Professor Newton is sitting under his favorite apple tree, thinking about the mo

Question

Professor Newton is sitting under his favorite apple tree, thinking about the moon. All of a sudden, a ripe apple falls from the tree, 1.5 meters above him, and bounces off of his head. At the instant that it leaves his head, the apple has a velocity of 4 m/s upwards. The apple has a mass of 0.2 kg. a) What is the velocity of the apple when it hits Prof. Newton? (you will have to remember back to chapter 2 for this – assume the apple is in freefall and that you can ignore air resistance or drag). Be sure you include the direction of the velocity (positive or negative)

b) What is the change in momentum of the apple during the collision?

c) What impulse did Prof. Newton’s skull impart to the apple? (ignore his scalp, hair, etc.)

d) If the collision lasts 0.2s, what is the magnitude of the average force that the apple exerts on Prof. Newton’s head?

Explanation / Answer

a) velocity of the apple when it hits prof.newton is v = sqrft(2*g*h) = sqrt(2*9.8*1.5) = 5.42 m/s

since the direction is downwards then v = -5.42 m/s

b) change in momentum is m*(v+u) = 0.2*(4+5.42) = 1.884 Kg m/s

C) Impulse = change in momentum = 1.884 kg m/sec or N-s

d) impulse is Favg*dt

1.884 = Favg*0.2

Favg = 1.884/0.2 = 9.42 N

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