A 5 kg mass is initially at rest on a rough horizontal surface. A horizontal force is applied to it. The two figures below show how the force and velocity vary with time.
The mass moves with an acceleration of 7 ms-2 in the first 20 s.
Calculate
(i) the speed of the mass when t = 20 s,
(ii) the frictional force between the surfaces,
(iii) the acceleration at time t = 23 s,
(iv) the work done by the applied force in the last 5 s.
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Answer:
(i)
v = u + at
= 0 + 7 Χ 20
= 140 m/s
(ii)
F = ma
= 5 Χ 7
= 35 N
Frictional force = 50 - 25 = 15 N
(iii)
Resultant force = 25 - 15
= 10 N
Acceleration = F / m
= 10 / 5
= 2 ms-2
(iv)
s = ut + 0.5 at2
= 140 Χ 5 + 0.5 Χ 2 Χ 52
= 700 + 25
= 725 m
Hence, work done = F Χ dist
= 25 Χ 725
= 18125 J
