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?
To find the average force exerted by the boy on the ball, we can use Newton's second law of motion, which states that the force (F) is equal to the mass (m) multiplied by the acceleration (a). In this case, the acceleration can be calculated using kinematic equations.
First, we need to find the time it takes for the ball to reach its maximum height. When the ball reaches its highest point, its velocity will be zero. We can use the equation:
vf = vi + at
Where:
- vf is the final velocity (in this case, 0 m/s)
- vi is the initial velocity (11 m/s)
- a is the acceleration (which we need to find)
- t is the time
Rearranging the equation, we have:
t = (vf - vi) / a
Since vf = 0, the equation becomes:
t = (0 - 11) / a
Next, we can find the distance traveled by the ball during this time. Using the equation:
d = vi * t + (1/2) * a * t^2
We know the initial velocity (11 m/s), the time, and the distance (1.5 m) moved by the boy's arm while throwing the ball. We can rearrange the equation to solve for acceleration:
a = (d - vi * t) * (2 / t^2)
Substituting the known values:
a = (1.5 - 11 * t) * (2 / t^2)
Now we can substitute the value of t into the equation above. Solving for t:
t = (0 - 11) / a
Substituting this into the equation, we can find the acceleration (a).
Finally, we can calculate the average force exerted by the boy on the ball using Newton's second law. The formula is:
F = m * a
Substituting the obtained values for mass (0.15 kg) and acceleration (a), we can calculate the average force.