Mass, Acceleration, Work, and Potential Energy

Abstract:

In this lab,  we learn about the mass, work, potential energy, and power. We use a motor to pull up weights, which is attached to the motor with string and a wheel.

Introduction:

Potential energy is the energy that a body has and not yet being spent. A book on the table can fall on the ground, so it has the potential energy of:

where Mass = mass of the book, and Height = height of the table.

Work exists when a force is being applied to change the speed or direction of an object. The general formula for work is:

If the book were to be lifted to a higher position, there would be work done. And the formula for this case would be:

The unit for work and potential energy is joules.

The concept of Power is the time rate of work. The formula is:

Work/Time

The unit for power is Joules/s or Watts.

Equipments:

Lego motor

String

Excel

Lab View

Wheel

Weights (250 grams in total)

 

Experiment 1:

We first record the data of the weights being pulled up by the motor. The data includes speed, battery discharge, mass, power level, time, and acceleration. For more accurate data, we run six times for each different mass (100g, 150g, 200g, and 250g), and take the average of the data.

Speed (RPM)	Battery Discharge (mV)	Mass (kg)	Power Level (%)	Time (s)	Acceleration (RPM/s)
93.40	62.83	0.10	75	1.53	61.16
88.76	56.00	0.15	75	1.66	53.50
83.65	71.83	0.20	75	1.78	47.02
79.01	53.67	0.25	75	1.89	41.96

Acceleration (RPM/s)	h (m)	g (m/s^2)	mgh (J)	Power =mgh/t
61.16	0.11	9.80	0.108	0.070411
53.50	0.11	9.80	0.162	0.097429
47.02	0.11	9.80	0.216	0.121112
41.96	0.11	9.80	0.270	0.142681

Work is the product of Mass, Gravity, and Height. Setting the table as h=0, we say the highest that the weights will go is 11cm.

More work is done when mass increases. Therefore the power increases as well.

With the data collected, we analyze the relationship between acceleration & mass, and battery discharge & mass.

Figure 1.

The acceleration clearly goes down as mass increases. More power is required to pull  heavier objects at same speed. If the power does not change, the speed and acceleration can only decrease.

 

Figure 2.

The battery discharge measurement by the program is not very precise because the voltage usage is very low. Luckily the data still gives a positive slope, which means the voltage usage is increasing. In general cases, the heavier the object is the more energy is required to move such object.

Experiment 2:

This is a similar experiment to Experiment 1. Only this time we keep the same mass, 250 grams, and vary the power level, 45, 55, 65, 75.

	Speed (RPM)	Battery Discharge (mV)	Mass (kg)	Power Level (%)	Time (s)	Acceleration (RPM/s)
	82.39	27.00	0.25	75	1.86	44.27
	67.19	96.00	0.25	65	1.90	35.46
	52.04	83.00	0.25	55	2.90	17.98
	36.77	69.00	0.25	45	4.19	8.780

h (m)	g (m/s^2)	Work (J)	Power =mgh/t
0.11	9.80	0.27	0.145
0.11	9.80	0.27	0.142
0.11	9.80	0.27	0.093
0.11	9.80	0.27	0.064

The work for this experiment stays the same because the mass and distance traveled never changes.

Figure 3

The battery discharge is off for this experiment. The data point on the very right results a negative slope to the equation. If only looking at the three points on the left, the slope would be positive, which shows the increase of voltage usage. Therefore, we know when power level increases, the more energy, voltage in this case, is being used.

Figure 4

This graph shows that when there is more power driving the motor, the object moves faster.

Figure 5

The power level describes how hard the motor is being driven. The power shows the work that is being down among a limited time period.

When power level increases, time decreases. The same amount of work is done over a shorter period, so the power goes up.

Conclusion:

After this experiment, we have a better idea of how mass is a big factor when measuring the speed, acceleration, work, and power. Also the increase of the  power level would give a shorter time period, but requires more energy to drive.