Question

Newton’s Law of Motion

In this experiment, a cart is accelerated by a tension force, which is caused 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 of track
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 the following four cases. (Neglect friction and drag.) (Define coordinate systems for each object, where each coordinate system is aligned with the object’s acceleration.)

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

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

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

3. For cases 1b, 1c, and 1d, write out Newton’s 2nd Law in the x-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 the following quantities once per trial.

Reminder: If you use sine or cosine in MS Excel, it expects the angle to be entered in radians. You can input degrees by using “sin(radians(A1))” and “cos(radians(A1))”.    (Change “A1” to match your angle’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 tension value from part c!

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

6. For your TC/TH values, calculate the average, standard deviation, and percent error between your average and the accepted value.

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

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

Answer 1

1. To draw a free body diagrams for following four cases which are given below as :

(a) Hanging mass while accelerating down

(b) Cart on flat track while accelerating

(c) Cart on inclined track while accelerating

(d) Cart on declined track while accelerating

2. For case 1(a) above, the tension T_H will be given as :

From Newton’s 2^nd Law in the y-direction, we have

T_H - m_H g = 0

T_H = m_H g

3. For cases 1(b), 1(c) and 1(d), the tension T_C which will be given as :

From Newton’s 2^nd Law in the x-direction, we have

F_net - f_s = m_C a

T_C = m_C a                                                                { Neglect friction }