Two average forces. A steady stream of 0.239 kg snowballs is shot perpendicularl

Question

Two average forces. A steady stream of 0.239 kg snowballs is shot perpendicularly into a wall at a speed of 4.60 m/s. Each ball sticks to the wall. The figure gives the magnitude F of the force on the wall as a function of time t for two of the snowball impacts. Impacts occur with a repetition time interval delta t_r = 51.0 ms, last a duration time interval delta t_d = 11.0 ms, and produce isosceles triangles on the graph, with each impact reaching a force maximum F_max = 200 N. During each impact, what are the magnitudes of (a) the impulse and (b) the average force on the wall? (c) During a time interval of many impacts, what is the magnitude of the average force on the wall?

Explanation / Answer

(a) Since the graph is a triangle, the impulse = average force * time
100 * 11 ms = 1.1N s= 1.1 kg m/s
BUT the impulse = change in momentum = 0.239 kg *4.6 m/s =1.0994kg m/s
(b) the average force on the wall? Since the graph is a triangle, average force = maximum/2
Fmax/2 = 200 N/2 =100 N
BUT average force = impulse / time =1.0994 kg m/s/11 ms =99 N
(c) During a time interval of many impacts, what is the magnitude of the average force on the wall?
average force over 51 ms = impulse / 51 ms = 1.0994 kg m/s/51 ms =21.5 N

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