If a student measures the length of the pendulum to be 0.510m in a simple pendulum experiment and determines that the period of the pendulum is 1.44s. Determine the experimental value of the acceleration due to gravity

Question

Illustrate an image of a school laboratory setup with a simple pendulum experiment in progress. The pendulum should be made out of a thin, tightly held wire with a small, heavy sphere at its end, swinging back and forth. The length of the pendulum should approximately be represented as 0.510m. Also, depict a timer nearby registering the period of the pendulum swing as 1.44 seconds. Make sure to emphasize the gravity effect on the swinging motion of the pendulum. Do not include any text in the image.

If a student measures the length of the pendulum to be 0.510m in a simple pendulum experiment and determines that the period of the pendulum is 1.44s. Determine the experimental value of the acceleration due to gravity

Answer 1

We can use the equation for the period of a simple pendulum:

T = 2π√(L/g)

where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity.

Rearranging this equation to solve for g, we get:

g = (4π^2L) / T^2

Substituting the given values, we get:

g = (4π^2 x 0.510m) / (1.44s)^2

Simplifying this expression, we get:

g ≈ 9.69 m/s^2

Therefore, the experimental value of the acceleration due to gravity is approximately 9.69 m/s^2, based on the measurements of the length and period of the pendulum.

Answer 2

To determine the experimental value of the acceleration due to gravity using the length and period of a simple pendulum, you can use the following formula:

acceleration due to gravity (g) = (4 * π^2 * length) / (period^2)

Let's substitute the given values into the formula:

length = 0.510 m
period = 1.44 s

g = (4 * π^2 * 0.510) / (1.44^2)

To calculate this, first calculate π^2, then multiply it by 4, then multiply the result by the length. Finally, divide the result by the square of the period.

π^2 ≈ 9.87

g ≈ (4 * 9.87 * 0.510) / (1.44^2)

Now, simplify and solve the equation:

g ≈ (39.48 * 0.510) / (2.0736)

g ≈ 20.1708 / 2.0736

g ≈ 9.726

Therefore, the experimental value of the acceleration due to gravity is approximately 9.726 m/s^2.

Answer 3

To determine the experimental value of the acceleration due to gravity, we can use the following formula:

g = (4π²L) / T²

Where:
g is the acceleration due to gravity
π is a mathematical constant, approximately equal to 3.14159
L is the length of the pendulum
T is the period of the pendulum

In this case, the length of the pendulum (L) is given as 0.510m and the period of the pendulum (T) is given as 1.44s.

Let's substitute these values into the formula:

g = (4π² * 0.510) / (1.44)²

Now, let's calculate the value of g:

g = (4 * 3.14159 * 0.510) / (1.44)²
g = (4 * 3.14159 * 0.510) / 2.0736
g = (6.28318 * 0.510) / 2.0736
g = 3.2031758 / 2.0736
g ≈ 1.5443 m/s²

Therefore, the experimental value of the acceleration due to gravity in this simple pendulum experiment is approximately 1.5443 m/s².