Page 23 - SP015 Past Years PSPM Chapter 6 -14 Ver 2020

PSPM SP015

PSPM 2004/2005 SF017/2 No. 11(b)

35.

0.2 m

50 kg cable

9 N
FIGURE 8.14

FIGURE 8.14 shows a massless cable wound around a solid cylinder of mass 50 kg
and radius 0.2 m. When the free end of the cable is pulled through a distance of 2.0 m
by a constant force of 9 N, the cylinder initially at rest, rotates without friction about a
stationary horizontal axis. Calculate
(a) the final angular velocity of the cylinder. 5 m]

(b) the final speed of the cable. [2 m]
2
1
(Moment inertia of a solid cylinder of mass M and radius R is I = MR )
2

PSPM 2007/2008 SF017/2 No. 11(b), (c)

36. (a)

A 10 m

30
B
FIGURE 8.15

A solid cylinder of radius 30 cm and mass 2 kg starts from rest at A and rolls
without slipping down a plane inclined 30 to the horizontal. The cylinder
traverses a distance of 10 m along the plane to reach B as shown in
FIGURE 8.15. Calculate
(i) the potential energy of the cylinder at A. [2 m]
(ii) the linear velocity of the cylinder just before reaching B. [5 m]
(iii) the time taken for the cylinder to reach B. [3 m]

(b) If a hollow cylinder of similar mass and radius are released simultaneously with
the cylinder from A as in question (a), which cylinder will be the fastest to reach
B? Explain your answer. [3 m]
2
Given the moments of inertia of a solid cylinder and a hollow cylinder is 1 2 MR and
2
MR respectively.

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