Question

2. A railroad boxcar rolls on a track at 3.10 m/s toward two identical coupled boxcars, which are rolling in the same direction as the first, but a speed of 1.60 m/s. The first reaches the second two and all couples together. The mass of each is 4.65 x 104kg. (a) Present the physical principle in mathematical form and use it to determine the speed of the three coupled cars after the first couples with the other two. (b) Determine the amount of kinetic energy converted to other forms during the collision.

Answer 1

In rail road problem,

Applying conservation of momentum

0 = nա

As mass is equal for all boxcars

0 =n

3.10+1.6+1.6 = 3v

V =6.3/3 =2.1m/s

Lost in kinetic energy is

4.65×10⁴(u_{​​​​​​1^²}+u_{​​​​2}^{​​​​​2}+u₃²  - 3v²)/2

2.325×10000((3.1×3.1)+(1.6×1.6)2 - 3(2.1×2.1))= 34.875kJ

In racquet problem,

0.06 kg ball change its velocity to 60m/s to -40m/s

Impulse= sudden change in momentum

i.e., Impulse(J)= 0.06{65-(-40)} = 6.3N

Work done by racquet = force× distance travelled in that direction

Work done(W) = 6.3N × 40 m/s = 252 joules

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