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:a. the angle θ of the inclineb. the distance d the cart travels along the inclinec. the time t it takes the cart to move down the inclined. the speed v of the cart at the bottom of the incline

Answer 1

Answer:

E: Student 1 is correct, because as  θ is increased,  h remains the same.

Explanation:

The solve the question, we note that the object placed at height h has a potential energy P.E. also  known as the gravitational potential energy given by;

P. E. = m×g×h

Where:

m = Mass m

g = Acceleration due to gravity

h = vertical distance    

As such, from the principle of energy can neither be created nor destroyed, but can be changed from one form to another

Therefore the gravitational force on an object as it falls depends on only the vertical height as the mass, m and the acceleration due to gravity, g are both constant in the experiment.

Answer 2

Answer: The two students are both correct.

Explanation:

Student 1 is correct base on the fact that gravity does work on objects which move vertically. One can show that if the height in which the object fall has changed by an amount ∆y then

gravity has done an amount of work equal to Wgrav = −mg∆y

Student 2 is also correct because in an inclined plane,

h = dsinØ

Therefore, gravitational force does less work on an object that falls gradually along a shallow incline than one that falls along a steeper incline because of angle Ø

The work done on an object by the force of gravity does not depend on the path taken to get from one position to another.

In both cases we just need to know the initial and final coordinates to be able to find W, the work done by

that force.

This situation also occurs with the general law for the force of gravity as well as the electrical force.

If the net work done by a force does not depend on the path taken between two points, we say that the force is a conservative force. For such forces, it is also true that the net work done on a particle moving on around any closed path is zero.