answer to the nearest newton.

Q6:

A car is initially at rest before it starts to roll along a downward-sloping road with its engine turned off. While rolling, the car’s velocity increased by 1.4 m/s. What vertically downward distance does the car travel? Gravity is the only force that acts on the car.

Q7:

Which of the graphs (a), (b), (c), and (d) correctly shows the changes in kinetic energy (shown in red) and the gravitational potential energy (shown in blue) for a ball being thrown vertically upward and falling back to earth? The time axis of the graph starts at the instant the ball leaves the thrower’s hand, and the energy values cease to be plotted at the instant that the ball falls back to the height that it was released from. Air resistance is negligible.

  • A(c)
  • B(a)
  • C(b)
  • D(d)

Q8:

A spring in a pogo stick has a constant of 750 N/m. A pogoing child compresses the spring by 30 cm when they land on the tip of the pogo stick, and then the stick and child recoil into the air. The total mass of the child and pogo stick is 45 kg.

What instantaneous velocity does the pogo stick have as it loses contact with the ground? Answer to one decimal place.

The pogo stick rises 0.055 m into the air. How much of the kinetic energy of the pogo stick and child is dissipated by drag force?

Q9:

A boy stands on a chair and throws a ball vertically upward then catches it after it falls back downward. The boy’s friend stands on the floor and watches. Which of the graphs (a), (b), (c), and (d) correctly shows the changes in kinetic energy (shown in red) and gravitational potential energy (shown in blue) of the ball, measured from the floor? The time axis of the graph starts at the instant the ball leaves the boy’s hand, and the energy values cease to be plotted at the instant the ball falls back to the height that it was released from. Air resistance is negligible.

  • A(c)
  • B(b)
  • C(d)
  • D(a)

Q10:

A skateboarder rolls upward along a curved ramp, as shown in the diagram, and nearly reaches the top of the ramp.

What is the skateboarder’s speed at the point that is 1.1 m vertically above the base of the ramp? Give your answer to one decimal place.

What would the initial speed at the base of the ramp required for the skateboarder to reach the top of the ramp be? Give your answer to one decimal place.

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