Two toy cars A and B are moving towards each other on a hard surface. A has a mass of 60g and it move towards right with a velocity of 60cm/s while B has a mass of 100g and moves towards left with a velocity of 20cm/s. THe two cars collide and get stuck to one another>What is their velocity after collision?
Answers
Answer:
m1 =60g
u1 = 60 cm / s
m2= 100 g
u2 = 20 cm / s
m1u1+ m2u2= m1 v1+ m2 v2
60×60+100×20=160×v
5600/160 =10m/s
The combined velocity of the cars after the collision is 10 cm/s.
Given: Car A has a mass of 60 g and it moves towards the right with a velocity of 60 cm/s while B has a mass of 100 g and moves towards the left with a velocity of 20 cm/s. The two cars collide and get stuck to one another.
To Find: The velocity of the cars after the collision.
Solution:
- Whenever we find two bodies getting stuck together after collision and having a single velocity, we can say that it is a case of inelastic collision.
- The inelastic collision is based on the concept of conservation of linear momentum before and after the collision.
- The equation of inelastic collision can be shown by the formula,
( mA×vA ) + ( mB×vB) = ( mA + mB ) × V .....(1)
Where mA = mass of body A, mB = mass of body B, vA = velocity of body A, vB = velocity of body B, V = combined velocity after collision.
Coming to the numerical, we are given;
The mass of body A ( mA ) = 60 g
The mass of body B ( mB ) = 100 g
Now, since it is said that the bodies are moving toward each other, so if we consider the velocity of body A ( approaching from right ) to be positive, then we shall consider the velocity of body B ( approaching from left ) to be negative.
The velocity of body A ( vA ) = 60 cm/s
The velocity of body B ( vA ) = - 20 cm/s
Putting respective values in (1), we get;
( mA × vA ) + ( mB × vB) = ( mA + mB ) × V
⇒ ( 60 × 60 ) + ( 100 × (- 20 )) = ( 100 + 60 ) × V
⇒ 3600 - 2000 = 160 × V
⇒ 160 × V = 1600
⇒ V = 1600 / 160
= 10 cm/s
Hence, the combined velocity of the cars after the collision is 10 cm/s.
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