Question

The block in the figure below has a mass of 5.1 kg and it rests on an incline of angle . You pull on the rope with a force F = 34 N. Assume the incline is smooth and determine the angle of the incline if the block moves with constant speed.

Answer 1

42.9°

Step-by-step explanation:

Let's assume that the x-axis is aligned with the incline and the positive direction is up the incline. We can then apply Newton's 2nd law as follows:

`x:\;\;\;\;F - mgsin(\theta) = 0\;\;\;\;`

`\Rightarrow mgsin(\theta) = F`

Note that the net force is zero because the block is moving with a constant speed when the angle of the incline is set at
`\theta.` Solving for the angle, we get

`sin(\theta) = (F)/(mg)`

or

`\theta = \sin^(-1)\left((F)/(mg)\right)`

`\;\;\;= \sin^(-1)\left[\frac{34\:\text{N}}{(5.1\:\text{kg})(9.8\:\text{m/s}^2)}\right]`

`\;\;\;=42.9°`