Question

A child hits an ice cube with a mass of 10 grams on a table with a force of 10 N. The impact lasts 0.02 seconds. The ice cube flies off the table, which is 1 meter high and lands some distance away. Assume there is no friction between the ice cube and the table.

a. What is the velocity of the ice cube when it leaves the table?

b. What is the final velocity of the ice cube just before it hits the floor?

c. What is the momentum of the ice cube just before it hits the floor?

d. What distance will the ice cube land from the foot of the table?

e. Suppose the ice cube had broken into two pieces just after the child hit the ice and moved away from each other while falling to the floor. How would the total momentum of the two pieces just before they hit the floor compare to the momentum you found in part (c)?

Answer 1

Since Force has impact of 0.02sec, so, Impulse by the force = Force*time= 10*0.02 =0.2 N-s

part(a)

We know that impulse is changed in momentum. initially, the ice is at rest, So initial momentum will be 0

final momentum - initial momentum = Impulse

final momentum -0 =0.2 N-s

m*V =0.2

so, V =0.2/(m) =0.2/(0.01)=20 m/s( since no friction, the velocity of ice just before leaving the table will be same)

part(b)

now after leaving the table ice will follow the projectile motion

initially, verticle direction velocity will be 0 and horizontal velocity=20m/s

time to cover the vertical distance of 1m, using (H = u*t +1/2*g*t^2)

since initial vertical velocity is 0,

so,

final vertical velocity

and velocity is horizontal direction will be constant 20m/s( since there is no net force in the horizontal direction

So velocity just before hit the ground=

(i and j are unit vectors in horizontal and vertical up direction.)

part(c)

momentum =mass *velocity

part(d)

The ice cube travels in the horizontal direction for t=0.447s

horizontal distance = 20*0.447 m= 8.94 m

part(e) we need to use conservation of momentum to relate,

momentum before collision = momentum after collision and breaking

so, the momentum of the center of mass will have same as momentum in part(c)

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