Exercise of Mechanics
Set 7 (A) --- Plane Kinetics of Rigid Bodies ---
1. A 1500-kg travels up a slope 5.7o from the horizon and accelerates with 2.68 m s-2. The distance
between the axles of the front and rear wheels is 3 m. The C.G. of the car is 0.6 m above the road
and equidistant from the front and rear wheels. Find the normal reaction on each pair of wheels and
the friction exerted on the rear driving wheels by the road, assuming no friction on the front wheels.
Neglect the mass of the wheels.
Ans : 6.22 kN, 8.24 kN, 5.48 kN
2. A 5-kg uniform bar AB is suspended from an accelerating vehicle. It is kept in a vertical position by
a cable BC as shown. The acceleration of the vehicle is 5.89 m sˉ². Determine the tension in the cable
and the magnitude of the force supported by the pin A.
Ans : 24.5 N, 32.9 N
0.3 m
C
a
A
0.4 m
B
3. A drum has a mass of 150 kg and a radius of 300 mm. If the mass of the cable and the frictional
torque at O are negligible, determine (a) the acceleration of the 20-kg weight, and (b) the resultant
force exerted by the bearing at O.
Ans : 2.07 m s-2; 1.63 kN
300 mm
O
20 kg
4. Bar AB of mass 30 kg is released from rest. Assume that the wall and the floor are smooth. Find the
angular acceleration of the bar and the reactions at ends A and B immediately after the release of the
bar.
Ans : 5.88 rad sˉ², clockwise; 153 N, 106 N
B
2m
A
37o
1
5. Flywheel A of the tire tester drives two wheels B and C simultaneously. The flywheel has a mass of
227 kg, a diameter of 1.83 m, and a radius of gyration of 0.76m. Each of the wheels B and C has a
mass of 16 kg, a diameter of 0.76 m, and a radius of gyration of 0.27 m about the axle. Initially A, B
and C are at rest. A counterclockwise torque of 2.71 kN m about the axis of rotation is applied to the
flywheel A. Neglecting friction at the axles and assuming no slipping, find the number of
revolutions that flywheel A has to turn before the angular speed of wheel B is what it would be in a
car traveling at 241 km hˉ¹.
Ans : 22.8
B
C
A
6. A force of 200 N is applied at the free end of the cable wrapped around the spool as shown in the
following diagram. The spool has a mass of 40 kg and a centroidal radius of gyration of 0.15 m. The
spool starts from rest and rolls without slipping. Find the speed of its centre of mass after moving 5
m up the incline.
200 N
Ans : 6.24 m sˉ¹
0.25 m
0.1 m
10o
7. One end of a light spring of unstrained length 95 mm and stiffness 4.0 kN mˉ¹ is fixed on the wall.
The other end pushes against a uniform cubic block which is held by a light thread AB through the
spring as shown. The spring has been compressed to 80 mm between the block and the wall. The
mass of the block is 0.98 kg and the length of each its sides is 50 mm. The spring suddenly breaks,
then the block slides to the right on the horizontal floor for a distance of 0.1 m before it strikes the
small step O with negligible rebound. The kinetic friction between the block and the floor is 3.8 N.
Calculate the angular velocity of rotation about O and the kinetic energy of the block immediately
after the impact.
Ans : 5.68 rad sˉ¹; 0.026 J
A
B
O
80 mm
50 mm100 mm
Note : Moment of a block Iz passing through:
z
Iz = m(a2+ b2)/3
2a
2
2b