Study of velocity and kinetic energy, a cart was tested in 9 different trials. The cart carried different masses down 3 different inclinations. Table I shows the mass carried by the cart, the height from which it was released.And that is rolled to get to the end of the ramp. The table also lists the speed and kinetic energy of the cart released the of the ramp.Doubling both the mass of the cart and the height from which it is released changes the kinetic energy by a factors of
Correct answer: D. 4
- A. 1/4
- B. 1/2
- C. 2
- D. 4
Explanation
Kinetic energy is given by the formula KE = 1/2 m v^2, where m is the mass and v is the velocity. When the cart's mass is doubled, the kinetic energy doubles due to the mass term. Additionally, doubling the height from which it is released doubles the velocity (as velocity is proportional to the square root of height), leading to a velocity squared term that quadruples the kinetic energy. Therefore, the kinetic energy increases by a factor of 4. Options A, B, and C do not correctly account for these changes and their impact on kinetic energy.
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