Given : A block of mass m , which is initially at rest, sits on an inclined hori

Question

Given:

A block of mass m, which is initially at rest, sits on an inclined horizontal plane as shown. The applied constant force FA of 100 N is parallel to the plane. The angle theta that the force makes with the horizontal is 20degrees. The coefficient of kinetic friction (uk) between the block and the plane is 0.30, and the mass of block m is 5 kg.

Find:

a) Complete the free body diagram below.

b) The equation of motion of the system.

c) The magnitude of the force frictional force Ff.

d) The acceleration of the block up the incline.

e) The time required for the block to move 2 meters.

Explanation / Answer

b)let N = normal reaction

then friction force u.N = 0.3 N

also N = m.g.cos 20

so equation of motion = F -frtiction = ma

so, 100 - 0.3 x m x g cos 20 = ma

where a = accelration

and m = mass

c) magnitude of the force frictional force Ff. = 0.3 x m x g cos 20 = 0.3 x 5 x 9.81 x cos 20 = 14 N

d) aceleration = (100 - 0.3 x 5 x 9.81 x cos 20 )/5

= (100- 14)/5

= 17.2 m/s^2

e) time = sqrt(2s/a)

= sqrt(2 x 2/17.2)

= 0.4822 s

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