Question

A box of unknown mass is sliding with an initial speed
vi = 5.30 m/s
across a horizontal frictionless warehouse floor when it encounters a rough section of flooring
d = 2.00 m
long. The coefficient of kinetic friction between the rough section of flooring and the box is 0.100. Using energy considerations, determine the final speed of the box (in m/s) after sliding across the rough section of flooring.

Answer 1

Answer on Question #82153, Physics / Mechanics | Relativity

Question:

A box of unknown mass is sliding with an initial speed

$$v_i = 5.30 \, \mathrm{m/s}$$

across a horizontal frictionless warehouse floor when it encounters a rough section of flooring

$$d = 2.00 \, \mathrm{m}$$

long. The coefficient of kinetic friction between the rough section of flooring and the box is 0.100. Using energy considerations, determine the final speed of the box (in m/s) after sliding across the rough section of flooring.

Solution:

Using energy considerations, we can write that $0.5mv_1^2 = 0.5mv_2^2 + \mu mgd$ and respectively

$$v_2 = v_1 \sqrt{1 - \frac{2\mu g d}{v_1^2}} = 5.3 \sqrt{1 - \frac{20 \cdot 0.1 \cdot 2}{28.1}} = 4.9 \, \mathrm{m/s}.$$

The answer:

The final speed $v_2 = v_1 \sqrt{1 - \frac{2\mu g d}{v_1^2}} = 4.9 \, \mathrm{m/s}$.

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