Two masses of 1 kg and 2 kg are tied together with an inextensible string of negligible mass. These are pulled on a frictionless horizontal surface with a force of 9 N. (a) What is the acceleration? (b) What is the force acting on 1 kg mass?
Answers
Explanation:
Net pulling force on the system is
F
net
=2g−1g=20−10=10N
Total mass being pulled m=(1+2)=3kg
Therefore, acceleration of the system will be a=
m
F
net
=
3
10
m/s
2
Displacement of both the blocks in 1 s is
S=
2
1
at
2
=
2
1
(
3
10
)(1)
2
=
3
5
Net pulling force on the system is
F
net
=2g−1g=20−10=10N
Total mass being pulled m=(1+2)=3kg
Therefore, acceleration of the system will be a=
m
F
net
=
3
10
m/s
2
Displacement of both the blocks in 1 s is
S=
2
1
at
2
=
2
1
(
3
10
)(1)
2
=
3
5
m
From free body diagram of 2 kg block
Using ΣF=ma, we get
20−T=2a=2(
3
10
)
or T=20−
3
20
=
3
40
N
∴ Work done by string (tension) on 1 kg block in 1 s is
W
1
=(T)(S)cos0
∘
=(
3
40
)(
3
5
)(1)=
9
200
J
Similarly, work done by string on 2 kg block in 1 s will be
W
2
=(T)(S)(cos180
∘
)
=(
3
40
)(
3
5
)(−1)=−
9
200
J
solution
m
From free body diagram of 2 kg block
Using ΣF=ma, we get
20−T=2a=2(
3
10
)or T=20− 320
= 340N
∴ Work done by string (tension) on 1 kg block in 1 s is W 1
=(T)(S)cos0∘
=( 340 )( 35)(1)= 9200J
Similarly, work done by string on 2 kg block in 1 s will be W2
=(T)(S)(cos180 ∘)
=( 340 )( 35 )(−1)
=− 9200 J solution