A boy throws a ball straight up into the air so that it leaves his hand at 11 m/s. If the ball has mass 0.15 kg and the boy's arm moved through 1.5 m as he threw the ball, then what average force did he exert on the ball?
I'm completely confused. I looked over my notes and don't know how to apply it to the problem
To find the average force exerted on the ball, we can use the impulse-momentum principle. According to this principle, the change in momentum of an object is equal to the impulse applied to it. In equation form, this can be written as:
Impulse = Change in momentum
The impulse can also be expressed as the product of the average force applied to an object and the time interval over which the force is applied:
Impulse = Average force × Time interval
For the given problem, we need to find the average force. Here's how you can approach it step by step:
1. Determine the initial momentum of the ball:
The initial momentum (p) of the ball can be calculated using the formula:
p = mass × initial velocity
In this case, the mass of the ball is 0.15 kg and the initial velocity is 11 m/s. So, the initial momentum is:
p = (0.15 kg) × (11 m/s)
2. Determine the final momentum of the ball:
When the ball reaches its maximum height, it comes to a temporary stop before falling back down. At this moment, the final velocity (v) of the ball is 0 because it momentarily stops. Therefore, the final momentum (p') is:
p' = mass × final velocity
p' = (0.15 kg) × (0 m/s)
3. Calculate the change in momentum:
Change in momentum (Δp) is the difference between the initial momentum and the final momentum:
Δp = p' - p
4. Find the average force applied:
The average force exerted on the ball is equal to the impulse applied, which is equal to the change in momentum:
Average force = Δp / time interval
Now that you have the general steps, you can substitute the given values and calculate the average force exerted on the ball by the boy's arm.
To solve this problem, we can use the work-energy principle. The work done on an object is equal to the change in its kinetic energy.
The work done by the boy on the ball is equal to the force exerted multiplied by the displacement, given by:
Work = Force * Displacement
However, we need to calculate the average force exerted. Therefore, we need to determine the work done by the boy and then divide it by the displacement.
Now let's break down the steps to find the average force exerted:
Step 1: Calculate the gravitational potential energy of the ball at its maximum height.
- The potential energy (PE) is given by the equation PE = m * g * h, where m is the mass of the object, g is the acceleration due to gravity, and h is the height.
- Since the ball is thrown straight up, the height reached by the ball is double the displacement, h = 2 * 1.5 m.
- The acceleration due to gravity is approximately 9.8 m/s^2.
- The mass of the ball is given as 0.15 kg.
PE = (0.15 kg) * (9.8 m/s^2) * (2 * 1.5 m)
Step 2: Calculate the initial kinetic energy of the ball.
- The initial kinetic energy (KE_initial) is given by the equation KE_initial = 0.5 * m * v^2, where m is the mass and v is the velocity.
- The mass of the ball is given as 0.15 kg.
- The initial velocity is given as 11 m/s.
KE_initial = 0.5 * (0.15 kg) * (11 m/s)^2
Step 3: Calculate the final kinetic energy of the ball.
- The final kinetic energy (KE_final) is equal to zero since the ball reaches its maximum height and comes to a stop momentarily.
KE_final = 0
Step 4: Calculate the work done by the boy on the ball.
- The work done (W) is equal to the change in kinetic energy, given by W = KE_final - KE_initial.
W = KE_final - KE_initial
Step 5: Calculate the average force exerted by the boy.
- The average force (F_avg) is equal to the work done divided by the displacement.
F_avg = W / Displacement
Substituting the values calculated in the previous steps, we can now find the average force exerted by the boy on the ball.