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Engineering Mechanics
Problem Sheet – 6
Module - 6 Kinetics of Particle
1. Find acceleration of block A, B and C shown in the figure when the system is released from rest. Mass
of block A, B and C is 5 kg. 10 kg and 50 kg respectively. Coefficient of friction for block A and B is 0.3.
Neglect weight of pulley and rope friction.
[Ans: 𝒂𝑨 = 𝟏𝟐. 𝟓𝟐𝒎/𝒔𝟐 , 𝒂𝑩 = 𝟎. 𝟗𝟐𝒎/𝒔𝟐 , 𝒂𝑪 = 𝟔. 𝟕𝟐 𝒎/𝒔𝟐 ]
2. At a certain instant a body of mass 15 kg is falling freely under gravity was found to be falling at a
speed of 25 m/s. What force will stop the body in 2 seconds?
[Ans : 187.5 N]
3. A 2 kg particle rests on a very smooth horizontal plane and is acted upon by force components FX=0
and Fy=3N. If x=0, y=0 Vx=2m/s when t=0, determine the equation y=f(x) which describes the path of
𝒙𝟐
[Ans :y = 𝟒𝟖 +
the particle.
4. The system of pulleys, masses and connecting inextensible cables as
shown pulleys are massless and frictionless. If the system is released
from rest, find the acceleration of each of the three masses and tension
in the circle.
Ans: aA=4.04m/sec2( ),
aB=2.885 m/sec2( ),
aC=0.576 m/sec2( ),T=27.7N
5. At a given instant the 50 N block A is moving
downward with a speed of 1.8 m/s. Determine its
speed 2 seconds later. Block ‘B’ has a weight 20 N,
and the coefficient of kinetic friction between it
and the horizontal place is µk=0.2. Neglect the mass
of pulley’s and chord. Use D’Alemberts principle.
𝒙
𝟑
]
Engineering Mechanics
Problem Sheet – 6
Module - 6 Kinetics of Particle
Ans: Va=8.14m/sec2( )
6. A vertical lift of weight 10kN moving from rest with
constant acceleration acquires an upward velocity of 4
m/s over a distance of 5 m. Determine the tension in
the cables supporting the lift.
Ans: 116314N
7. Two blocks A weight 500 N and B of weight 300 N are
10 m apart on an inclined plane as shown in figure. The
coefficient of friction for blocks A and B with inclined
plane are 0.2 and 0.3 respectively. If the blocks being to
slide down simultaneously calculate the time and
distance travelled by each block when block A touches
block B.
Ans:
5.16 sec,
54.03sec, 64.03 sec
8. Determine the tension developed in chords attached to each block and the accelerations of the
blocks when the system shown is released from rest. Neglect the mass of the pulleys and chords.
Ans: TA=77.63N, TB=19.34N
aA=1.244m/sec2( ), aB=4.976m/sec2( ),
9. Two blocks A(mass 10 kg), B(mass 28 kg) are separated by 12 m
as shown in the figure. If the blocks start moving, find the
time‘t’ when the blocks collide. Assume µ=0.25 for block A and
plane µ=0.10 for block B and plane.
Ans: 4.34 sec
10. Masses A(5 kg), B(10 kg), C(20kg) are connected as shown in figure by inextensible cord passing over
massless and frictionless pulleys. The coefficient of friction for masses A and B with ground is 0.2. If
the system is released from rest, find the acceleration of the blocks and tension in the cords.
Ans: aA= aB= aC=4.765m/sec, T1=33.63 N ,T2=67.27 N
Engineering Mechanics
Problem Sheet – 6
Module - 6 Kinetics of Particle
11. Three weights A, B and C of weights 3kg, 2kg and 7kg are connected as
shown fig. Determine the
accelerations of A,B and C. Also find the tension on the strings.
Ans: aA=0.5m/sec2( ), aA=4.15m/sec2( ), aA=1.83m/sec2( )
T1=27.93 N T1=55.83 N
12. Find ‘P’ required to accelerate the block shown in figure below at 2.5m/sec2.
Take µ=0.3
Ans: P=208.63 N
13. Determine the weight ‘W’ required to bring the system in
following figure to stop in 5 second if at the instant as
shown, 500 N block is moving down at 3m/sec. The
pulley is frictionless.
Ans:415.14 N
the
14. The system shown in figure is released from
rest. What is the height lost by bodies A, B and
C in 2 seconds? Take coefficient of kinetic
friction at rubbing surfaces as 0.4. Find also the
tension in wires.
Ans:T1= 21.42N,T1=,38.86N, a=5.79m/sec2
15. A vertical lift of total mass 750kg acquires an upward velocity of 3m/s over a distance of 4m moving
with constant acceleration starting from rest. Calculate the tension in the circle.
Ans:T=8201.25 N
Engineering Mechanics
Problem Sheet – 6
Module - 6 Kinetics of Particle
16. Three m1, m2 & m3 of masses 1.5kg respectively are placed on a rough surface with µ=0.20 as show.
If a force F is applied to accelerate the blocks at 3m/s2, what will be the force that 1.5kg block exerts
on 2kg block?
Ans: P=14.886 (
)
17. State D’Alembert’s principle with two examples.
18. Find the velocity of block A and B when block A has travelled 1.2 m along inclined plane. Mass of A is
10 kg and that of B is 50 kg. Coefficient of friction between block A and inclined plane is 0.25. Pulley
are mass less and frictionless use work energy principle. Refer figure.
Ans:VA=4.175 m/sec2,VB=20.87, m/sec2
19. State and prove Work-Energy principle.
20. A block of mass m=80kg is compressed against a spring as shown Fig.
How far from point B[distance x] will the block
strike on the plane at point A. Take free length of
spring as 0.9m and spring stiffness as K=40 * 102
N/m.
Ans:x=0.667m
21. A collar A of mass 10kg moves in a vertical guide as shown. Neglecting
friction between guide and the collar, find its velocity when it passes
through position (2), after starting from rest in position (1). The spring
constant is 200 N/m and the free length of the spring is 200mm.
Ans:V=3.85m/sec
22. A 5 kg mass drops 2m upon a spring whose modules is 10N/mm. What will be the speed of the block
when the spring is deformed 100mm?
Ans: V=4.604 m/sec
23. Find the work done in rolling a 20 kg wheel a distance 1.5 m up a plane
inclined 30o with the horizontal as shown in figure. Assume coefficient
of friction as 0.25.
Ans: 47.85 J
24. Explain the term in short : Work-energy principle.
Engineering Mechanics
Problem Sheet – 6
Module - 6 Kinetics of Particle
25. State and prove energy principle.