## Sunday, December 1, 2013

### Sledding

As I was driving back to Colgate yesterday night, I noticed a man and his child sledding down the slope in front of the admissions building. I decided to calculate their final velocities when they reached the bottom of the slope. I assumed that the mass of the man is 70kg, the mass of the child is 28kg, mass of the sled is 2kg, and the angle ϴ is 20˚. µk of a plastic sled on snow is 0.3.

To find the final velocity of the man:
ΔKE = - ΔPE + WNC
½ mvf2 = mghi + Ffr d cosϴ
½ (72kg) vf2 = (72kg)(9.8m/s2)(4m) + µFN dcosϴ
½ (72kg) vf2 = (72kg)(9.8m/s2)(4m) + µ(mg cos 20) dcosϴ
½ (72kg) vf2 = (72kg)(9.8m/s2)(4m) + 0.3(72kg*9.8m/s2 * cos 20) (5m) cos180
vf = 7.13 m/s

To find the final velocity of the child:
ΔKE = - ΔPE + WNC
½ mvf2 = mghi + Ffr d cosϴ
½ (30kg) vf2 = (30kg)(9.8m/s2)(4m) + µFN dcosϴ
½ (30kg) vf2 = (30kg)(9.8m/s2)(4m) + µ(mg cos 20) dcosϴ
½ (30kg) vf2 = (30kg)(9.8m/s2)(4m) + 0.3(30kg*9.8m/s2 * cos 20) (5m) cos180
vf = 7.13 m/s

Thus, both the final velocities of the man and the child are the same.