Why Might a Box on a Cart Being Pulled Continue Moving if the Cart Suddenly Stops
Lab 3 - Newton's Second Law
Introduction
Sir Isaac Newton put forth many important ideas in his famous book The Principia. His three laws of motion are the best known of these. The first law seems to be at odds with our everyday experience. Newton's first law states that any object at rest that is not acted upon by outside forces will remain at rest, and that any object in motion not acted upon by outside forces will continue its motion in a straight line at a constant velocity. If we roll a ball across the floor, we know that it will eventually come to a stop, seemingly contradicting the First Law. Our experience seems to agree with Aristotle's idea, that the "impetus" given to the ball is used up as it rolls. But Aristotle was wrong, as is our first impression of the ball's motion. The key is that the ball does experience an outside force, i.e., friction, as it rolls across the floor. This force causes the ball to decelerate (that is, it has a "negative" acceleration). According to Newton's second law an object will accelerate in the direction of the net force. Since the force of friction is opposite to the direction of travel, this acceleration causes the object to slow its forward motion, and eventually stop. The purpose of this laboratory exercise is to verify Newton's second law.
Discussion of Principles
Newton's second law in vector form is This force causes the ball rolling on the floor to decelerate (that is, it has a "negative" acceleration). According to Newton's second law an object will accelerate in the direction of the net force. If F m ( 2 ) a = = m a or F net = m a a = x y z
F m
are written in vector form. This means that Newton's second law holds true in all directions. You can always break up the forces and the resultant acceleration into their respective components in the F m
Consider a cart on a low-friction track as shown in Fig. 1. A light string is attached to the cart and passes over a pulley at the end of the track and a second mass is attached to the end of this string. The weight of the hanging mass provides tension in the string, which helps to accelerate the cart along the track. A small frictional force will resist this motion. We assume that the string is massless (or of negligible mass) and there is no friction between the string and the pulley. Therefore the tension in the string will be the same at all points along the string. This results in both masses having the same magnitude of acceleration but the direction of the acceleration will be different. The cart will accelerate to the right while hanging mass will accelerate in the downward direction as shown in Fig. 1. Figure 1 : Two-mass System Figure 2 : Free-body diagrams for the two masses m 1 W = m 1 g T y ( 6 ) F net,1 = m 1 g − T = m 1 a m 2 + x − x x y ( 7 ) F net,2x = T − f = m 2 a ( 8 ) F net,2y = F N − m 2 g = 0 F net,1 = m 1 g − T = m 1 a F net,2x = T − f = m 2 a F net,1 = m 1 g − T = m 1 a F net,2x = T − f = m 2 a T ( 9 ) m 1 g = ( m 1 + m 2) a + f m 1 g = ( m 1 + m 2) a + f y = mx + b b y
Objective
The objective of this experiment is to verify the validity of Newton's second law, which states that the net force acting on an object is directly proportional to its acceleration. Eq. (9) m 1 g = ( m 1 + m 2) a + f
Equipment
- Low-friction track with pulley
- Cart
- String
- Balance
- DataStudio software
- Two photogates
- Assorted masses
- Weight hanger
- Computer
- Signal interface
Procedure
You will conduct several trials, keeping the total mass M = m 1 + m 2 m 1 m 2 a m 1 a m 1 g M m 1 g = ( m 1 + m 2) a + f v 1 v 2 Δ t a v 1 v 2
Setting up the equipment
1
Using the adjusting screws underneath level the track so that the cart does not move when placed by itself in the center of the track. Since the cart has some friction, test to see if the track is level by giving the cart a slight nudge to the right and comparing the motion with a similar push to the left.
2
Place the photogates sufficiently far apart. Make sure the cart's flag is before the first gate when the hanger is all the way up near the pulley as shown in Fig. 3a. Also, make sure the cart's flag passes the second photogate before the hanger hits the ground. See Fig. 3b. This will ensure that the cart is being accelerated in the region between the two photogates.
3
Adjust the height of each photogate so that the small metal flag on the cart blocks the photogate light beam as it passes.
Figure 3 : Photogate set-up
Figure 4 : Experimental set-up
4
Connect photogate 1 to digital channel 1 and photogate 2 to digital channel 2. If the photogates are plugged in properly, the red LED on the photogate will light up when the infrared beam is blocked.
5
Open the appropriate Capstone file associated with this lab. Fig. 5 shows the opening screen in Capstone.
Figure 5 : Newton's second law display
6
The length of the small metal flag on the cart is different for each cart. Measure for your cart and record it on the worksheet.
7
You must input the value of the flag length and the spacing between photogates, as shown in Fig. 6. Remember to click on the Save button.
Figure 6 : Entering the flag length
Data Aquisition
8
Place the cart at the end of the track away from the pulley. Add three 50-gram masses to the cart.
9
Weigh the weight hanger, and record the mass M h
10
Connect one end of the string to the weight hanger and the other end to the cart, placing the string over the pulley. See Fig. 3.
11
Hold the cart in position so that the cart will accelerate when released. When ready to record data, click the Start button. Release the cart and catch it when it reaches the end of the track. Click the Stop button to end data recording. The time and speed data for each photogate will be reported automatically in the Table. See Fig. 7.
Figure 7 : Sample data table
12
The cart's speed increases smoothly during the time interval while the flag passes through the photogate beam. At some instant during that time interval the cart's instantaneous speed equals the average speed for the interval. That instant of time is shown in the "Time (s)" column next to its associated velocity.
13
The time it took for the cart to travel between photogates 1 and 2 is Δ t Δ t
14
Use this time interval together with the two velocities v 1 v 2 a =
15
Move one 50-gram mass from the cart to the weight hanger. Note: You must keep the total mass constant, so any mass removed from the cart must be added to the weight hanger.
16
Repeat steps 11 through 15 three more times, until you have a total of four runs with a different value of the hanging mass for each run. Calculate and record the acceleration for each case.
Checkpoint 1:
Ask your TA to check your table values before proceeding.
Analyzing the Results
17
Using Excel plot m 1 g a
18
Use the trendline option in Excel to draw a best fit line to the data and determine the slope and y
19
From the value of the slope determine the total mass of the system.
20
Use a balance to measure the mass of the cart. Add this to the mass of the weight hanger and the added masses to find the total mass M
21
Compare this measured mass to the mass determined from the slope of the graph by calculating the percent difference. Record this on the worksheet. See Appendix B.
Checkpoint 2:
Ask your TA to check your Excel worksheet and graph.
Source: https://www.webassign.net/labsgraceperiod/ncsulcpmech2/lab_3/manual.html
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