A golf ball has a mass of 0.05 kg and acquires a speed of 80.0 m/s when hit with a force of 3000 N. how long was the club in contact with the golf ball?
(Force)*(Contact time) = (Change in momentum) = 0.05*80 = 4.0 kg*m/s
Contact time
= (4.0 kg*m/s)/(3000 kg*m/s^2)
= 1.33*10^-3 s
To find the duration of contact between the club and the golf ball, you can use the impulse-momentum principle.
Step 1: Determine the initial velocity of the golf ball.
The initial velocity of the golf ball can be assumed to be zero since it starts from rest.
Step 2: Calculate the change in momentum.
The change in momentum (Δp) is given by the product of the force (F) and the time duration (Δt) of contact. Mathematically, Δp = F * Δt.
Step 3: Calculate the change in momentum using the mass (m) and final velocity (v) of the golf ball.
The change in momentum can also be expressed as Δp = m * (v - 0), where 0 represents the initial velocity.
Step 4: Equate the two expressions for change in momentum and solve for Δt.
F * Δt = m * (v - 0)
Δt = m * (v - 0) / F
Step 5: Substitute the given values and calculate the solution.
Δt = 0.05 kg * (80.0 m/s - 0) / 3000 N
By evaluating the above expression, the duration of contact between the club and the golf ball will be obtained.
To find the time the club was in contact with the golf ball, we need to use the concept of impulse.
Impulse is defined as the product of force and time: Impulse = Force × Time.
In this case, the force applied to the golf ball is 3000 N, and we need to find the time. Since impulse is equal to the change in momentum of an object, we can use the equation:
Impulse = Change in momentum
The initial momentum of the golf ball is 0 since it was initially at rest, and the final momentum can be calculated using the equation:
Final momentum = Mass × Final velocity
Given that the mass of the golf ball is 0.05 kg and the final velocity is 80.0 m/s, we can calculate the final momentum:
Final momentum = 0.05 kg × 80.0 m/s = 4 kg·m/s
Now, we can equate the impulse to the change in momentum:
Impulse = Change in momentum
3000 N × Time = 4 kg·m/s
To find the time, we rearrange the equation:
Time = Change in momentum / Force
Time = 4 kg·m/s / 3000 N
Dividing the product of mass and velocity by force, we can find the time:
Time = 0.00133333333 s (rounded to six decimal places)
Time ≈ 0.0013 s
Therefore, the club was in contact with the golf ball for approximately 0.0013 seconds.