question 16 of 29\nin the image below, a worker is pushing a crate with a mass of 20 kg up a ramp at a…

question 16 of 29\nin the image below, a worker is pushing a crate with a mass of 20 kg up a ramp at a constant rate. ignoring friction, how much force must the worker apply so that the crate continues to move at the same speed? (recall that g = 9.8 m/s²)\n\na. 37.3 n\nb. 62.5 n\nc. 48.6 n\nd. 50.7 n

question 16 of 29\nin the image below, a worker is pushing a crate with a mass of 20 kg up a ramp at a constant rate. ignoring friction, how much force must the worker apply so that the crate continues to move at the same speed? (recall that g = 9.8 m/s²)\n\na. 37.3 n\nb. 62.5 n\nc. 48.6 n\nd. 50.7 n

Answer

Explanation:

Step1: Find the component of weight along the ramp

The weight of the crate is $W = mg$, where $m = 20$ kg and $g=9.8$ m/s². The component of the weight along the ramp is $F = mg\sin\theta$, with $\theta = 15^{\circ}$.

Step2: Calculate the force

$F=20\times9.8\times\sin(15^{\circ})$. We know that $\sin(15^{\circ})=\sin(45^{\circ}- 30^{\circ})=\sin45^{\circ}\cos30^{\circ}-\cos45^{\circ}\sin30^{\circ}=\frac{\sqrt{2}}{2}\times\frac{\sqrt{3}}{2}-\frac{\sqrt{2}}{2}\times\frac{1}{2}=\frac{\sqrt{6}-\sqrt{2}}{4}\approx0.259$. Then $F = 20\times9.8\times0.259 = 50.7$ N.

Answer:

D. 50.7 N