A golf ball is struck by a golf club at 55 m/s at an angle of 28.0o above the horizontal. The mass of the ball is 45 grams and is in contact with the golf club for 1.5 m/s. Calculate the average force exerted on the ball by the club.
a=(V-Vo)/t
a = (55-0)/1.5*10^-3=36670 m/s^2
F = m*a = 0.045 * 36,670 = 1650 N.
No. I believe the answer should be 1460 N Henry. The initial velocity of the club is striking the ball at a 28 degree angle and not straight on so the x component of velocity from the club would be 48.5621 m/s, which is from cos(28)*55m/s.
The force of the golf club acts in parallel with the motion of the ball
which is 28o. So my answer is 1650 N. @
28o. Since they did not ask for the
direction of the force, I did not include the angle. Your answer is not
the full force acting on the ball; it is
the hor. component of the force.
If the motion of the ball was hor., I
would use your procedure.
To calculate the average force exerted on the golf ball by the club, we can follow these steps:
Step 1: Convert the mass of the ball to kilograms.
Given that the mass of the ball is 45 grams, we need to convert it to kilograms by dividing it by 1000:
mass = 45 grams = 45 / 1000 = 0.045 kilograms
Step 2: Calculate the vertical velocity component of the ball after impact.
The vertical velocity component can be calculated using the initial velocity and the angle of impact. The vertical velocity (Vy) can be found using the equation:
Vy = V * sin(θ)
Where:
V = initial velocity = 55 m/s
θ = angle of impact = 28.0 degrees
Vy = 55 m/s * sin(28.0 degrees) = 24.8 m/s
Step 3: Calculate the time of contact between the ball and the club.
The time of contact (t) is given as 1.5 milliseconds, which needs to be converted to seconds:
t = 1.5 ms = 1.5 / 1000 = 0.0015 seconds
Step 4: Calculate the change in momentum of the ball.
The change in momentum can be calculated using the formula:
Δp = m * Δv
Where:
Δp = change in momentum
m = mass of the ball = 0.045 kg
Δv = change in velocity
Since we are given the initial velocity (55 m/s) and the vertical velocity component (24.8 m/s), we can calculate the change in velocity as:
Δv = Vy = 24.8 m/s
Δp = 0.045 kg * 24.8 m/s = 1.116 kg·m/s
Step 5: Calculate the average force exerted on the ball.
The average force (F) can be calculated using the formula:
F = Δp / t
F = 1.116 kg·m/s / 0.0015 s = 744 N
Therefore, the average force exerted on the ball by the club is 744 Newtons.