Question

Two students make the following claims: Student 1 claims that the work done by the gravitational force on an object as it falls depends only on the vertical distance of the fall. Student 2 claims that the gravitational force does less work on an object that falls gradually along a shallow incline than one that falls along a steeper incline.

The students run several trials of an experiment in which a cart is allowed to travel down an incline that can be set at different angles. The cart is released from the same height h in each trial and the following measurements are made:
the angle θ of the incline
the distance d the cart travels along the incline
the time t it takes the cart to move down the incline
the speed v of the cart at the bottom of the incline

Which of the following indicates which student made the correct claim and has data to support this claim?

a) Student 2 is correct because as θ is increased, t decreases.
b) Student 2 is correct because as θ is increased, d increases.
c) Student 2 is correct because as θ is increased, h is the same.
d) Student 1 is correct because as θ is increased, v is the same.
e) Student 1 is correct because as θ is increased, h is the same.

Answer 1

Student 2 is correct because as the angle (θ) of the incline is increased, the distance (d) the cart travels along the incline increases.

Step-by-step explanation:

Student 2 is correct because as the angle (θ) of the incline is increased, the distance (d) the cart travels along the incline increases. This indicates that the gravitational force does less work on the cart that falls gradually along a shallow incline compared to one that falls along a steeper incline. This is because as the incline gets steeper, more gravitational potential energy is converted into kinetic energy, resulting in a greater distance traveled by the cart.