A motorcycle of mass 2000kg is moving over a horizontal road, with uniform velocity. If this
motorcycle has to be stopped with a negative acceleration of -1.5m/s2
, then what is the force of
friction between the tyres of motorcycle and the road?
2) A bus of mass 5000kg starts from rest and rolls down a hill. If it travels a distance of 200m in
10seconds. Calculate (i) acceleration of the bus and (ii) the force on the bus.
3) A ball of mass 100g moving with velocity of 10m/s is stopped by a boy in 0.2seconds. Calculate
the force applied by the boy to stop the ball.
4) A gun fires a bullet of mass 50g. The bullet moving a velocity of 100m/s strikes a sand bag and
gets embedded after travelling 10cm. Calculate (i) the resistive force exerted by the sand on the
bullet and (ii) the time taken by the bullet to come to rest.
5) A force of 5N produces an acceleration of 8m/s2 on a mass m1, and an acceleration of 24m/s2 on
a mass m2. What acceleration would the same force provide if both the masses are tied
together.
Answers
Explanation:
(1).
mass= 2000kg
acceleration= - 1.5m/s^2
Force= mass X acceleration
=2000kg X - 1.5m/s^2
= -3000kg.m/s^2
= - 3000N
(2).
mass = 5000kg
initial velocity= 0m/s. (since it starts from rest)
s =200m
t = 10s
(i). s = ut+ 1/2at^2
200 =0x10 + 1xax10x10/2
200 = 50a
a = 4m/s^2
(ii). f = m.a
= 5000 X 4 kg.ms^2
= 20000N
(3).
mass = 100 g =100/1000kg=1/10kg
initial velocity= 10 m/s =u
t = 0.2s
final velocity= 0m/s
v =u+at
0 = 10 + a X 0.2
-10 = 0.2a
-10/0.2 = a
a= -50 m/s^2
now,
f = ma
= 1/10 X -50 kg.m/s^2
= -5 kg.m/s^2
= -5 N
(4).
mass = 50g= 50/1000kg=1/20kg
initial velocity =100m/s
s =10cm=1/10m
final velocity= 0m/s
(i). v^2 - u^2 =2as
= 0 - (100)^2 =2.a.1/10
= -10000 = 1 X a/5
= -50000 m/s^2 = a
f = m.a
= 1/20 X -50000 kg.m/s^2
= -2500N
(ii).
v = u + at
0 = 100 + -50000 X t
-100 = - 50000t
t = 0.002s
(5).
case. 1.
f =5N
a= 8m/s^2
m1= F/a
=5/8 kg
case.2.
f =5N
a = 24m/s^2
M2 = 5/24 kg
- both are tied ,
=m1 + m2
=5/8+ 5/24
= 20/24kg
now,
a = F/m
=5x24/20
= 6 m/s^2