Lab 10: Work and Power

Title: Work and Power

Purpose:
The goal of this lab is to physically demonstrate then calculate work and power first by lifting an object directly upwards then by walking and running up stairs.

Theory:
Work is a function of force exerted in the direction of motion over some distance. Power is a function of work per unit time. By lifting a known mass a known distance while also timing the process, work and power may be calculated.

Apparatus:

• Meter stick
• Stopwatch
• 9kg weight
• Rope
• Long wooden plank
• Pulley

Procedure:

Have a group of 3 students. Find a flight of stairs and an easily accessible moderately high balcony area. Set up a pulley system on the balcony to lift the 9kg weight. Measure the height from the ground to where the 9kg weight is to be lifted. Take turns lifting and timing each other for a total of 1 trial per person. Proceed to the stairs and find the total height by measuring the height of a single step and finding the number of steps. Have each group member walk up the stairs while timed. Then have each group member run up the stairs while timed. Estimate the mass of each group member.

Data and Graphs:

Photo of pulley setup

Stairs on which walk/run were timed

Collected data and calculations

h (cm)	17,3	M1 (kg)	68	g (m/s^2)	9,81
steps	26	M2 (kg)	108
h total	449,8	M3 (kg)	59
	Time (s)			Work (J)			Power (W)
Trial	Lifting 9kg	Walking	Running	Lifting 9kg	Walking	Running	Lifting 9kg	Walking	Running
1	8,08	14,16	4,60	397,1	3001	3001	49,15	211,9	652,3
2	7,62	13,27	4,99	397,1	4766	4766	52,12	359,1	955,0
3	16,26	14,75	4,60	397,1	2603	2603	24,42	176,5	566,0

Data analysis:

Work was calculated according to the equation W=mgh where m is mass of the object, g is the gravitational constant, and h is the change in height from the original height. Power was calculated by dividing work by time taken to complete the task.

Conclusion:

1. In calculating total work done, kinetic energy was assumed to be negligible. Kinetic energy is equal to 1/2mv^2 and is thus most dependent on the speed at which the object moves. Lifting and walking experiments were conducted at low velocities while the running experiment is likely to have greater error due to kinetic energy. For lifting the 9kg mass, 397.1J of work as potential energy was done on the masses while only 1.57J of work was done for trial 2, the fastest trial. For trial 1 of running up the stairs, 3001J of work was done as potential energy while 98.9J of work was done as kinetic energy. The percentage errors for each of these two trials are .365% and 3.30% respectively. Based on these calculations we can expect our error to be less than 5% for all trials.
2. Based on personal data in trial 3 for work per flight of stairs, a climb rate of approximately 11 steps per second is needed to match the power output of a 1100W microwave.
3. The total amount of steps required to cook a potato for 6 minutes in the same microwave would be 3955 steps.
4. The power output needed for 12.5MJ of energy in 10 minutes is 20.8kW.
   The number of people needed to supply this amount of power at 100W per person is 209 people.
   To generate 12.5MJ of energy with a single person supplying 100W, a total of 1.45 days would be needed.