Question

During an in-class demonstration of momentum change and impulse, Mr. H asks Jerome (102 kg) and Michael (98 kg) to sit on a large 14-kg skate cart. Mr. H asks Suzie (44 kg) to sit on a second 14-kg skate cart. The two carts are placed on low friction boards in the hallway. Jerome pushes off of Suzie's cart. Measurements are made to determine that Suzie's cart acquired a post-impulse speed of 9.6 m/s. Determine the expected recoil speed of Jerome and Michael's cart.

Answer 1

Answer:

2.6 m/s

Explanation:

mass of Jerome (Mj) = 102 kg

mass of Micheal (Mm) = 98 kg

mass of each cart (Mc) = 14 kg

recoil speed of Jerone and Micheal after push (Vi) = ?

mass of Suzie (Ms) = 44 kg

Suzie's speed after push (Vs) = 9.6 m/s

From the conservation of momentum, initial momentum = final momentum

Since they all are initially at rest the initial momentum is 0 and hence the final momentum is also 0.

Therefore for the final momentum we have

(Mj + Mm + Mc) Vi - (Ms + Mc) Vs = 0  ( the negative sign is because they move in opposite directions)

((102 + 98 + 14) x Vi ) - ((44 + 14) x 9.6) = 0

(214 x Vi) - (58 x 9.6) = 0

214 Vi = 556.8

Vi = 556.8 / 214 = 2.6 m/s

Answer 2

The expected recoil speed of Jerome and Michael's cart is 2.6 m/s.

From the law of Conservation of momentum:

Initial momentum = Final momentum

At rest,  initial momentum = final momentum = 0.

Final momentum = (Mj + Mm + Mc) Vi - (Ms + Mc) Vs = 0  (Opposite directions hence the negative sign)

where mass of Jerome (Mj) = 102 kg , mass of Michael (Mm) = 98 kg , mass

of each cart (Mc) = 14 kg . recoil speed of Jerome and Michael after push

(Vi) = ? , mass of Suzie (Ms) = 44 kg , Suzie's speed after push (Vs) = 9.6 m/s

((102 + 98 + 14) x Vi ) - ((44 + 14) x 9.6) = 0

(214 x Vi) - (58 x 9.6) = 0

214 Vi = 556.8

Vi = 556.8 / 214 = 2.6 m/s

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