A golf club strikes a 0.040-kg golf ball in order to launch it from the tee. For simplicity, assume that the average net force applied to the ball acts parallel to the ball's motion, has a magnitude of 7050 N, and is in contact with the ball for a distance of 0.014 m. With what speed does the ball leave the club?
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To find the speed with which the golf ball leaves the club, we can use the work-energy principle. According to this principle, the work done on an object is equal to the change in its kinetic energy.
The work done (W) on the golf ball can be calculated using the formula:
W = (force) * (distance)
In this case, the force acting on the ball is 7050 N, and the distance over which the force is applied is 0.014 m. Plugging these values into the equation, we can find the work:
W = 7050 N * 0.014 m
W = 98.7 N·m
Since the work done on the ball is equal to the change in its kinetic energy, we can write:
98.7 N·m = (1/2) * (mass) * (velocity)^2
The mass of the ball is given as 0.040 kg. Rearranging the equation and solving for the velocity, we get:
(1/2) * 0.040 kg * (velocity)^2 = 98.7 N·m
Now, we can solve for the velocity:
(velocity)^2 = (98.7 N·m) / (0.020 kg)
(velocity)^2 = 4935 N·m/kg
velocity = √(4935 N·m/kg)
Using a calculator, we find that the velocity is approximately 22.20 m/s.
Therefore, the golf ball leaves the club with a speed of approximately 22.20 m/s.
To find the speed at which the golf ball leaves the club, we can use the equation for work done on an object:
Work = Force * Distance * cos(θ)
where:
- Work is the energy transferred to the ball
- Force is the magnitude of the net force applied to the ball
- Distance is the distance over which the force is applied
- θ is the angle between the force vector and the direction of motion (in this case, θ = 0, since the force and motion are parallel)
In this problem, we are given the force (7050 N) and the distance (0.014 m). Therefore, we can plug in these values to calculate the work done on the ball.
Work = 7050 N * 0.014 m * cos(0°)
Work = 98.7 Joules
Now, since the work done on the ball is equal to the change in its kinetic energy, we can equate the work done to the kinetic energy using the equation:
Work = Kinetic Energy
Kinetic Energy = (1/2) * mass * velocity^2
In this case, we need to find the velocity (speed) at which the ball leaves the club. Rearranging the equation, we get:
velocity = sqrt(2 * (Work / mass))
Plugging in the values of the work done (98.7 J) and the mass of the ball (0.040 kg), we can calculate the velocity.
velocity = sqrt(2 * (98.7 J / 0.040 kg))
velocity = sqrt(4935 m^2/s^2)
velocity ≈ 70.23 m/s
Therefore, the ball leaves the club with a speed of approximately 70.23 m/s.