Two carts with masses of 4.76 kg and 2.70 kg move toward each other on a frictionless track with speeds of 4.95 m/s and 3.59 m/s respectively.Two carts with masses of 4.76 kg and 2.70 kg move...

Two carts with masses of 4.76 kg and 2.70 kg move toward each other on a frictionless track with speeds of 4.95 m/s and 3.59 m/s respectively.

Two carts with masses of 4.76 kg and 2.70 kg move toward each other on a frictionless track with speeds of 4.95 m/s and 3.59 m/s respectively.

The carts stick together after colliding head-on. Find the final speed.

Asked on by tortor44

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ndnordic | High School Teacher | (Level 2) Associate Educator

Posted on

This is an example of an inelastic collision involving momentum of two objects. So you can use the general equation:

m1v1 + m2v2 = (m1+m2)v

where m1 and v1 are the mass and velocity of one cart before colliding and where m2 and v2 are the mass and velocity of the other cart before colliding. Since they stick together their masses combine and have one velocity, v.

Since the carts are moving in opposite directions, and velocity is a vector, one cart will have a positive velocity and the other a negative velocity.

Let's assume that the cart of mass 4.76 kg is moving to the right with a positive velocity of 4.95 m/s and the cart of mass 2.7 kg is moving to the left with a negative velocity of 3.59 m/s.

Using the above equation you get:

4.76 kg * 4.95 m/s + 2.7 kg * (-3.59 m/s) = 7.46 kg*v

v = +1.86 m/s so the two carts, after the collision, are moving to the right.

 

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