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Q.

A block of 7 kg is placed on a rough horizontal surface and is pulled through a variable force F(in N) = 5t, where ‘t’ is time in second, at an angle of 37° with the horizontal as shown in figure. The coefficient of static friction of the block with the surface is one. If the force starts acting at t = 0 s, Find the time ( in second ) at which the block starts to slide. (Take g = 10 m/s²) :

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Detailed Solution

The block begins to slide if
F cos 37° = µ (mg - F sin 37°)
5t [cos 37° + µ sin 37°] = µ mg
$5 t [\frac{4}{5} + \frac{3}{5}] = 70 or t = 10 second$

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A block of 7 kg is placed on a rough horizontal surface and is pulled through a variable force F(in N) = 5t, where ‘t’ is time in second, at an angle of 37° with the horizontal as shown in figure. The coefficient of static friction of the block with the surface is one. If the force starts acting at t = 0 s, Find the time ( in second ) at which the block starts to slide. (Take g = 10 m/s2) :