Question

1. a boy is pulling a girl in a child’s wagon at a constant speed. he begins to pull harder, which increases the speed of the wagon. which of the following describes two ways you could calculate the change in energy of the wagon and girl if you had all the information you needed?

a. calculate work done from the force and the velocity.
calculate work done from the change in the potential energy of the system.
b. calculate work done from the force and the displacement.
calculate work done from the change in the potential energy of the system.
c. calculate work done from the force and the velocity.
calculate work done from the change in the kinetic energy of the system.
d. calculate work done from the force and the displacement.
calculate work done from the change in the kinetic energy of the system.

Explanation:

Step1: Recall Work-Energy Concepts

Work is calculated as \( W = F \cdot d \) (force times displacement, when force is parallel to displacement). The work - energy theorem states that the net work done on a system is equal to the change in its kinetic energy (\( W_{net}=\Delta KE \)). In this case, the boy pulling the wagon increases its speed, so kinetic energy changes. Potential energy (related to height) doesn't change here as there's no change in height.

Step2: Analyze Each Option

• Option a: Work is not calculated from force and velocity (\( W = Fd \), not \( Fv \)), and potential energy doesn't change, so wrong.
• Option b: Potential energy doesn't change (no height change), so calculating work from change in potential energy is wrong.
• Option c: Work is not calculated from force and velocity, so wrong.
• Option d: Work can be calculated as \( W = Fd \) (force and displacement), and by the work - energy theorem, work done is equal to the change in kinetic energy (since speed increases, kinetic energy changes). This matches the concepts.

Answer:

d. Calculate work done from the force and the displacement. Calculate work done from the change in the kinetic energy of the system.