Lesson: Work-Energy Theorem Physics • 9th Grade

In this lesson, we will learn how to compare the work done to and done by objects to energy conversions and transfers between objects.

Lesson Plan

Students will be able to

recall that when no energy is dissipated, the work done on an object is equal to the change in the energy of the object,
recall that the work done on an object minus the change in the energy of the object is equal to the energy dissipated, where the work done on the object exceeds the change in the energy of the object,
express energy dissipated as negative-valued work done on an object,
express potential energy relative to a reference value as either positive or negative valued.

Lesson Worksheet

Q1:

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 . The height of the center of mass of the box above the base of the slope after the move is . The angle of the slope above the horizontal is . 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?

Q2:

A positively charged point object can take two paths between the points and 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?

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

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

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 to point instead of from point to point ?

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

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.