A roller coaster cart begins from rest at the top of a track with 50{}000\text{ J} of grav… — Armed Services Vocational Aptitude Battery (ASVAB)

A roller coaster cart begins from rest at the top of a track with $50{}000\text{ J}$ of gravitational potential energy. Assuming no energy is lost to friction, what is the cart's kinetic energy when its potential energy decreases to $15{}000\text{ J}$ ?

A
$15{}000\text{ J}$
B
$50{}000\text{ J}$
$35{}000\text{ J}$ Answer
D
$65{}000\text{ J}$

Answer

35{}000\text{ J}

According to the Law of Conservation of Energy, the total mechanical energy in a frictionless system remains constant. Since the cart starts with

50{}000\text{ J}

of potential energy and zero kinetic energy, the total energy is

50{}000\text{ J}

. When potential energy drops to

15{}000\text{ J}

, the lost potential energy (

50{}000\text{ J} - 15{}000\text{ J} = 35{}000\text{ J}

) is entirely converted into kinetic energy.

Step-by-Step Solution

Determine the total initial mechanical energy of the cart.

E_{\text{total}} = 50{}000\text{ J}

Since the cart starts from rest, its initial kinetic energy is zero, making total mechanical energy equal to initial potential energy.

Apply the Law of Conservation of Mechanical Energy at the lower height.

E_{\text{total}} = PE + KE \implies 50{}000\text{ J} = 15{}000\text{ J} + KE

In a frictionless system, the sum of kinetic and potential energy remains constant at all points.

Subtract the remaining potential energy from the total mechanical energy to solve for kinetic energy.

KE = 50{}000\text{ J} - 15{}000\text{ J} = 35{}000\text{ J}

The decrease in gravitational potential energy directly converts into an equal increase in kinetic energy.

Key Concept

Conservation of Mechanical Energy

Estimated Time:1m 0s

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Topics

More questions from this topic