Question

# hello I would like to ask about phy 221 Newton's laws. Please just I want to know the way that we answer Q1 and 2

Please help me just give me the formula.

EXPERIMENT 4

Newton's Laws

I. OBJECTIVES

1. To explore the relationship between the acceleration of a block and the force applied to it, i.e. apply

the Newton's 2"d law.

2. To use your data to obtain an estimate for the gravitational acceleration.

II. EQUIPMENT

- Air track and glider - the glider has a two-post assembly (or a flag) that is used to measure its

horizontal speed as it passes through a photogate, similar with the procedure used in Experiment 2-

Motion with Constant Acceleration.

- Hanging mass - this consists of a hanger with removable masses.

- Tape or string - to connect the masses.

- One photogate and one timing system -to measure the speed of the glider you will be using either:

- a timing system using a 2 MHz (2 megahertz = 2 million counts per second) clock. This timing

system will read the photogate time with microsecond precision. All the time values will be

displayed in seconds through the "Event Timing" program from your desktop. Make the following

settings in the program: (i) select 2 as the number of events; (ii) check the "Photogate 1" box; (iii)

check the "Intervals" setting. Press "Go", when ready to acquire data.

or

a timing system using the Pasco Data Studio. To use this timing system, open the Data Studio

"Photoevent Timing" program from you desktop. Some instructions on how to use this program

are provided within the application. Press "Run" to start collecting the data.

If the distance d between the two posts (or the length of the flag) is known, the speed of the glider will be

given based on the time interval At measured using the timing system by:

veluct ov = At

(1)

Page 2) as:

Assuming that the glider is released from rest, its acceleration can then be calculated (see Experiment 2,

accelraction

a = =

1 2

2Ax

(2)

where Ar is the distance between the release point of the glider and the photogate.

Glider (M-m)

Photogate

FAX

Pulley

Air Track

Posts

Figure 1. Experimental set-up.

Floor

Newton's Laws

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Page 1

2" Law Problem (based on Problem 5-4, page 100-101, form the HRW textbook)

The experiment shown in Figure I can be modeled by applying Newton's 2" law to the two objects, i.e.

the glider (with mass M) and the hanging mass (with mass m). The force diagram for the two objects is

shown in the figure below.

Notes: - in the analysis below the friction between the

FNA

glider and the airtrack is neglected.

the hanging mass m includes both the mass of

the hanger/removable masses as well the mass of

M

the below the pulley portion of the string used to

connect the mass M with the hanger.

T

Glider

FOM

Onx:

1 = Ma

(3)

Omy:

FN - Mg = 0

( 4 )

Hanger/removable masses:

Fam

On yr:

mg - T = ma

(5)

Using the equations (3) and (5) the acceleration a of the system can be determined as a function of the

hanging mass m, the mass of the glider M and the gravitational acceleration g:

a =

(6)

VERY IMPORTANT - before you come to the lab you will have determine the correct equation (6)

for the acceleration a. You will have to show your work and the formula for a to your TA before

starting the lab. Failure to do so will result in lost points for the lab. Also be advised that if you

have to determine the formula for a during the lab, you might not have time to finish the lab and

will lose additional points accordingly.

I PROCEDURE & DATA ANALYSIS

NOTES!

- Before beginning your experiment, make sure that with the air blower on, the glider movement is as

frictionless as possible. If this is not the case inform your TA.

Also make sure that the air track is level by adjusting the single screw which supports the track. As

you have seen in Experiment 2, even a slight tilt of the air track will cause a substantial acceleration.

In this set-up, as the hanger with removable masses moves downwards, the length of the tape/string

between the hanger and the pulley increases. This increases the total hanging mass accordingly,

complicating the analysis of your experimental data. To avoid this, as shown in Figure 1, the vertical

piece of magnetic tape is cut sufficiently long so that it reaches the floor during the entire descent of

entire measurement.

the mass m. This ensures that the mass associated with the tape/string does not change through the

If you are going to share the set-up with another group, each group should perform the experiment

with different gliders and different distances between the two posts.

Il. Measure the distanceed between the posts of the glider by measuring the distance between their

inner and outer sides and taking the average.

d =

Page 2

2. Measure the mass of the glider and posts:

M =

3. Cut a length of magnetic tape sufficiently long that it will be able to drape on the floor, and connect

the glider and the hanger as shown in Figure 1.

4. Measure the distance L from the side of the pulley to the floor:

5. Ask your TA to provide you with the density (i.e. mass per unit length) of the tape/string used:

H =

6. Calculate the mass of the vertical portion of the tape/string used. As explained in the notes, if the

constant:

tape/string is cut so that it drapes on the floor through the entire measurement this mass is a

mtape =

7. Choose a distance Ar along the airtrack from which to release the glider. This distance is measured

by noting the initial position of the back edge of the airtrack and then this position when the two-

posts of the glider are equally spaced around the photogate. The Ar distance should be less than 100

cm.

AX =

You should use the same distance Ax for all the experiments.

8. Begin with 5 masses, 2-5 grams each, with one of those masses being the 5 gram hanger. Begin

with the 5 gram hanger on the tape (or string) and the other masses carefully centered and taped on

the glider.

9. Record the total hanging mass m as the sum of:

m = Mtape + mhanger - Mremovable masses

10. Release the glider from the distance Ax along the airtrack and record the time interval At measured

by the photogate.

11. Repeat this measurement at least two more times and calculate the mean At and then the final speed

v of the glider.

12. Calculate and record the corresponding acceleration a of the glider (Equation 2).

13. Remove one mass from the hanger and place it on the glider.

14. Repeat steps 10 through 13 four more times, each time removing one mass from the hanger and

placing it on the glider.

NOTES:

The procedure from step 13, in which any mass removed from the hanger is placed on the glider, insures

that the total mass of the system (glider, tape, hanger, removable masses) remains constant as the

hanging mass is changed. This makes the analysis of the experiment simpler.

13. Plot the dependence of the acceleration a as a function of the hanging mass m.

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Question 1: Find the best linear fit for your a vs. m data and calculate its slope. Make sure to specify

units:

Slope =

Question 2: Based on the equation (6), the measured masses, and the slope determined in Question 1,

explain how can the gravitational acceleration be estimated.

Based on this experiment what is the gravitational acceleration:

g =

m/s

Compare the value determined with the accepted value gaccepted = 9.81 m/s'. Also, identify and rank the

main sources that could lead to errors in this experiment.