Question

A student must determine the effect of friction on the mechanical energy of a small block as it slides up a ramp. The block is launched with an initial speed v₀ from point A along a horizontal surface of negligible friction. It then slides up a ramp, where friction is not negligible, that is inclined at an angle θ with respect to the horizontal, as shown in the figure. The student measures the maximum vertical height h attained by the block while on the ramp, labeled as point B in the figure. At point B, the block comes to rest. The student performs three trials with the ramp at different angles, launching the block at the same initial speed v₀ for each trial. Consider the trial with the 45° ramp. Suppose the block is launched up the ramp such that it comes to rest at point B and then travels down the ramp. Which of the following best describes the block's kinetic energy Kₐ when it again reaches point A at the bottom of the ramp in comparison to the initial kinetic energy K₀ before it travels up the ramp? a) Kₐ > K₀, because the object will have a higher speed at the bottom of the ramp after sliding down the ramp than its original launch speed. b) Kₐ = K₀, because the law of the conservation of energy states that mechanical energy must be conserved for a closed system. c) It is impossible to predict how the kinetic energy of the block at point A will compare to the original kinetic energy without knowing the magnitude of the force of friction that is exerted on the block as it travels up and back down the ramp.

Answer 1

The block's final kinetic energy at point A after sliding down the ramp with friction cannot be predicted in comparison to the initial kinetic energy without information about the force of friction. Friction is a non-conservative force that reduces mechanical energy, thus conservation of energy does not apply.

Step-by-step explanation:

The block's kinetic energy Ka when it again reaches point A at the bottom of the ramp after sliding down the ramp in comparison to the initial kinetic energy K0 is best described by option (c): It is impossible to predict how the kinetic energy of the block at point A will compare to the original kinetic energy without knowing the magnitude of the force of friction that is exerted on the block as it travels up and back down the ramp.

While the law of conservation of energy states that mechanical energy must be conserved in a closed system, the presence of friction introduces a non-conservative force, therefore mechanical energy is not conserved in this case. As the block moves up and then down the ramp, friction does work against it, thereby reducing its total mechanical energy. Because there is no way to determine the exact amount of energy lost to friction without additional information, the final kinetic energy at point A after descending may be less than the initial kinetic energy K0.