A golf ball of mass 0.045 kg is hit off the tee at a speed of 48 m/s. The golf club was in contact with the ball for 5.4 10-3 s.
(a) Find the magnitude of the impulse imparted to the golf ball.
(b) Find the magnitude of the average force exerted on the ball by the golf club.
a)
J=m*(change)v
J=0.045kg*48m/s
J=2.16kg*m/s
b)
J=F*t
F=J/t
F=2.16kg*m/s/5.4*10-3s
F=400N
Impulse= mass*changeinvelocity
Force*time= Impulse solve for avg force.
Well, this is a swinging question! Let's get swinging with the answers:
(a) To find the magnitude of the impulse imparted to the golf ball, we can use the formula: Impulse = Change in momentum. The change in momentum is given by the mass of the ball multiplied by its final velocity minus its initial velocity. So the impulse is:
Impulse = (0.045 kg) * (48 m/s - 0 m/s) = 2.16 kg·m/s
(b) The magnitude of the average force exerted on the ball by the golf club can be calculated using the formula: Force = Impulse / Time. We already know the impulse from part (a), and the contact time is given as 5.4 * 10^-3 s. So the average force is:
Force = (2.16 kg·m/s) / (5.4 * 10^-3 s) = 400 N
That's one impressive force! Let's hope the golf ball doesn't get too teed off about it.
To find the magnitude of the impulse imparted to the golf ball, you can use the formula for impulse:
Impulse = Force × Time
Since you have the mass of the golf ball and the time of contact, you first need to find the force applied to the ball. This can be done by using Newton's second law:
Force = mass × acceleration
The acceleration in this case can be calculated using the formula:
acceleration = change in velocity / time
Given that the initial velocity of the ball is 0 m/s (since it is at rest on the tee) and the final velocity is 48 m/s, you can calculate the change in velocity.
Once you have the force and the time, you can find the impulse.
After finding the impulse, you can solve part (b) by using the average force formula:
Average force = Impulse / time
Now, let's solve it step by step:
(a) Find the magnitude of the impulse imparted to the golf ball:
1. Calculate the change in velocity:
change in velocity = final velocity - initial velocity
change in velocity = 48 m/s - 0 m/s
change in velocity = 48 m/s
2. Calculate the force applied to the ball:
Force = mass × acceleration
Here, the mass of the ball is given as 0.045 kg.
So, acceleration = change in velocity / time
acceleration = 48 m/s / (5.4 × 10^-3) s
acceleration = 8888.89 m/s^2 (rounded to 5 significant figures)
Force = 0.045 kg × 8888.89 m/s^2
Force ≈ 400 kg*m/s^2
3. Calculate the impulse:
Impulse = Force × Time
Impulse = 400 kg*m/s^2 × 5.4 × 10^-3 s
Impulse ≈ 2.16 kg*m/s
So, the magnitude of the impulse imparted to the golf ball is approximately 2.16 kg*m/s.
(b) Find the magnitude of the average force exerted on the ball by the golf club:
Average force = Impulse / Time
Average force = 2.16 kg*m/s / 5.4 × 10^-3 s
Average force ≈ 400 kg*m/s^2
So, the magnitude of the average force exerted on the ball by the golf club is approximately 400 kg*m/s^2.