Power

A lathe has a motor with an input power of $P_{in} = 7.5$ kW and an efficiency of $\eta_1 = 90\%$. The motor shaft has a pulley with diameter $d_1 = 6.0$ cm. This drives a second pulley with diameter $d_2 = 24.0$ cm via a belt. The driven pulley is coaxial with the workpiece. The belt drive efficiency is $\eta_2 = 95\%$. The motor rotates at $n_1 = 1200$ r/min.

An object on a horizontal surface is moved from rest over the same distance $d$ in two different ways. Case 1: It is pulled by a force $F$ at an angle $\theta$ above the horizontal. Case 2: It is pushed by a force $F$ of the same magnitude at the same angle $\theta$ below the horizontal.

The rotational kinetic energy of the Earth is given by the formula $E_k = c/T^2$, where $T = 8.64 \times 10^4$ s is the Earth's rotational period and $c = 1.65 \times 10^{39}$ J·s² is a constant. Astronomical observations show that Earth's rotation is slowing down, with its period increasing at a rate of approximately 16 s per million years.

As shown in Figure below, an object of mass $m$ is pulled by a fixed pulley, causing the object to accelerate upwards from rest at a constant acceleration $a$. The weight of the rope and friction on the pulley axle are negligible.

As shown in Figure below, an object is lifted by an ideal movable pulley. A constant pulling force $F$ is applied, causing the object to accelerate upwards from rest at a constant acceleration $a_{obj}$.

A funny car accelerates from rest through a measured track distance in time $T$ with the engine operating at a constant power $P$.