A 3.2-kg mass is placed at the top of a rough incline ( $\mu = 0.1$ ). The incline makes an angle of 32º with the horizontal, and the height of the incline is 2.5 m. The mass is released and slides down to the bottom. The amount of mechanical energy lost is

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Quizplus · Accepted Answer

The mechanical energy lost is due to the work done against friction. The work done against friction (energy lost) can be calculated using the formula: $W = f \cdot d = \mu \cdot m \cdot g \cdot \cos(\theta) \cdot d$, where $f$ is the frictional force, $d$ is the distance slid down the incline, $\mu$ is the coefficient of friction, $m$ is the mass, $g$ is the acceleration due to gravity (9.8 m/s$^2$), and $\theta$ is the angle of the incline. First, we need to find $d$ using the height ($h$) and the angle ($\theta$) of the incline: $d = \frac{h}{\sin(\theta)}$. Substituting the given values, $d = \frac{2.5}{\sin(32^\circ)}$, and then calculating the work done against friction gives us the energy lost, which is approximately 13 J.

A 32-Kg Mass Is Placed at the Top of a Rough