Collisions in One Dimension

[pstfleur]

1. Kevin has a mass of 87kg and is skating with in-line skates. He sees his 22-kg younger brother up ahead standing on the sidewalk, with his back turned. Coming up from behind, he grabs his brother and rolls off at a speed of 3.4 m/s. Ignoring friction, find Kevin's speed just before he grabbed his brother.



2. VF(ma+mb)=MTVF



3. From the problem I know it is an inelastic collision..
I did v= 87*v+22*2.4/109
v=2.4 which is wrong. the answer is suppose to be 3.0

Please help.. I really don't think I've grasped the idea of collisions

 

[Kurdt]

You have the correct equation in the second part. I will rewrite it for you.

$$Mv=(M+m)v_f$$

All you have to do is rearrange and find v.

The answer should also be greater than 3. How can he gain speed if he picks up his little brother as well.

 

[baba89]

in one dimension.



I can provide some clarification and guidance on the concept of collisions in one dimension. First, it is important to understand that there are two types of collisions: elastic and inelastic. In an elastic collision, kinetic energy is conserved, meaning that the total kinetic energy before the collision is equal to the total kinetic energy after the collision. In an inelastic collision, kinetic energy is not conserved and some of it is lost in the form of heat or sound.

In this problem, we are dealing with an inelastic collision since the two objects, Kevin and his brother, stick together after the collision. In this type of collision, the total momentum before the collision is equal to the total momentum after the collision. This is represented by the equation given in the problem, where V is velocity, M is mass, and T is time.

To solve this problem, we can use the conservation of momentum equation: MV=MTV. We know the masses of both Kevin and his brother, as well as the final velocity after the collision (3.4 m/s). However, we are trying to find the initial velocity of Kevin before the collision. We can rearrange the equation to solve for V: V=MTV/M. Plugging in the values, we get V=(87*3.4+22*0)/109=2.7 m/s. This is the correct answer, and I believe the mistake in the previous calculation was due to using the wrong values for the masses.

In summary, it is important to understand the type of collision you are dealing with and to use the correct equations and values to solve the problem. I hope this explanation helps in your understanding of collisions in one dimension.