Two carts with masses of 4.52 kg and 2.42 kg move toward each other on a frictionless track with speeds of 5.08 m/s and 3.58 m/s respectively. The carts stick together after colliding head-on. Find the final speed.

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Physics

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1 December, 18:50

Two carts with masses of 4.52 kg and 2.42 kg move toward each other on a frictionless track with speeds of 5.08 m/s and 3.58 m/s respectively. The carts stick together after colliding head-on. Find the final speed.

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Amy Weber · Answer 1

Answer: The final speed is 4.56m/s

Explanation:

According to law of conservation of momentum, the sum of momentum of the bodies before collision is equal to the sum of their momentum after collision. After collision they both move with a common velocity v.

Let the masses of the carts be m1 and m2 respectively

u1 and u2 be their velocities

and v be their common velocity

Since momentum is mass * velocity

Momentum before collision will be;

For 4.52kg body with speed of 5.08m/s, its momentum before collision is

m1u1 = 4.52*5.08 = 22.96kgm/s

For 2.42kg body with speed of 3.58m/s, its momentum before collision is

m2u2 = 2.42*3.58 = 8.66kgm/s

Momentum of the bodies after collision will be (m1+m2) v

= (4.52+2.42) v

Using the law of conservation of momentum we have;

22.96+8.66 = (4.52+2.42) v

31.62 = 6.94v

V = 31.62/6.94

V = 4.56m/s

The final speed is 4.56m/s