Inclined Plane Lab PDF

Preview

Summary

Inclined Plane Lab...

Description

Kachi Anyanwu PHYS.1030L-813 Motion of a Block on an Inclined Plane 12 October 2017 Ngan Trinh, Kristen Geraghty Sanjanee Waniganeththi Objective: The angle of the incline on which a cart is placed and the mass of the cart are varied to determine the effect of each on the motion of a block as it accelerates down the inclined plane.

Background and Predictions When an object an incline plane, it is affected by two forces – normal force and the force of gravity. The normal force acting on the object is perpendicular to the surface of the incline plane. Meanwhile, the force of gravity acting on the object points towards the ground. However, if the motion of the object on the inclined plane is referenced with the x axis parallel to the incline, the y component of gravity acting on the object is equal to its normal force. Therefore, the sole force acting on the object is the x component of gravity, and can be represented by (1) Fnet =mgsinθ , where Fnet is the net force acting on the object, m is the mass of the object, g is gravitational acceleration, and θ is the angle of the inclined plane. According to Newton’s Second Law of Motion, (2) Fnet =ma , where Fnet is the net force acting on the object, m is the mass of the object, and a is its acceleration. Therefore, (3) ma=mgsinθ and a=gsinθ ; the acceleration of an object on an incline is independent of its mass. As such, we expected the acceleration of the cart to increase as the angle of the inclined plane increased. When the mass of the cart was varied at the same angle, we did not expect any significant changes in acceleration. Apparatus and Procedure Figure 1. Apparatus setup

List of Materials:  inclined plane  cart/object  2 blocks  position sensor with plum line

Procedure Part 1. The effect of the incline on acceleration With the incline plane set at an angle of 5°, the cart was placed against the position sensor. The displacement was recorded as zero in the LoggerPro program. The cart was then released without any additional mass. Using the LoggerPro, the position sensor recorded the displacement of the cart at intervals of 0.05 s. This was repeated with the incline plane set to 10° and 15°. Part 2. The effect of mass on acceleration With the incline plane set at an angle of 10°, the cart was placed against the position sensor. The displacement was recorded as zero in the LoggerPro program. The cart was then released with one mass block. Using LoggerPro, the position sensor recorded the displacement of the cart at intervals of 0.05 s. This was repeated with two mass blocks. Results and Analysis

Figure 2. The Effect of an Inlined Plane on Acceleration 2.5

Velocity, m/s

2

f(x) = 2.3 x − 0.07 5 degrees Linear (5 degrees) 10 degrees Linear (10 degrees) 15 degrees Linear (15 degrees)

f(x) = 1.59 x − 0

1.5

f(x) = 0.8 x + 0.01 1

0.5

0

0

0.2

0.4

0.6

0.8 Time, s

1

1.2

1.4

1.6

Figure 3. Velocity vs. Time on an Inclined Plane When the Mass Is 810.1 g 1.8 f(x) = 1.71 x − 0.01

1.6 1.4

Velocity, m/s

1.2 1 0.8 0.6 0.4 0.2 0 0.00

0.20

0.40

0.60

0.80

1.00

1.20

Time, s

Figure 4. Velocity vs. Time on an Inclined Plane When the Mass Is 1301.2 g 2 1.8 1.6

f(x) = 1.7 x − 0.04

1.4 Velocity, m/s

1.2 1 0.8 0.6 0.4 0.2 0 0.00

0.20

0.40

0.60 Time, s

Sample Calculations

0.80

1.00

1.20

1. Change in time ∆ t=t 2−t 1 ¿ 0.05 s−0.00 s ¿ 0.05 s 2. Change in position ∆ s=s 2−s1 ¿ 0.003 m−0.000 m ¿ 0.003 m

3. Velocity ∆t ∆s 0.003m−0.000 m ¿ 0.05 s−0.00 s m ¿ 0.06 s 4. Expected acceleration a=gsinθ m = 9.8 × sin ( 5 ° ) s m ¿ 0.854 2 s v =

Analysis As show in Tables 1, 2, and 3 and Figure 2, as the angle of the incline increases, so does the slope. The slopes demonstrate the rate at which the cart’s velocity changes in respect to time, or the cart’s acceleration. Since each of the velocities changes at a constant rate, velocity and time have a linear relationship; the acceleration of the cart does not change as time passes (Figure 2). This is consistent with what would be expected because the only force acting on the block is the force of gravity in line with the angle of the incline. When the mass is varied at an approximate incline of 10°, there was no significant change in acceleration (Figure 3, Figure 4). Discussion The results of this experiment were very reliable; the percent error for an incline of 5°, 10, and 15° were 6.32%, 6.634%, and 9.15% respectively. In the second experiment, the acceleration only differed by 0.0071 m/s2. In this case, the experimental data is consistent with the predicted acceleration modeled by the equation a=gsinθ because the only force acting on the cart on the incline plane was the force of gravity. In addition, the second experiment supported the idea that the acceleration of the incline is determined by the angle of the incline and is independent of its mass.

However, the measured accelerations of the cart during the first experiment did differ slightly from the expected values. This could be due the precision of the plum line because it was only able the measure the angle of the inclined plane to the nearest degree, whereas using a digital sensor would allow for a more precise angle. As the angle of the incline increases, the percent error also increases; a possible cause of this phenomenon is the uncertainty associated with the position of the cart as the velocity increases. This uncertainty can be reduced using a positon sensor that records the positon of the cart in shorter intervals or by decreasing the angles of the incline plane. Conclusion The acceleration an object on an incline plane increases as the angle of the incline increases independent of mass. In this case, the acceleration of the cart was 0.800 m/s2, 1.589 m/s2, and 2.304 m/s2 when placed on an incline of 5°, 10, and 15° respectively....