The physics of a golf ball and kinetic energy.

When a 0.045 kg golf ball takes off after being hit, its speed is 41 m/s.
a) What is the kinetic energy of the ball after it has been hit?
b) How much work is done on the ball by the club?
c) Assume that the force of the club acts parallel to the motion of the ball and that the club is in contact with the ball for a distance of 0.010 m. Ignore the weight of the ball and determine the average force applied to the ball by the club?
d) In moving through the air, the golf ball slows down to a speed of 31 m/s. What work has the air done on the ball?
e) If the ball travelled through the air a distance of 84 m, what must be the average force of resistance caused by the air?

a) The kinetic energy of the golf ball can be calculated using the formula:

Kinetic Energy = (1/2) * mass * velocity^2

Substituting the values, we get:

Kinetic Energy = (1/2) * 0.045 kg * (41 m/s)^2

b) The work done on the ball by the club can be calculated using the formula:

Work = force * distance

Since the force applied by the club is parallel to the motion, the work done can be calculated as:

Work = force * distance = average force * distance

c) To determine the average force applied to the ball by the club, we can use the equation:

Average Force = Work / Distance

Substituting the values, we get:

Average Force = (Work done on the ball / distance of contact) = (Work / 0.010 m)

d) The work done by air resistance can be calculated using the equation:

Work = force * distance

However, since the ball is slowing down, the work done by air resistance is negative.

e) To calculate the average force of resistance caused by the air, we can use the equation:

Average Force = Work / Distance

Substituting the values, we get:

Average Force = (Work done by air resistance / distance traveled through the air)

a) To find the kinetic energy of the golf ball, we can use the formula for kinetic energy:

Kinetic energy (KE) = 0.5 * mass * velocity^2

Given:
Mass of the golf ball (m) = 0.045 kg
Speed of the golf ball (v) = 41 m/s

Plugging these values into the formula, we have:

KE = 0.5 * 0.045 kg * (41 m/s)^2

Simplifying:

KE = 0.5 * 0.045 kg * 1681 m^2/s^2

KE = 37.8225 J

Therefore, the kinetic energy of the ball after it has been hit is 37.8225 Joules.

b) Work is defined as the product of force applied on an object and the distance over which that force is applied. In this case, the work done on the ball by the club is given as:

Work (W) = force * distance

To find the work done on the ball by the club, we need to know the force applied by the club. Unfortunately, this information is not provided.

c) The average force applied to the ball by the club can be calculated using the work done and the distance over which the force is applied. We can rearrange the work formula to find the force:

Force (F) = Work / Distance

Given:
Work done on the ball (W) = [unknown]
Distance over which the club is in contact with the ball (d) = 0.010 m

Since the work done is unknown, we are unable to calculate the average force applied by the club.

d) To find the work done by the air on the ball, we again use the work formula:

Work (W) = force * distance

Given:
Initial speed of the ball (v_initial) = 41 m/s
Final speed of the ball (v_final) = 31 m/s
Mass of the golf ball (m) = 0.045 kg

Using the work-energy principle, we know that the work done by an external force is equal to the change in kinetic energy of the object. Therefore:

Work (W) = KE_initial - KE_final

Since we know the initial and final speeds of the ball, we can calculate the initial and final kinetic energies using the formula from part a.

Initial KE = 37.8225 J
Final KE = 0.5 * 0.045 kg * (31 m/s)^2

Now we can calculate the work done by the air:

W = Initial KE - Final KE

e) To find the average force of resistance caused by the air, we can again use the work formula:

Work (W) = force * distance

Given:
Work done by the air (W) = [unknown]
Distance traveled by the ball (d) = 84 m

Since the work done by the air is unknown, we are unable to calculate the average force of resistance caused by the air.

To answer these questions, we will use the formulas from physics related to kinetic energy and work.

a) The kinetic energy of an object is given by the formula:

Kinetic Energy = (1/2) * mass * velocity^2

Plugging in the values, we get:

Kinetic Energy = (1/2) * 0.045 kg * (41 m/s)^2

Solving this equation will give us the answer.

b) Work done can be calculated using the formula:

Work = Force * Distance

We need to determine the force applied by the club on the golf ball. Since the force is assumed to be acting parallel to the motion of the ball and the distance is given as 0.010 m, we can substitute these values into the formula to calculate work.

c) Average force applied by the club can be found by rearranging the formula for work:

Average Force = Work / Distance

Plugging in the values of work and distance calculated in the previous question will give us the answer.

d) The work done on the ball by the air can be calculated using the formula:

Work = Change in kinetic energy = Initial Kinetic Energy - Final Kinetic Energy

We already know the initial kinetic energy from part a (as it remains the same), so we need to calculate the final kinetic energy using the new speed of 31 m/s. Substituting these values into the formula will give us the answer.

e) The average force of resistance caused by the air can be determined using the formula:

Average Force = Work / Distance

Here, the work done by the air would be the negative value of the work calculated in part d since it acts in the opposite direction of motion. Again, substituting the values of work and distance calculated in the previous question will give us the answer.

By following these steps, you should be able to find the answers to all the questions related to the physics of a golf ball.

a

Ke = (1/2) m v^2 = (.045/2)(41)(41)

b
Work in = increse in energy = Ke = answer to a

c
F * d = work = same Ke

d
new Ke = (.045/2)(31)(31)
so answer = this - answer to a
which is negative, force opposite to motion

e
again work done = change of energy = F (84)