Motion lab - Lab Report PDF

Preview

Summary

Lab Report...

Description

Francesca Wight Sean Patrick Lees Sarah Worthington Tristan Yerger

Due: 02/10/2021

Experiment 3 - Motion of a Cart on a Ramp

Application/Problem Observe the movement of a cart moving up and down an inclined track. What is the relationship between gravity, velocity, position, and mass? Hypothesis The higher the angle, the greater the velocity of the cart as it comes down because as the angle increases, the force in the z direction increases as it is equal to m * g * sin(theta). Velocity is the first derivative of position and acceleration is the second derivative of position. Variables Independent: The angle of the ramp. Dependent: Velocity; position. Control: Gravity; mass of the cart. Assumptions In this experiment, air resistance and friction are negligible. The acceleration due to gravity is 9.81m/s^2. Each run, the same amount of force was used to push the cart up the ramp. This leads to the assumption that it had the same initial velocity. The velocity at the top of the ramp was 0 each run.

Uncertainty: Personal: The personal uncertainties that exist in these experiments include but are not limited to; changes in force of push involving moving the cart up the ramp. This is the normal force and must be equal and opposite to the perpendicular gravity component. This can be mathematically represented by the equation: N = +m×g×(cos(θ) Also a horizontal force has to be accounted for to keep the block from sliding in its track. This can be mathematically represented by: F = +m×g×sin(θ) Mismanaging this force can lead to uncertainty in the friction coefficient created by the cart on the ramp. Statistical: Some of the uncertainties in this category pertaining to our experiments can be identified as debris on the track surface, deformations in the track surface (bent), and cart axle deformation (bearing surface friction coefficient). This can be represented mathematically as follows, respectively: μ=f / N Average Plastic/Aluminum Friction Coefficient: 0.325 (tribiology-abc.com) .0325 = f

f /[ .2574 kg(9.81 m/ s / s )]

≅ 0.821 kg. m. s-2 (Friction Force of Cart)

This value as well as accounting for other statistical uncertainties can alter our experiment results.

Systematic: These uncertainties can be found in uncalibrated equipment or physically deformed measuring devices. These can also be a result of thermal properties in the lab environment or measured object. Solutions: There are many effective ways to combat these uncertainties in a Lab environment. The best ways to prevent or minimize these in our lab environment would be to establish an automatic force lever mechanism to exclude human error, be sure of equipment calibration, and account for lab environmental change that would affect measurements and equipment.

Experimental Setup: We started the experiment off with dusting off the ramp and doing all the basics to ensure an accurate experiment and such. Next, take the angle between the ramp and horizontal and repeat for each new angle of the ramp. After doing this for each new angle take the data and report it into logger pro to create graphs that represent the collected data and then draw conclusions between the variables and how they affected each other in the experiment/lab.

Experiment 1: 7.58 angle (sin Θ) Experiment 2: angle 10.13 Experiment 3: 12.70 Experiment 4: 15.29 Conclusion:

In conclusion we observed that the relation between the angle of the cart and the velocity of the cart on its return to the zero position are correlative. The higher the angle the lower the displacement. Mathematically represented by: F = mg[sin(θ)] s = s0 + vt v = v0 + at Using these equations of motion we can deduce wanted variables and provide proof of the acceleration of gravity.

Improvement: Overall, the experiment ran almost seamlessly through and through. Some minor improvements that could be made are testing how the weight of the cart affects the velocity and acceleration down the ramp and relate it back to the data we have already collected. In addition, we could have switched the variables around in order to see if the data would stay the same when we adjusted different variables.

Page 1 Questions: I.

While moving uphill, acceleration is negative and therefore decreasing, while at the peak acceleration is 0. While moving downhill, acceleration is positive and therefore increasing.

II.

The velocity is positive and the acceleration is negative and vice versa.

III.

Both the velocity and acceleration are positive or negative.

Interactive Lab (Online):

Works Cited:

Coefficient of friction, rolling resistance, air resistance, aerodynamics. (n.d.). Retrieved February 9, 2021, from https://www.tribology-abc.com/abc/cof.htm...