You are standing on a sled which can slide without friction on a large lake of i

Question

You are standing on a sled which can slide without friction on a large lake of ice. You and the empty sled together have a mass of 100 kg. On the sled with you are 900 1.0 kg rocks. You have the ability to throw each rock with a velocity (relative to yourself) of 10.0 m/s. a) How fast will you be going after you throw all of the rocks (one at a time) as hard as you can? b) How many rocks should you throw (one at a time) such that the final momentum of the sled (with all remaining rocks) is maximized? (Hint, the answer is not “all of them.”) c) How fast will you be going with respect to the ground when you have your maximum momentum? d) Does throwing an additional rock after you have reached your maximum momentum still increase your speed? Why does throwing an additional rock decrease your total momentum?

Explanation / Answer

a)

m = mass of sled + person = 100kg

M = mass of rocks = 900 kg

v = velocity gained by sled + person

V = velocity of rocks = 10 m/s

Using conservation of momentum

mv + MV = 0

100 v + 900 (10) = 0

v = - 90 m/s

b)

let the number of rocks = n

m = mass of sled + person + rocks left = 100 + 900 - n kg

M = mass of rocks = n kg

v = velocity gained by sled + person

V = velocity of rocks = 10 m/s

Using conservation of momentum

mv + MV = 0

(1000 - n) v + n (10) = 0

v = - 10n / (1000 - n)

dv/dn = - [10 (1000 - n) - 10 n] = 0

n = 500

c)

v = - 10n / (1000 - n) = - 10(500) / (1000 - 500) = - 10 m/s

d)

it will decrease the momentum as the mass decreases with throwing the stones

Related Questions

Navigate

• Browse (All)
• Browse Y
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.