Question

A horizontal force Fa of magnitude 20.0 N is applied to a 3.00 kg psychology book as the book slides a distance d =0.500 m up a frictionless ramp at angle θ = 30.0° .
(a) During the displacement, what is the net work done on the book by Fa, the gravitational force on the book, and the normal force on the book?
(b) If the book has zero kinetic energy at the start of the displacement, what is its speed at the end of the displacement?

Answer 1

(a) Net work done on the book is 8.66 J

(b) Speed at the end of the displacement is 2.40 m/s.

(a) Work done is defined as the product of force and displacement.

Mathematically Work done (W) = F.s

F = force applied on the object = 20N

s = displacement travelled by the object due to force applied = 0.5m

When the object is placed at an angle (A)

W = F * d * cos(A)

where, A = angle of ramp = 30°

Therefore, work done is:

W = 20 * 0.5 * cos30

W = 8.66 J

(b) Speed is the rate of change of distance with respect to time.

Also, Work done is equal to change in Kinetic energy.

Since the initial kinetic energy is zero:

W = KE(final)

W = (1/2) * m * v²

where v = final velocity

m = mass of the book = 3 kg

=> 8.66 =(1/2) * 3 * v²

v² = 5.773

v = 2.40 m/s

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