In the absence of friction do we expect the final velocity of the cart to be...

In the absence of friction do we expect the final velocity of the cart to be affected by adding mass to it? Support your answer using energy conservation.

Expert Solution

In te absence of friction, the final velocity of the cart won't be affected by adding mass to it.

Suppose we are sliding a cart on an inclined frictionless surface. Let the mass of the cart is m, and the initial height of the cart is h.

Therefore, the velocity of the cart at the bottom of the inclined plane can be calculated by using conservation of energy.

Initially the cart has only potential energy. So, initial energy of the system is

And at the bottom of the plane, the cart will have only kinetic energy. i.e.

Where v is velocity of the cart at the bottom of the plane.

In the absence of friction, using conservation of energy, we can write

or,

Here we can see that, the final velocity of the cart is independent of mass if the friction is not present.

Hence, if we add extra mass to the cart, it won't effect the final velocity of the cart.

genius_generous answered 2 years ago

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