Question

A 2400 W engine pulls a 200 kg block at constant speed up a 12.0 m long, 25.0° incline. Determine how long does it take to cover this distance.

Answer 1

Answer on Question#39995 – Physics - Mechanics | Kinamatics | Dynamics

A 2400 W engine pulls a 200 kg block at constant speed up a 12.0 m long, $25.0{}^{\circ}$ incline. Determine long does it takes to cover this distance

Solution:

$\mathrm{mg} = 200\mathrm{kg}$ – mass of the block;

$\alpha = 25{}^{\circ}$ – angle of the plane with the horizontal;

$\mathrm{P} = 2400\mathrm{W}$ – power of the engine;

$\mathrm{S} = 12.0\mathrm{m}$ – traveled distance

$F$ – force which engine acts of the block

The first law of equilibrium ($V = \text{const}$) along the X axis:

$$F - m g _ {x} = 0$$ $$F = m g _ {x}$$

From the right triangle ABC:

$$\sin \alpha = \frac {m g _ {x}}{m g}; m g _ {x} = m g \cdot \sin \alpha$$

(2)in(1):

$\mathrm{F} = \mathrm{mg}\cdot \sin \alpha$

Work done by the engine:

$$\mathrm {A} = \mathrm {F} \cdot \mathrm {S} = \mathrm {m g} \cdot \mathrm {S} \sin \alpha$$

Formula of the power (t – time of the work):

$$P = \frac {A}{t} \Rightarrow t = \frac {A}{P} = \frac {m g \cdot S \sin \alpha}{P} = \frac {2 0 0 k g \cdot 9 . 8 \frac {N}{k g} \cdot 1 2 m \cdot \sin 2 5 {}^ {\circ}}{2 4 0 0 W} = 4. 1 s$$

Answer: time to cover distance 12m is equal to 4.1s