Question

A block slides down an inclined plane whose roughness varies. Only during time interval 1 does the block slide with negligible friction. The coefficient of kinetic friction during time interval 3 is twice the coefficient of kinetic friction during time interval 2. The graph shows the block’s velocity as a function of time. The table lists the mechanical energy dissipated due to friction over the different time intervals. Which of the following claims is true? (Answer option attached as images).

Answer 1

The true claim about mechanical energy dissipated due to friction on each block is $W_2 = W_4 \ > \ W_3$.

The given parameters:

• Velocity at time 0, v₀ = 2v₀
• Velocity at time interval 1, v₁ = 3v₀
• Velocity at time interval 2, v₂ = 3v₀
• Velocity at time interval 3, v₃ = 2v₀
• Velocity at time interval 4, v₄ = 2v₀

The change in kinetic energy of the blocks is equal to the mechanical energy dissipated.

$W = \Delta K.E= \frac{1}{2}(v_2^2 - v_1^2) \\\\W_2 = \frac{1}{2} m(3v_0^2- 3v_0^2) = 0\\\\W_3 = \frac{1}{2} m((2v_0)^2 - (3v_0)^2) = -2.5 mv_0^2 \\\\W_4 = \frac{1}{2}m( 2v_0^2 - 2v_0^2) = 0$

Thus, we can conclude the following for the mechanical energy dissipated due to friction on each block;

$W_2 = W_4 \ > \ W_3$.

Learn more about energy lost to friction here: brainly.com/question/12315903