A ball of moist clay falls 10.4 m to the ground. It is in contact with the ground for 20.5 ms before stopping.
(a) What is the average acceleration of the clay during the time it is in contact with the ground?
(Treat the ball as a particle.)
m/s2
(b) Is the average acceleration up or down?
To find the average acceleration of the clay, we can use the formula:
Average acceleration = Change in velocity / Time
In order to find the change in velocity, we need to determine the initial and final velocities of the clay.
Considering that the ball is falling from a height, we can use the equation of motion:
Final velocity^2 = Initial velocity^2 + 2 acceleration × distance
where Final velocity = 0 m/s (since the ball stops),
Initial velocity^2 = 2 × acceleration × distance
Simplifying this equation, we get:
2 × acceleration × distance = Initial velocity^2
We can rearrange the equation to solve for the initial velocity:
Initial velocity = sqrt(2 × acceleration × distance)
Given that the ball falls 10.4 m to the ground, we can substitute the values and calculate the initial velocity.
Initial velocity = sqrt(2 × acceleration × 10.4 m)
Now, we know that the ball is in contact with the ground for 20.5 ms (milliseconds) before stopping. We need to convert the time to seconds:
Time = 20.5 ms ÷ 1000 (to convert milliseconds to seconds)
Now, we can use the formula for average acceleration to calculate it:
Average acceleration = (0 m/s - Initial velocity) / Time
Substituting the values we have:
Average acceleration = (0 m/s - sqrt(2 × acceleration × 10.4 m)) / (20.5 ms ÷ 1000)
Simplifying and solving for average acceleration will give us the answer to part (a).
To determine whether the average acceleration is up or down, we need to consider the direction of the acceleration. In this case, since the ball is falling downwards, the acceleration will be in the downward direction. Therefore, the average acceleration is down, as indicated in part (b).