When a 0.045 kg golf ball takes off after being hit, its speed is 35 m/s.
A)How much work is done on the ball by the club?
B)Assume that the force of the golf club acts parallel to the motion of the ball and that the club is in contact with the ball for a distance of 0.007 m. Ignore the weight of the ball and determine the average force applied to the ball by the club.
To find the work done on the golf ball by the club, we can use the equation:
Work = Force x Distance
A) Work = Force x Distance
Given:
Mass of the golf ball (m) = 0.045 kg
Speed of the golf ball (v) = 35 m/s
We know that work is done to change the kinetic energy of the ball. The initial kinetic energy (Ki) is zero, as the ball is initially at rest.
So the final kinetic energy (Kf) is given by:
Kf = (1/2) * m * (v^2)
Kf = (1/2) * 0.045 kg * (35 m/s)^2
= 0.0490625 kg m^2/s^2
The work done on the ball is equal to the change in kinetic energy:
Work = Kf - Ki
= 0.0490625 kg m^2/s^2 - 0
= 0.0490625 kg m^2/s^2
Therefore, the work done on the ball by the club is 0.0490625 kg m^2/s^2.
B) To find the average force applied to the ball by the club, we can use the equation:
Force = Work / Distance
Given:
Distance (d) = 0.007 m
Using the value of work we calculated in part A:
Force = 0.0490625 kg m^2/s^2 / 0.007 m
= 7.00892857 N
Therefore, the average force applied to the golf ball by the club is approximately 7.009 N.
To find the answers to the given questions, we need to use the concepts of work and force.
A) To find the work done on the ball by the club, we can use the formula:
Work = Force * Distance * cos(θ)
However, since we are assuming that the force of the golf club acts parallel to the motion of the ball, the angle (θ) between the force and displacement is 0 degrees, meaning cos(0) = 1. Therefore, the formula simplifies to:
Work = Force * Distance
Substituting the given values, we have:
Distance = 0.007 m
The mass of the golf ball is given as 0.045 kg and its speed is 35 m/s. From the kinetic energy formula, we know that:
Kinetic Energy = (1/2) * Mass * Velocity^2
Simplifying this equation to solve for velocity, we have:
Velocity = √(2 * Kinetic Energy / Mass)
Substituting the given values, we can find the kinetic energy:
Velocity = √(2 * 0.045 kg * (35 m/s)^2)
Now that we have the velocity, we can calculate the kinetic energy:
Kinetic Energy = (1/2) * 0.045 kg * (35 m/s)^2
Now, use the formula Work = Force * Distance to find the work done on the ball:
Work = Force * Distance
B) To determine the average force applied to the ball by the club, we can use the formula:
Force = Work / Distance
Substituting the values we know:
Distance = 0.007 m (given)
Work is calculated using the formula from part A.
Plug the values into the formula to find the average force.