A 0.05 kg golf ball is placed on a tee. The golf ball is hit by a golf club and has a final speed of 40
m/s. 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 0.02 m. How much work is done on the ball by the club?
Calculate the average force applied to the ball by the club.
A two man bobsled is pushed along a horizontal, frictionless track by the brakeman. The driver and
bobsled have a mass of 280 kg. The brakeman pushes with a net force of 160 N a distance of 50
m. What is the final speed of the bobsled just before the brakeman jumps into the sled? The sled
was pushed for 6.61 s. How much power does the brakeman expend on the sled?
To calculate the work done on the ball by the club, we can use the work-energy principle, which states that the work done on an object is equal to the change in its kinetic energy.
Step 1: Calculate the initial kinetic energy of the ball.
The initial speed of the ball is not given in the question, so we need to find it. However, we know the final velocity and the distance over which the force is applied.
Using the formula: v^2 = u^2 + 2as, where v = final velocity, u = initial velocity, a = acceleration, and s = distance,
we can rearrange the formula to find the initial velocity:
u^2 = v^2 - 2as
Since the ball starts from rest, the initial velocity, u, is 0 m/s. Substituting the given values:
u^2 = 40^2 - 2 * 0.02
u^2 = 1600 - 0.04
u^2 = 1599.96
Taking the square root of both sides:
u ≈ √1599.96
u ≈ 39.99 m/s (approximately 40 m/s)
Step 2: Calculate the initial kinetic energy of the ball.
The formula for kinetic energy is: KE = (1/2) * m * v^2,
where m = mass of the ball and v = initial velocity.
Substituting the given values:
KE = (1/2) * 0.05 * 40^2
KE = 0.5 * 0.05 * 1600
KE = 40 J
So, the initial kinetic energy of the ball is 40 J.
Step 3: Calculate the final kinetic energy of the ball.
The formula for kinetic energy is the same as above:
KE = (1/2) * m * v^2
Substituting the given values:
KE = 0.5 * 0.05 * 40^2
KE = 0.5 * 0.05 * 1600
KE = 40 J
So, the final kinetic energy of the ball is also 40 J.
Step 4: Calculate the work done on the ball.
The work done on the ball is equal to the change in kinetic energy:
Work Done = Final KE - Initial KE
Work Done = 40 J - 0 J
Work Done = 40 J
So, the work done on the ball by the club is 40 J.
Step 5: Calculate the average force applied to the ball by the club.
The formula for work is: Work = Force * Distance.
Rearranging the formula to find force:
Force = Work / Distance
Substituting the given values:
Force = 40 J / 0.02 m
Force = 2000 N
So, the average force applied to the ball by the club is 2000 N.
To calculate the work done on the ball by 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 equation for work is given by:
Work = Force x Distance x Cos(θ)
Where:
- Force is the magnitude of the force applied on the object,
- Distance is the displacement of the object,
- θ is the angle between the direction of the force and the direction of displacement.
In this case, since the force of the golf club acts parallel to the motion of the ball, the angle θ is 0 degrees, and the cosine of 0 degrees is 1. Therefore, the equation simplifies to:
Work = Force x Distance
We know that the distance is 0.02 meters and the mass of the ball is 0.05 kg. We need to calculate the force applied to the ball and then use it to find the work.
To calculate the force applied to the ball, we can use Newton's second law of motion:
Force = Mass x Acceleration
The acceleration can be calculated using the final velocity and the initial velocity of the ball. We assume the initial velocity is zero, so the equation becomes:
Acceleration = Final Velocity / Time
The time can be calculated using the formula:
Time = Distance / Velocity
Substituting the values we have, we can calculate the acceleration. Then, using the equation Force = Mass x Acceleration, we can find the force applied to the ball.
Finally, using the calculated force, we can substitute it into the work equation to find the work done on the ball.
Let's solve these calculations step by step:
Step 1: Calculate the time
Time = Distance / Velocity
Time = 0.02 m / 40 m/s
Time = 0.0005 s
Step 2: Calculate the acceleration
Acceleration = Final Velocity / Time
Acceleration = 40 m/s / 0.0005 s
Acceleration = 80000 m/s^2
Step 3: Calculate the force applied to the ball
Force = Mass x Acceleration
Force = 0.05 kg x 80000 m/s^2
Force = 4000 N
Step 4: Calculate the work done on the ball
Work = Force x Distance
Work = 4000 N x 0.02 m
Work = 80 Joules
So, the work done on the ball by the club is 80 Joules and the average force applied to the ball by the club is 4000 Newtons.