A soccer player applies an average force of 180 N during a kick. The kick accelerates a 0.45 kg soccer ball from rest to a speed of 18 m/s. What is the impulse imparted to
the ball? What is the collision time?
Impulse = Force x Time
Impulse = 180 N x Time
Time = (18 m/s) / (180 N)
Time = 0.1 s
Impulse = 180 N x 0.1 s
Impulse = 18 Ns
To find the impulse imparted to the ball, we can use the formula:
Impulse = Force × Time
We are given that the force applied is 180 N. Let's assume the time for which the force is applied is 't'.
So the equation becomes:
Impulse = 180 N × t
The impulse imparted to the ball is given by its change in momentum. We can find the change in momentum using the formula:
Change in momentum = mass × final velocity - mass × initial velocity
We are given the mass of the soccer ball as 0.45 kg, the initial velocity as 0 m/s (since it starts from rest), and the final velocity as 18 m/s.
Change in momentum = 0.45 kg × 18 m/s - 0.45 kg × 0 m/s
= 8.1 kg m/s
We know that impulse is equal to the change in momentum, so:
Impulse = 8.1 kg m/s
To find the collision time, we can rearrange the impulse formula as:
Impulse = Force × Time
Time = Impulse / Force
Substituting the given values, we get:
Time = 8.1 kg m/s / 180 N
Time ≈ 0.045 s
Therefore, the impulse imparted to the ball is 8.1 kg m/s and the collision time is approximately 0.045 seconds.
To calculate the impulse imparted to the ball, you can use the formula:
Impulse = Force x Time
First, we need to find the time it takes for the ball to reach its final speed. To do this, we can use the formula:
v = u + at
Where:
v = final velocity (18 m/s)
u = initial velocity (0 m/s)
a = acceleration (unknown)
t = time (unknown)
Since the ball is starting from rest, its initial velocity is 0 m/s. Therefore, the equation simplifies to:
18 m/s = 0 m/s + a * t
Next, we need to find the acceleration. We can use Newton's second law of motion:
Force = mass x acceleration
180 N = 0.45 kg * a
Solving for a, we find:
a = 180 N / 0.45 kg
a = 400 m/s^2
Now we can substitute the acceleration value back into the first equation:
18 m/s = 0 m/s + 400 m/s^2 * t
Simplifying, we have:
18 m/s = 400 m/s^2 * t
To solve for t, we divide both sides of the equation by 400 m/s^2:
t = 18 m/s / 400 m/s^2
t = 0.045 seconds
Now that we have the time, we can calculate the impulse. Substituting the values into the impulse formula:
Impulse = Force x Time
Impulse = 180 N * 0.045 seconds
Impulse = 8.1 N.s (or kg.m/s)
Therefore, the impulse imparted to the ball is 8.1 N.s (or kg.m/s), and the collision time is 0.045 seconds.