The head of a golf club exerts a force of 350N on a golf ball for 0.3m. The golf ball has a mass of 85g. What speed should the golf ball have when it leaves the club head?
Work done on ball = F*X
= kinetic energy given to golf ball
= (1/2) M V^2
V = sqrt(2FX/M)
X = 0.3 m
F = 350 N
M = 0.085 kg
Solve for V
To determine the speed of the golf ball when it leaves the club head, we can use the principle of conservation of energy. The initial kinetic energy of the ball will be equal to the work done on it by the club head.
First, let's convert the mass of the golf ball from grams to kilograms:
85g = 0.085kg
The work done on the golf ball is given by the formula:
Work = Force × Distance
In this case:
Force = 350N
Distance = 0.3m
So, the work done on the ball is:
Work = 350N × 0.3m
Next, we can calculate the work done:
Work = 105 joules
According to the principle of conservation of energy, the work done on the golf ball will be converted into its kinetic energy:
Work = Kinetic Energy
So, the kinetic energy of the ball is:
Kinetic Energy = 105 joules
Finally, we can use the kinetic energy formula to find the speed of the golf ball:
Kinetic Energy = (1/2) × mass × velocity^2
Since we want to find the velocity, we rearrange the formula:
velocity^2 = (2 × Kinetic Energy) / mass
Substituting the values, we get:
velocity^2 = (2 × 105 joules) / 0.085kg
Simplifying further, we have:
velocity^2 = 2470.59 m^2/s^2
To find the velocity, we take the square root of both sides:
velocity = √2470.59 m^2/s^2
Therefore, the speed at which the golf ball should leave the club head is approximately 49.7 m/s.