A child\'s sled has rails that slide with little friction across the snow. Logan

Question

A child's sled has rails that slide with little friction across the snow. Logan has an old wooden sled with heavy iron rails that has a mass of 9.0 kg quite a bit for a 27 kg child! Logan runs at 3.7 m/s and leaps onto the stationary sled and holds on tight as it slides forward. The impact time with the sled is 0.21 s . Immediately after Logan jumps on the sled, how fast is it moving? What was the force on the sled during the impact? How much energy was "lost" in the impact? Where did this energy go?

Explanation / Answer

let

m1 = 27 kg, u1 = 3.7 m/s

m2 = 9 kg, u2 = 0

let v is speed of child and sled after jumpig.

Apply conservation of momentum

m1*u1 + m2*u2 = (m1+m2)*v

27*3.7 + 0 = (27 + 9)*v

==> v = 27*3.7/(27 + 9)

= 2.775 m/s

b) Apply Impulse-momentum thorem

Impulse on sled = change in momentum of sled

F*dt = m2*(v - 0)

F = m2*v/dt

= 9*2.775/0.21

= 118.9 N

c) Energy lost in the impact = KI - Kf

= 0.5*m1*u1^2 - 0.5*(m1+m2)*v^2

= 0.5*27*3.7^2 - 0.5*(27+9)*2.775^2

= 46.2 J

d) The loss of energy converted to thermal energy.

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