Newton’s Law of Motion

In thisexperiment, a cart is accelerated by a tension force, which iscaused by a hanging weight. We will use several trials to test Newton’s 2nd and 3rd Laws.
Lab Data
Part 1: Flat Track
Mass of cart	493.9g
Mass of black bar	494.9g

mc (g)	mH (g)	a (m/s^2)
493.9	50	0.837
493.9	100	1.54
493.9	130	1.77
493.9 + 494.9	50	0.419
493.9 + 494.9	100	0.781
493.9 + 494.9	130	1.02

Part 2 data: Tilted Track

mc (g)	mH (g)	Angle (degrees)	a (m/s^2)	Description
493.9	100	1.5	1.39	Cart going up track w/ 1 wood block under right side oftrack
493.9	100	3	1.11	2 blocks under the right
493.9	100	-2	1.63	1 block under left side of track (no blocks on the right)
493.9	100	-3.5	1.92	2 blocks under the left

(PLEASE SHOW ALL WORK)

1. Draw four FBD (free body diagrams) with Fnet vectors for thefollowing four cases. (Neglect friction and drag.) (Definecoordinate systems for each object, where each coordinate system isaligned with the object’s acceleration.)

a. Hanging mass while accelerating down (b). Cart on flat trackwhile accelerating (from part 1 data)

c. Cart on inclined track while accelerating (d). Cart ondeclined track while accelerating (this is from part 2 data)

2. For case 1a above, write out Newton’s 2nd Law in they-direction and solve for the tension: TH.

3. For cases 1b, 1c, and 1d, write out Newton’s 2nd Law in thex-direction and solve for the tension: TC.

4. Start an Excel data table and organize all your data (angles,mC, mH, and cart accelerations)

5. Nearby, start an Excel results table. Here, calculate thefollowing quantities once per trial.

Reminder: If you use sine or cosine in MSExcel, it expects the angle to be entered in radians. You can inputdegrees by using “sin(radians(A1))” and“cos(radians(A1))”.    (Change “A1” to match yourangle’s location.)

a. the net force acting on the cart, using Fnet=ma.

b. the net force acting on the hanging mass, using Fnet=ma.

c. the tension force, TH, acting on mH.

d. the tension force, TC, acting on mC. Do not use the tensionvalue from part c!

e. the fraction TC/TH.     (What should thisratio be if your data was perfect?)

6. For your TC/TH values, calculate the average, standarddeviation, and percent error between your average and the acceptedvalue.

7. Make a single scatter plot showing the cart’s accelerationvs. the net force on the cart. Use three data series: 1) first fourtrials, 2) heavy cart, and 3) tilted track.

8. Add a linear trend line to each data set. For each trendline, use “Set Intercept” with a value of zero. Display theequation for each trend line.   (When the net force iszero, the acceleration had better be zero. Thus, the y-interceptshould be 0 m/s2.)