A golf ball with a mass of 48.0 g can be blasted from rest to a speed of 69.4 m/s during impact with a club head. Assume that the impact lasts only about 1.010 ms. Calculate the change in momentum of the ball. Calculate the average force applied.
momentum at start = 0
momentum at end = .048*69.4
F = change in momentum/change in time
(That is the original form Newton gave for the second law. If m is constant that is F=mA)
= .048*69.4 / .00101 Newtons
To calculate the change in momentum of the golf ball, we need to know the initial and final momentum.
1. The initial momentum (p_initial) of the golf ball can be calculated using the equation:
p_initial = m * v_initial
where m is the mass of the golf ball (48.0 g) and v_initial is the initial velocity (0 m/s, since it is at rest).
So, p_initial = 0 g.m/s = 0 kg.m/s
2. The final momentum (p_final) of the golf ball can be calculated using the equation:
p_final = m * v_final
where v_final is the final velocity of the golf ball after being blasted (69.4 m/s).
Therefore, p_final = (48.0 g) * (69.4 m/s) = 3312 g.m/s
3. The change in momentum (Δp) of the golf ball is given by the equation:
Δp = p_final - p_initial
Hence, Δp = 3312 g.m/s - 0 kg.m/s = 3312 g.m/s
To convert the change in momentum to kg.m/s:
1 kg = 1000 g
1 kg.m/s = 1000 g.m/s
So, 3312 g.m/s = 3.312 kg.m/s.
Therefore, the change in momentum of the golf ball is 3.312 kg.m/s.
To calculate the average force applied:
The average force (F_avg) can be calculated using the equation:
F_avg = Δp / Δt
where Δt is the duration of the impact in seconds.
1. First, we need to convert the time duration from milliseconds to seconds:
Δt = 1.010 ms = 1.010 × 10^(-3) s
2. Now, we can calculate the average force:
F_avg = (3.312 kg.m/s) / (1.010 × 10^(-3) s)
F_avg ≈ 3.275 N (rounded to three decimal places)
Therefore, the average force applied by the club head to the golf ball is approximately 3.275 N.