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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.
Solution
Free body diagram of the block for this case is as follows:
From the adove diagram:
F − ma − μkR + mg sin 30° = 0
4 − 4a − μkR + 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
`=> 4-4a-0.11xx4xx10xxsqrt3/2+4xx10xx1/2=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+1/2at^2`
`=0+(1/2)5xx2^2`
= 10 m
Therefore, the block will move 10 m.
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