A 3.16-kg steel ball strikes a massive wall at 10.0 m/s at an angle of 𝜃 = 60.0° with the plane of the wall. It bounces off the wall with the same speed and angle (see the figure below). If the ball is in contact with the wall for 0.226 s, what is the average force exerted by the wall on the ball?magnitude Your response differs from the correct answer by more than 10%. Double check your calculations. Ndirection
Question
A 3.16-kg steel ball strikes a massive wall at 10.0 m/s at an angle of 𝜃 = 60.0° with the plane of the wall. It bounces off the wall with the same speed and angle (see the figure below). If the ball is in contact with the wall for 0.226 s, what is the average force exerted by the wall on the ball?magnitude Your response differs from the correct answer by more than 10%. Double check your calculations. Ndirection
Solution
To solve this problem, we first need to find the change in momentum of the steel ball.
The initial momentum (p_initial) of the ball can be found using the formula:
p_initial = mass * velocity
p_initial = 3.16 kg * 10.0 m/s = 31.6 kg*m/s
However, since the ball strikes the wall at an angle, we need to consider only the component of the momentum that is perpendicular to the wall. This can be found using trigonometry (specifically, the sine of the angle):
p_initial_perpendicular = p_initial * sin(60.0°) = 31.6 kgm/s * sin(60.0°) = 27.36 kgm/s
Since the ball bounces off the wall with the same speed and angle, its final momentum (p_final) is the same in magnitude but opposite in direction. Therefore, the change in momentum (Δp) is:
Δp = p_final_perpendicular - p_initial_perpendicular = -27.36 kgm/s - 27.36 kgm/s = -54.72 kg*m/s
The average force (F_avg) exerted by the wall on the ball can be found using the formula:
F_avg = Δp / Δt
where Δt is the time the ball is in contact with the wall. Substituting the given values:
F_avg = -54.72 kg*m/s / 0.226 s = -242.3 N
The negative sign indicates that the force is exerted in the direction opposite to the initial motion of the ball, i.e., into the wall.
So, the average force exerted by the wall on the ball is 242.3 N, directed into the wall.
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