Question

Question 1

This question is a long free-response question. Show your work for each part of the question.


In a physics lab, a group of students are provided with a sphere of unknown mass, a roll of string, a ring stand, and measuring devices that are commonly found in a physics lab. The students must graphically determine the acceleration due to gravity near Earth’s surface by putting the sphere into simple harmonic motion.

(a) State a basic physics principle, law, or equation that the students could use to graphically determine the acceleration due to gravity near Earth’s surface by putting the sphere into simple harmonic motion.

Question 2
(b) Design an experimental procedure the students could use to graphically determine the acceleration due to gravity near Earth’s surface by putting the sphere into simple harmonic motion.

In the table below, list the quantities and associated symbols that would be measured in the experiment and the equipment that would be used to measure each quantity. You do not need to fill in every row. If you need additional rows, you may add them to the space just below the table.

Quantity to Be Measured Symbol for Quantity Equipment for Measurement





Describe the overall procedure to be used, referring to the table. Include any steps necessary to reduce experimental uncertainty. Provide enough detail so that another student could replicate the experiment. As needed, use the symbols listed in the table and include a circuit diagram of the setup.

Question 3
(c) The students must graph the data that they have collected so that they can determine the acceleration due to gravity near Earth’s surface.

i. Indicate below which quantities could be graphed on the horizontal axis or the vertical axis to determine the acceleration due to gravity near Earth’s surface by using a best fit line. You may use the remaining columns in the table above, as needed, to record any quantities (including units) that are not already in the table.

Vertical axis: Horizontal axis:

Question 4
ii. The students determine that the slope of the line is m. Derive an equation that can be used to determine the acceleration due to gravity near Earth’s surface by using the slope of the graph that is described by the quantities plotted from part (c)i. Express your answer in terms of the slope m and any other fundamental constants.

Question 5
The figure presents a diagram that consists of a string and a sphere. The top end of the string is attached to a horizontal surface, and the other end of the string is attached to the sphere. The sphere is shown at three positions. At position Y, the string is vertical. At position X, the string slants downward and to the left. At position X, the sphere is above the sphere at position Y. At position Z, the string slants downward and to the right. At position Z, the sphere is above the sphere at position Y.
In a second experiment, the students attach a sphere to a string such that it undergoes simple harmonic motion between points X, Y, and Z, as shown in the figure. Points X and Z are at the sphere’s maximum displacement from its equilibrium position, and point Y is at the sphere’s equilibrium position. As the sphere swings along its arc, a student cuts the string at point Z.

(d) Predict the motion of the sphere after the string is cut in terms of the sphere's displacement, initial speed, and acceleration.

Answer 1

1) g = 4π² / m, 3) xaxis the length of the pendulums and the y axis the period squared

Step-by-step explanation:

a) students can approximate this system to a simple pendulum, in this case the angular velocity is

w = √ g / l

angular velocity, frequency and period are related

w = 2π f = 2π / T

we substitute

T = 2π√ l / g

with this equation they can determine the value of the acceleration of gravity, for this they measure the period for various lengths of the pendulum and graph

T² = 4π² l / g

We graph T² vs l

where this is the equation of a line if the independent variable is y = T² and x = l

y = (4π² / g) l

so the slope is

m = 4π² / g

clearing

g = 4π² / m

where the slope can be found with the values ​​of the line not the experimental values.

2) to carry out the experiment, or the thread is attached to the sphere, the length of the pendulum that goes from the pivot point to the center of the sphere is measured with a tape measure and a small finished angle is turned or less than 10th is released, it is good to wait for the first oscillation to walk, the time of a determined number of oscillations is generally measured 10 or 20, the period is calculated

T = t / n

a table of T² against the length is made and it is plotted with the length in the ax ax, we look for the slope and hence the acceleration of gravity

3) on the independent x-axis, the controlled variable must be plotted, which is the length of the pendulums, and on the y-axis, the dependent variable is the period squared

4) of the equation of the line

m = 4pi2 / g

where it ends up reaching the floor

g = 4pi2 / m

5) when the spring is cut, the sphere remains under the effect of gravity acceleration, the harmonic movement disappears and the sphere is in a vertical movement