You are standing in the middle of a frozen lake There is no

You are standing in the middle of a frozen lake. There is no wind and the ice is so smooth it is frictionless. (I know, this type of thing happens to me all the time, too!) Luckily you are carrying a slingshot and 100 marbles each with a mass of 0.05kg. Your sling shot requires 250 N/m to pull it back and you have a reach of 1 m. Estimate your final velocity after you have shot all the marbles one at a time. Would you get any benefit (increased velocity) by shooting more than one marble at a time? Explain.

Solution

Given data : Spring constant K of slingshot = 250 N/m, Max stretching of the spring (x) = 1 m, Mass of 100 marbles (m) = 5 Kg.

Work done by stretching the string = = 1/2 x K (x)² = 125J which is converted into KE of marbles

i.e 125J = 1/2 m v² Hence velocity of marble = 7.07 m/sec

By principle of conservation of momentum mv = MV (where M is your mass and V is your velocity)

By substituting appropriate values, V can be determined.

No additional benefit by shooting more than one marble at at time as Momentum is conserved.