Chapter 5, Problem 1EP

What effect might the distance of fall have on your experimental measurements and results? (Consider the following cases.)

1. (a) How long would it take the object to reach the floor if you dropped it from a height of 0.50 m? Could you measure this accurately with a stopwatch? Explain.
2. (b) What if an object were dropped from a height of 10 m? Could you measure this distance accurately with a meterstick? Would the acceleration remain constant? Explain.

To determine

The time taken by the object to reach the floor if it is dropped from a height of $0.50\text{m}$, and whether this time is accurately measurable with a stop watch or not.

Answer to Problem 1EP

The time taken by the object to reach the floor if it is dropped from a height of $0.50\text{m}$ is $\underset{\_}{0.32\text{s}}$, and this time cannot be measured accurately by a laboratory stopwatch.

Explanation of Solution

Write the expression for the vertical distance travelled by an object under free-fall.

  $y=\frac{1}{2}g{t}^2$        (I)

Here, $y$ is the vertical distance, $g$ is the acceleration due to gravity, and $t$ is the time.

Solve equation (I) for $t$.

  $t=\sqrt{\frac{2y}{g}}$        (II)

Conclusion:

Substitute $0.50\text{m}$ for $y$, and $9.8{\text{m/s}}^2$ for $g$ in equation (II) to find $t$.

  $\begin{array}{c}t=\sqrt{\frac{2\left(0.50\text{m}\right)}{9.8{\text{m/s}}^2}}\\ =0.32\text{s}\end{array}$

Since this time is very less than a second, it is impractical to measure this time accurately with a laboratory stopwatch.

Therefore, the time taken by the object to reach the floor if it is dropped from a height of $0.50\text{m}$ is $\underset{\_}{0.32\text{s}}$, and this time cannot be measured accurately by a laboratory stopwatch.

To determine

The time taken by the object to reach the floor if it is dropped from a height of $10\text{m}$, and whether it is possible to measure this distance accurately with a meter stick, and whether the acceleration of the object remain constant or not.

Answer to Problem 1EP

The time taken by the object to reach the floor is $1.43\text{s}$. It is possible to measure the distance of $10\text{m}$ accurately using a meter stick. The acceleration of the freely falling body remain constant.

Explanation of Solution

Equation (II) gives the time taken by the freely falling object to reach the ground.

  $t=\sqrt{\frac{2y}{g}}$

Conclusion:

Substitute $10\text{m}$ for $y$, and $9.8{\text{m/s}}^2$ for $g$ in equation (II) to find $t$.

  $\begin{array}{c}t=\sqrt{\frac{2\left(10\text{m}\right)}{9.8{\text{m/s}}^2}}\\ =1.43\text{s}\end{array}$

The height of $10\text{m}$ can be measured accurately with a meter stick. Since the object is under free fall, neglecting the air resistance, the acceleration of the object remain constant, and it would be equal to the acceleration due to gravity.

Therefore, the time taken by the object to reach the floor is $1.43\text{s}$. It is possible to measure the distance of $10\text{m}$ accurately using a meter stick. The acceleration of the freely falling body remain constant.