A toy car is released from rest at the top of a ramp. The car speeds up as it moves down the ramp. When it reaches the bottom of the ramp, the toy car rolls across the floor and eventually stops.
Which two statements identify evidence that energy was conserved?
A. As the car rolls down the ramp, it speeds up because gravitational potential energy is transformed into kinetic energy.
B. As the car rolls down the ramp, it speeds up because thermal energy due to friction is transformed into kinetic energy.
C. As the car rolls across the floor, it stops because its kinetic energy is transformed into gravitational potential energy,
D. As the car rolls across the floor, it stops because its kinetic energy is transformed into thermal energy due to friction
The correct Answer and Explanation is:
The correct answer is:
A. As the car rolls down the ramp, it speeds up because gravitational potential energy is transformed into kinetic energy.
D. As the car rolls across the floor, it stops because its kinetic energy is transformed into thermal energy due to friction.
Explanation:
Energy conservation is a fundamental principle of physics stating that energy cannot be created or destroyed; it can only change forms. In this scenario with the toy car, different forms of energy are transformed, but the total amount of energy remains constant throughout the motion.
- Gravitational Potential Energy to Kinetic Energy: When the toy car is at the top of the ramp, it has gravitational potential energy due to its position above the ground. This energy is proportional to its height and mass, given by the formula:Potential Energy=mgh\text{Potential Energy} = mghPotential Energy=mghwhere mmm is the mass of the car, ggg is the acceleration due to gravity, and hhh is the height of the ramp. As the car is released and moves down the ramp, gravitational potential energy is converted into kinetic energy, which is the energy of motion. The faster the car moves, the more kinetic energy it gains. The relationship for kinetic energy is given by:Kinetic Energy=12mv2\text{Kinetic Energy} = \frac{1}{2}mv^2Kinetic Energy=21mv2Therefore, the car speeding up as it descends the ramp is evidence that gravitational potential energy is being transformed into kinetic energy. This transformation is described in Statement A, correctly identifying one way energy is conserved.
- Kinetic Energy to Thermal Energy (Friction): Once the toy car reaches the bottom of the ramp, it rolls across the floor. On a frictionless surface, the car would continue to move indefinitely. However, in this case, friction between the car’s wheels and the floor slows it down until it eventually stops. Friction converts the car’s kinetic energy into thermal energy (heat). The loss of kinetic energy and the generation of heat are signs that energy is being transformed, not lost. This process is described in Statement D, showing another way energy is conserved.
Incorrect Statements:
- Statement B is incorrect because it implies that thermal energy is responsible for speeding up the car, which contradicts the principle that friction slows objects down, not speeds them up.
- Statement C is incorrect because kinetic energy is not converted back into gravitational potential energy when the car moves on a flat surface.
In summary, Statements A and D provide clear evidence of energy conservation, as they illustrate how energy is transformed from gravitational potential to kinetic energy while moving down the ramp, and from kinetic to thermal energy as the car slows due to friction.