An 8-kg ball rolling at 2m/s bumps into a pillow and stops in 0.5s (a) Show that the force exerted by the pillow is 32N. (b) How much force does the ball exert on the pillow?
To solve this problem, we can use Newton's second law of motion, which states that the force acting on an object is equal to the rate of change of its momentum.
(a) To find the force exerted by the pillow on the ball, we need to calculate the rate of change of momentum.
The momentum of an object is given by the product of its mass and velocity:
Momentum (p) = mass (m) × velocity (v)
In this case, the ball's initial momentum (p_initial) is given by:
p_initial = mass × velocity = 8 kg × 2 m/s = 16 kg·m/s
The ball comes to a stop, so its final momentum (p_final) is zero:
p_final = 0 kg·m/s
The change in momentum is given by:
change in momentum = p_final - p_initial
Plugging in the values, we get:
change in momentum = 0 kg·m/s - 16 kg·m/s = -16 kg·m/s
The time taken for the ball to stop is 0.5 seconds. Using the formula for force:
force (F) = change in momentum / time
Plugging in the values, we get:
force = -16 kg·m/s / 0.5 s = -32 N
Therefore, the force exerted by the pillow on the ball is 32 N (opposite in direction to the ball's motion).
(b) According to Newton's third law of motion, the forces exerted by two objects on each other are equal in magnitude but opposite in direction.
Since the force exerted by the pillow on the ball is 32 N, the force exerted by the ball on the pillow is also 32 N but in the opposite direction.
To find the force exerted by the pillow and the force exerted by the ball on the pillow, we can use Newton's second law of motion, which states that force (F) is equal to mass (m) times acceleration (a), or F = m * a.
(a) To find the force exerted by the pillow on the ball, we can use the equation F = m * a. Given that the ball's mass (m) is 8 kg and it comes to a stop in 0.5 seconds, we need to find the acceleration (a) that caused the ball to decelerate. To do this, we can use the equation a = (v_f - v_i) / t, where v_f is the final velocity, v_i is the initial velocity, and t is the time taken.
Initial velocity of the ball (v_i) = 2 m/s (given)
Final velocity of the ball (v_f) = 0 m/s (since it comes to a stop)
Time taken (t) = 0.5 s (given)
Plugging these values into the equation, we have:
a = (0 - 2) m/s / 0.5 s
a = -2 m/s^2
Now, we can find the force exerted by the pillow by using F = m * a:
F = 8 kg * (-2 m/s^2)
F = -16 N
Since force is a vector quantity, the negative sign indicates that the force exerted by the pillow is in the opposite direction of the motion of the ball. To find the magnitude of the force, we consider its absolute value, so the force exerted by the pillow is 16 N.
(b) To find the force exerted by the ball on the pillow, we can use the principle of action and reaction, which states that for every action, there is an equal and opposite reaction.
Therefore, the force exerted by the ball on the pillow is also 16 N.
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(a) Initial momentum = impulse
8 kg * 2 m/s = Force * 0.5 s
Force = __ Newtons
(b) Use Newton's third law
action = reaction
(This refers to forces objects exert on each other)