Question

In an attempt to measure the gravitational field intensity (this is the same as the acceleration due to gravity) of an object in free-fall, Latoya used a stopwatch to time how long it took a ball, dropped from rest, to hit the ground. She found it was 3.3 s and she dropped the ball from a height of 50.0 m. (9 marks)

a. Calculate the average velocity of the ball.
b. We know that when she dropped the ball it would be moving quite slowly and when the ball hit the ground it would be moving quite fast. At what point during the ball’s fall will the average speed equal the instantaneous speed? Explain your answer.
c. Calculate the final velocity of the ball as it hits the ground.
d. Using Sally’s measurements from this experiment, calculate the gravitational field intensity (acceleration due to gravity) for the object in free fall.
e. The accepted value for the gravitational field intensity (acceleration due to gravity) is 9.8 m/s2 [down]. Give one reason why the value calculated in part d is less than this.

Answer 1

The gravitational field intensity or acceleration due to gravity (g) for the object in free fall is calculated to be approximately 9.18 m/s² using the kinematic equation y = Vi•t + 1/2a•t². This value is less than the accepted 9.8 m/s², likely due to measurement errors.

Step-by-step explanation:

To calculate the gravitational field intensity, also known as the acceleration due to gravity (g), we can use the kinematic equation for one-dimensional motion under constant acceleration (g) which is:

y = Vit + ½at2

Here, y is the displacement (50.0 m), Vi is the initial velocity (0 m/s, since the ball is dropped), a is the acceleration (which will be g), and t is the time (3.3 s). Substituting the given values, we get:
50.0 m = 0 m/s(3.3 s) + ½(g)(3.3 s)2

Simplifying this equation to solve for g gives:

50.0 m = ½(g)(10.89 s2)

g = (2 × 50 m) / 10.89 s2

g = 100 m / 10.89 s2 ≈ 9.18 m/s2

The value calculated for g is slightly less than the accepted value of 9.8 m/s2. This discrepancy could be due to measurement errors, such as reaction time in starting and stopping the stopwatch, or accuracy in measuring the height from which the ball was dropped.