Question

Two magnets are sliding towards each other. One of the magnets, which has a mass of 125 grams, is moving in the positive x-direction at a speed of 7.33 m/s. The other magnet, which has a mass of 85.0 grams, is moving in the negative x-direction at a speed of 11.9 m/s. When they collide, they bind together and move as a single unit. What is the velocity of this single unit immediately after the collision?

Answer 1

0.45 m/s in the negative x-direction

Step-by-step explanation:

From the law of conservation of momentum, the sum of initial momentum equals the sum of final momentum

Momentum, p=mv where m is the mass and v is the velocity

`m_1v_1+m_2v_2=(m_1+m_2)v_c` where
`v_c` is the common velocity,
`v_1` and
`v_2` are velocities of magnet moving in positive x-direction and magnet moving in negative x-direction respectively,
`m_1` and
`m_2` are masses of magnet moving in positive x-direction and magnet moving in negative x-direction respectively.

Substituting 125 g for
`m_1` and 85 g for
`m_2`, 7.33 m/s
`v_1`, -11.9 m/s for
`v_1` then

`125 g* 7.33 m/s + (85 g* -11.9)=(125 g+ 85 g)* v_c`

`-95.25 g. m/s=210 g v_c`

`v_c=\frac {-95.25 g.m/s}{210 g}=-0.453571429 m/s \approx -0.45 m/s`

Therefore, the velocity of single unit is 0.45 m/s in the negative x-direction