1. A stroboscopic photo of a club hitting a golf ball, such as the photo shown in Figure 6.3, was made by Harold Edgerton in 1933. The ball was initially at rest, and the club was shown to be in contact with the club for about 0.0022 s. Also, the ball was found to end up with a speed of 1.9 102 ft/s. Assuming that the golf ball had a mass of 55 g, find the average force exerted by the club on the ball.
a = V / t = 1.9102 Ft/s / 0.0022 s,
= 865.3 Ft/s^2.
a = 865.3 ft/s^2/3.3 Ft/m = 262.2m/s^2.
F = ma = 0.055 kg * 262.2 m/s^2 N.
CORRECTION:
F = ma = 0.055 kg * 262.2 m/s^2=14.4 N.
To find the average force exerted by the club on the ball, we can use Newton's second law of motion, which states that the force exerted on an object is equal to the rate of change of its momentum.
The momentum of an object can be calculated as the product of its mass and velocity.
Given:
Mass of the golf ball (m) = 55 g = 0.055 kg
Final velocity of the golf ball (v) = 1.9 × 10^2 ft/s
First, let's convert the final velocity from ft/s to m/s:
1 ft/s = 0.3048 m/s
Therefore, the final velocity (v) = 1.9 × 10^2 ft/s × 0.3048 m/s = 57.912 m/s
Next, we need to find the initial velocity (u) of the golf ball. Since the ball was initially at rest, we can assume its initial velocity is zero.
Now, we can calculate the change in velocity (∆v) of the golf ball:
∆v = v - u
= 57.912 m/s - 0 m/s
= 57.912 m/s
The average force (F) can be calculated using the formula:
F = (∆p) / ∆t
= (m∆v) / ∆t
The time (∆t) for which the club is in contact with the ball is given as 0.0022 s.
Substituting the values, we get:
F = (0.055 kg × 57.912 m/s) / 0.0022 s
Now, let's calculate the average force exerted by the club on the ball:
F = (3.1956 kg⋅m/s) / 0.0022 s
= 1452.5455 N
Therefore, the average force exerted by the club on the ball is approximately 1452.5455 Newtons.
To find the average force exerted by the club on the ball, we need to use Newton's second law of motion, which states that the force exerted on an object is equal to the rate of change of its momentum.
Step 1: Calculate the initial momentum of the ball.
The ball is initially at rest, so its initial momentum is zero.
Step 2: Calculate the final momentum of the ball.
We know the final speed of the ball, so we can calculate its final momentum using the formula:
Final momentum = mass × final velocity
First, convert the mass of the ball from grams to kilograms:
55 g = 0.055 kg
Then, calculate the final momentum:
Final momentum = 0.055 kg × 1.9 × 10^2 ft/s
Step 3: Calculate the change in momentum.
The change in momentum is the difference between the final and initial momentum:
Change in momentum = Final momentum - Initial momentum
Since the initial momentum is zero, the change in momentum is equal to the final momentum.
Step 4: Calculate the average force exerted by the club.
The average force exerted by the club is given by Newton's second law:
Average force = Change in momentum / Time
We know the change in momentum from step 3, and we are given the time of contact between the club and the ball, which is 0.0022 s.
Plug in the values to calculate the average force:
Average force = Final momentum / Time
Finally, substitute the values and calculate the average force exerted by the club on the ball.