Chapter 6, Problem 10TE

According to the work-energy theorem, in the absence of friction, if you do $100\text{J}$ of work on a cart while pushing it across a horizontal surface, how much will you increase its kinetic energy?

To determine

To-determine: The increase in the kinetic energy of the cart in the absence of friction.

Answer to Problem 10TE

The increase in the kinetic energy of the cart is $100\text{J}$ in the absence of friction.

Explanation of Solution

The work-energy theorem states that the work done on an object is same as the change in the energy of the object. If the friction is absent then the work done against the friction becomes zero. The work done by an object in the absence of friction then becomes equal to the change in the value of kinetic energy of the object.

The work done on the cart is $100\text{J}$ in the absence of friction. The friction is absent for the cart, so there is no loss of the energy. Due to no loss of energy, the increase in the kinetic energy of the cart also becomes same as the work done.

Conclusion:

Therefore, the increase in the kinetic energy of the cart is $100\text{J}$ in the absence of friction.