Question

Suppose the block of the previous problem is pushed down the incline with a force of 4 N. How far will the block move in the first two seconds after starting from rest? The mass of the block is 4 kg.

Answer 1

Free body diagram of the block for this case is as follows:



From the adove diagram:
F − ma − μ_kR + mg sin 30° = 0
4 − 4a − μ_kR + 4g sin 30° = 0 (1)
R − 4g cos 30° = 0 (2)
⇒ R = 4g cos 30° = 0

Substituting the values of R in Equation (1) we get
4 − 4a − 0.11 × 4g cos 30° + 4g sin 30° = 0
$\Rightarrow 4-4a-0.11\times 4\times 10\times \frac{\sqrt{3}}{2}+4\times 10\times \frac{1}{2}=0$
4 − 4a − 3.81 + 20 = 0
4 − 4a − 3.18 + 20 = 0
a ≈ 5 m/s²

For the block, u = 0, t = 2 s and a = 5 m/s².
According to the equation of motion,
​ ​$s=ut+\frac{1}{2}a{t}^2$
$$\begin{gathered} =0+\left(\frac{1}{2}\right)5\times 2^2 \\ =10\mathrm{m} \end{gathered}$$

Therefore, the block will move 10 m.