Rita accelerates a 0.40-kg ball from rest to 9.0 m/s during the 0.075 s in which her foot is in contact with the ball. What average force does she apply to the ball during the kick?
A) 48 N
B) 72 N
C) 24 N
D) 60 N
E) 76 N
To find the average force applied to the ball, we can use Newton's second law, which states that the force is equal to the mass times the acceleration.
Given:
Mass of the ball (m) = 0.40 kg
Final velocity (v) = 9.0 m/s
Time (t) = 0.075 s
First, we need to find the acceleration of the ball. We can use the equation:
v = u + at, where u is the initial velocity (which is 0 since the ball is at rest).
Rearranging the equation to solve for acceleration (a):
a = (v - u) / t
Substituting the given values:
a = (9.0 m/s - 0) / 0.075 s
a = 120 m/s²
Next, we can calculate the average force using the equation:
F = m * a
Substituting the given mass (m) and acceleration (a):
F = 0.40 kg * 120 m/s²
F = 48 N
Therefore, the average force that Rita applies to the ball during the kick is 48 N.
Thus, the correct answer is A) 48 N.
To find the average force that Rita applies to the ball during the kick, we can use Newton's second law of motion, which states that force (F) is equal to the change in momentum (p) divided by the change in time (Δt):
F = Δp/Δt
The change in momentum is given by the product of the mass (m) and the change in velocity (Δv):
Δp = m * Δv
In this case, the mass (m) of the ball is 0.40 kg, and the change in velocity (Δv) is the final velocity (9.0 m/s) minus the initial velocity (0 m/s):
Δv = 9.0 m/s - 0 m/s = 9.0 m/s
Now we can substitute these values into the equation:
Δp = 0.40 kg * 9.0 m/s = 3.6 kg·m/s
Next, we need to find the change in time (Δt). The problem states that Rita accelerates the ball from rest to 9.0 m/s during the 0.075 s in which her foot is in contact with the ball. Therefore, Δt is equal to 0.075 s.
Now we can calculate the average force:
F = Δp/Δt = 3.6 kg·m/s / 0.075 s ≈ 48 N
Therefore, the average force that Rita applies to the ball during the kick is approximately 48 N.
The answer is A) 48 N.
a)because F=mxa you have m , and you need acceleration that is a , and a is
a=v/t