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 1's claim is correct because the work done by the gravitational force depends only on the vertical height, independent of the incline angle, thus making option E the correct answer.

Step-by-step explanation:

Student 1 is correct in claiming that the work done by the gravitational force on an object as it falls depends only on the vertical distance of the fall. This is because the work done by gravity is calculated as the product of the force due to gravity, the displacement in the direction of the force, and the cosine of the angle between the force and the displacement. Since gravity only acts vertically, any horizontal component of displacement does not affect the work done by gravity. As a result, option E is the correct choice. This is evidenced because no matter what the angle θ of the incline is, the vertical height h from which the cart is released remains the same, and thus, the work done by gravity will be the same.

Student 2's claim that the gravitational force does less work on an object that falls along a shallower incline is incorrect. The work done by gravity is independent of the path taken; it depends only on the initial and final vertical positions. Therefore, the gravitational force does the same amount of work regardless of the angle of the incline, assuming the height from which the object is dropped remains constant.

Answer 2

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

Step-by-step explanation:

Here we have the object of a certain mass falling under gravity so the force acting on the it will depend on mass of the object and the acceleration due to gravity.

Mathematically:

`F=m.g`

As we know that the work done is evaluated as the force applied on a body and the displacement of the body in the direction of the force.

And for work we have:

`W=F.s\cos\theta`

where:

`s=` displacement of the object

`\theta=` angle between the force and displacement vectors

Given that the height of the object is same in each trail of falling object under the gravity be it a free-fall or the incline plane.

• In case of free-fall the angle between the force is and the displacement is zero.
• In case when the body moves along the inclined plane the force applied by the gravity is same because it depends upon the mass of the object. And the net displacement in the direction of the gravitational force is the height of the object which is constant in both the cases.

So, the work done by the gravitational force is same in the two cases.