Worksheet: Work-Energy Theorem

In this worksheet, we will practice comparing the work done to and done by objects to energy conversions and transfers between objects.

Q1:

A positively charged point object can take two paths between the points 𝐴 and 𝐵 shown in the diagram. The path shown in black is path I and the path shown in red is path II. Path I is an arc of a circle, path II is a chord of the same circle, and the dashed vertical line is the diameter of the same circle. The horizontal dashed line is perpendicular to the dashed vertical line. The point where the vertical and horizontal dashed lines intersect is the fixed position of a negatively charged point object.

Which of the paths can the positively charged object follow with zero work done on it by the negatively charged object at any time during the motion of the positively charged object?

  • ANeither path
  • BPath 1 only
  • CBoth paths
  • DPath 2 only

Which of the paths can the positively charged object follow with zero net work done on it by the negatively charged object?

  • APath 2 only
  • BPath 1 only
  • CNeither path
  • DBoth paths

Which of the paths can the positively charged object follow where the power supplied by the negatively charged object is constant?

  • ABoth paths
  • BNeither path
  • CPath 2 only
  • DPath 1 only

For which of the paths does the net work done on the positively charged object by the negatively charged object change if the object moves from point 𝐵 to point 𝐴 instead of from point 𝐴 to point 𝐵 ?

  • APath 1 only
  • BPath 2 only
  • CBoth paths
  • DNeither path

For which of the paths is the net work done on the negatively charged object by the positively charged object equal to zero?

  • ABoth paths
  • BPath 2 only
  • CPath 1 only
  • DNeither path

Q2:

A uniform box of mass 2.3 kg is moved upward along a slope, as shown in the diagram. The height of the center of mass of the box above the base of the slope before the move is = 1 5 c m . The height of the center of mass of the box above the base of the slope after the move is = 5 5 c m . The angle of the slope above the horizontal is 𝜃 = 2 8 . The work done on the box to move it is 15 J. What is the work done on the box by its friction with the slope surface per meter that the box moves along the surface?

  • A 5.1 J/m
  • B 32 J/m
  • C 6.0 J/m
  • D 18 J/m
  • E 7.0 J/m

Q3:

The surface of a lake is shown as altitude II in the diagram. The vertical displacement between a hilltop at altitude I and altitude II is 22 m. The vertical displacement between altitude II and a mud bank at altitude III is 18 m. The vertical displacement between altitude III and the lake bed at altitude IV is 27 m. A boat with a mass of 110 kg slides down the hillside to the lake surface, from altitude I to altitude II. The boat moves across the surface of the sea and starts to sink, coming to rest on the mud bank.

What is the gravitational potential energy of the boat just before it starts to sink? Take the lake bed at the base of the hill as the point of zero gravitational potential.

What is the gravitational potential energy of the boat just before it starts to sink? Take the lake surface as the point of zero gravitational potential.

What is the gravitational potential energy of a person with a mass of 75 kg who is on the hilltop? Take a person in the boat just before it starts to sink as the point of zero gravitational potential.

What is the gravitational potential energy of the boat when it comes to rest? Take a person at the top of the hill as the point of zero gravitational potential.

Q4:

A bag that is initially at rest at an airport is pushed horizontally across the flat ground by a constant force of 24 N, as shown in the diagram.

The bag moves 3.5 m in the direction of the force and after moving has a speed of 1.2 m/s in the direction of the force. The mass of the bag is 18 kg.

How much work is done on the bag in the direction of the applied force by the applied force?

How much work is done on the bag in the direction of the applied force by the friction of the bag with the ground?

How much energy is dissipated due to the motion of the bag?

Q5:

A bag at an airport is pushed horizontally across a flat ground by a constant force of 16 N, as shown in the diagram. The bag moves 7.2 m in the direction of the force and throughout its motion has a speed of 1.2 m/s in the direction of the force. The mass of the bag is 12 kg.

How much energy is dissipated by the motion of the bag across the ground per meter that the bag moves?

What is the power supplied to the ground due to the motion of the bag over it?

Q6:

An object has an initial upward velocity and a constant downward acceleration due to gravity. Which of the following formulas correctly represents the work done, 𝑊 , on the object by the air that the object moves through in the direction of motion of the object when it is launched upward and returns to its starting position? The mass of the object is 𝑚 , the initial velocity of the object is 𝑣 , the gravitational acceleration of the object is 𝑔 , and the increase in the height of the object is Δ .

  • A 𝑊 = 2 𝑚 𝑔 Δ 𝑚 𝑣
  • B 𝑊 = 2 𝑚 𝑣 + 𝑚 𝑔 Δ
  • C 𝑊 = 𝑚 𝑣 2 𝑚 𝑔 Δ
  • D 𝑊 = 𝑚 𝑣 + 𝑚 𝑔 Δ
  • E 𝑊 = 2 𝑚 𝑣 𝑚 𝑔 Δ

Q7:

An object has an initial upward velocity and a constant downward acceleration due to gravity. Which of the following formulas correctly represents the work done, 𝑊 , by the object on the air that it moves through when the object is launched upward and returns to its starting position? The mass of the object is 𝑚 , the initial velocity of the object is 𝑣 , the gravitational acceleration of the object is 𝑔 , and the increase in the height of the object is Δ .

  • A 𝑊 = 𝑚 𝑣 2 𝑚 𝑔 Δ
  • B 𝑊 = 2 𝑚 𝑣 𝑚 𝑔 Δ
  • C 𝑊 = 𝑚 𝑣 + 2 𝑚 𝑔 Δ
  • D 𝑊 = 2 𝑚 𝑣 + 𝑚 𝑔 Δ
  • E 𝑊 = 𝑚 𝑣 𝑚 𝑔 Δ

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