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Home , Acceleration, Energy transformation, Force, Horsepower, Joule, Kinetic energy

Work, , &

In , is done when a acting on an object causes it to move a . There are several good examples of work which can be observed everyday - a person pushing a grocery down the aisle of a grocery store, a student lifting a backpack full of books, a baseball player throwing a ball. In each case a force is exerted on an object that caused it to move a distance. Work () = force (N) x distance (m) W = f d The metric unit of work is one -meter ( 1 N-m ). This combination of units is given the name in honor of (1818-1889), who performed the first direct of the mechanical equivalent of energy. The unit of heat energy, , is equivalent to 4.18 joules, or 1 calorie = 4.18 joules.

Work has nothing to do with the amount of that this force acts to cause movement. Sometimes, the work is done very quickly and other the work is done rather slowly. The quantity which has to do with the at which a certain amount of work is done is known as the power.

The metric unit of power is the . As is implied by the equation for power, a unit of power is equivalent to a unit of work divided by a unit of time. Thus, a watt is equivalent to a joule/. For historical reasons, the is occasionally used to describe the power delivered by a . One horsepower is equivalent to approximately 750 . Power (watts) = work (joules) / time () P = w / t Objects can store energy as the result of its . For example, the heavy ram of a pile driver is storing energy when it is held at an elevated position. Gravitational energy is the energy stored in an object as the result of its height above the ground. The energy is stored as the result of the gravitational attraction of the for the object. The gravitational of the heavy ram of a pile driver is dependent on two variables - the of the ram and the height to which it is raised. GPE (joules) = mass (kg) x gravitational (9.8 m/s/s) x height (m) GPE = m g h

A second form of potential energy is elastic potential energy. Elastic potential energy is the energy stored in elastic materials as the result of their or compressing. Elastic potential energy can be stored in rubber bands, bungee chords, trampolines, springs, or the stretched strings of a tennis racket and the compressed tennis ball. The amount of elastic potential energy stored in such a device is related to the amount of stretch or of the device - the more stretch or compression, the more stored energy.

Kinetic energy is the energy of . An object which has motion - whether vertical or horizontal motion - has . There are many forms of kinetic energy. The amount of kinetic energy which an object has depends upon two variables: the mass (m) of the object and the (v) of the object. The following equation is used to represent the kinetic energy (KE) of an object. KE (joules) = ½ mass (kg) x (m/s)2 KE = ½ m v2

Work, Power & Energy 1 PART I: LEG POWER A person, like all , has a power rating. Some people are more powerful than others; that is, they are capable of doing the same amount of work in less time or more work in the same amount of time. Whenever you walk or run up stairs, you do work against the force of . The work you do is simply your times the vertical distance you , i.e., the vertical height of the stairs.

WORK = (YOUR WEIGHT IN NEWTONS) X (HEIGHT OF STAIRS IN METERS) PROCEDURE While your partner times you, run up a of stairs as fast as you can. Measure the vertical height of the stairs, and using your weight (no cheating!) calculate the work done and power developed. Then, walk up the flight of stairs. Record the information in the tables provided and calculate the work and power necessary to walk and run up the stairs.

Your Weight Height of Stairs Time Activity (Newtons) (meters) (seconds)

Running 60.0 kg = 588 N 2.30 m 2.25

Walking 60.0 kg = 588 N 2.30 m 4.50

WORK POWER

Activity Joules Watts Horsepower

Running 1350 323 600. 0.828

Walking 1350 323 300. 0.414

‘ How does the work compare walking up the stairs vs. running up the stairs?

1. The work running or walking up the stairs is equal. Since the mass of the student and the height of the stairs is constant then the work is constant. ____ ‘ How does the power compare walking up the stairs vs. running up the stairs?

2. Power is inversely proportional to time. Given that work is constant, performing the same amount of work in less time produces a greater power output.

PART II: POTENTIAL & KINETIC ENERGY IN A

A pendulum is a simple mechanical device consisting of an object (a mass called a bob) that is suspended by a string from a fixed point and that swings back-and-forth under the influence of gravity. In 1581, , while studying at the University of Pisa in Italy, began his study of the pendulum. According to legend, he watched a suspended lamp swing back and forth in the cathedral of Pisa. Timing the swing with the beat of his pulse, Galileo noted that the time that the pendulum swings back-and-forth does not depend on the arc of the swing. Eventually, this discovery would lead to Galileo's further study of time intervals and the development of his idea for a .

Work, Power & Energy 2 If a pendulum is pulled to some from the vertical but not released, potential energy exists in the system. When the pendulum is released, the potential energy is converted into kinetic energy as the pendulum bob descends under the i nfluence of gravity. The faster the pendulum bob moves, the greater its kinetic energy. The higher the pendulum bob, the Maximum greater its potential energy. This change from potential to Maximum GPE kinetic energy is consistent with the principle of conservation GPE of which states that the total energy of a system, kinetic plus potential, remains constant while the system is in motion. Maximum KE

When you pull the pendulum to the side, you increase the energy of the pendulum by an amount equal to the change in height times the mass times the acceleration of gravity. So we can write GPE=m g h, where GPE is the change in potential energy, m is the mass in , h is the vertical distance that the pendulum has been raised, and g is 9.80 m/s² as before.

Kinetic energy of motion is given by the formula K E= ½ m v², where m is mass in kilograms, and v is the velocity of the pendulum in m/s. If the energy is conserved, all of the potential energy at the top of the swing should be converted to kinetic energy at the bottom of the swing where the velocity is greatest. Let's test this.

PROCEDURE In this portion of the experiment, you will test whether energy is conserved in a pendulum by using a photogate timer that measures the time it takes the falling bob to pass through a narrow of . From this the speed of the falling bob can then be calculated. Comparing the kinetic energy at the bottom of the swing with the amount of potential energy at the release point will test the of the pendulum.

Make the following for your pendulum and record the data in the table below:

Mass of bob: 58.10 g 0.05810 kg

Diameter of bob: 2.00 cm 0.0200 m

Height of bob at rest above table: 9.00 cm 0.0900 m

You will collect the time it takes for the bob to pass through the photogate for 3 trials at two different release heights. Pull back the pendulum and measure the height of the bob above the table using a ruler. Try to keep the height of the bob the same for each of the three trials. Reset the timer between trials.

Release Height Time: Trial 1 Time: Trial 2 Time: Trial 3 Average 30.0 cm 0.0100 sec 15.0 cm 0.01850 sec

How much higher (vertically) is the pendulum at each release height than it was when it was hanging at rest? Convert this distance to meters and calculate the gravitational potential energy, GPE, of the bob. 30.0 cm Release Height 15.0 cm Release Height 30.00 cm – 9.00 = 21.00 cm (0.02100 m) 15.00 cm – 9.00 = 6.00 cm (0.0600 m)

(0.05810 kg) x (9.80 m/s2) x (0.2100 m) (0.05810 kg) x (9.80 m/s2) x (0.0600 m)

0.1196 joules 0.03311 joules

Work, Power & Energy 3 Calculate the velocity of bob at the bottom of the swing:

diameter of bob (m) = speed of bob (m / s ) average time (sec)

30.0 cm Release Height 15.0 cm Release Height

0.0200 m / 0.0100 sec = 2.00 m/s 0.0200 m / 0.01850 sec = 1.08 m/s

Calculate the kinetic energy of the bob at the bottom of the swing 30.0 cm Release Height 15.0 cm Release Height

½ (0.05810 kg) (2.00 m/s)2 ½ (0.05810 kg) (1.08 m/s)2

0.1162 joules 0.03388 joules

Compare the values for the gravitational potential energy and kinetic energy of the pendulum. Was energy conserved, that is, were they equal? If not, how might you account for the difference in ?

At 30.0 cm: GPE = 0.1196 j and KE = 0.1162 j (energy is conserved – within experimental error)

At 15.0 cm: GPE = 0.03311 j and KE = 0.03388 j (energy is conserved – within experimental error)

PART III: POTPOURRI Located on the side table are several objects that transforms one form of energy to another. Complete the table to identify the object that represents the energy transformation in the chart.

3

1 7 6 4

2

8 5

Mechanical Energy

1 5 Plant

2 GENERATOR 6 Animals

3 BATTERY 7 Light Bulb

4 CANDLE 8 Solar Cell

Work, Power & Energy 4 Part IV: The

1, Complete the data table below using the appropriate number of digits for the measurement.

Length of the Height of the Mass of Inclined Plane Inclined Plane

120.00 cm 20.00 cm 47.00 g

1.2000 m 0.2000 m 0.04700 kg

2. Use the stopwatch to determine the time for the car to roll down the of the track.

Trial 1 Trial 2 Trial 3 Average Time 2.35 s

For calculations below express your answer with the appropriate number of significant figures.

3. Determine the gravitational potential energy of the car at the top of the ramp.

G.P.E. = (0.04700 kg) x (9.80 m/s2) x (0.2000 m) = 0.09212 Joules

4. Determine the speed of the car at the end of the ramp.

Final Speed = (1.2000 m / 2.35 s) x 2 = 1.02 m/s

5. Determine the kinetic energy of the car at the bottom of the ramp.

K. E. = ½ x (0.04700 kg) x (1.02 m/s)2 = 0.0244 Joules

6. Determine the acceleration of the car along the ramp.

Acceleration = 1,02 m/s ÷ 2.35 s = 0.434 m/s2

7. Determine the accelerating force for the car.

Force = (0.04700 kg) x (0.434 m/s2) = 0.0204 Newtons

8. Compare the GPE at the top of the ramp with the KE at the bottom. Which is greater? How do you account for any differences in the two values?

0.09212 J – 0.0204 J = 0.07172 Joules converted to heat

9. If a more massive car were used, what changes, if any, would there be in the following:

 Gravitational Potential Energy at the top of the ramp: Increased (increased mass)

 Final speed of the car at the bottom of the ramp: No change (no change in time)

 Kinetic energy at the bottom of the ramp: Increased (increased mass)

 The acceleration of the car: No change (no change in time)

 The accelerating force for the car: Increased (increased mass)

10. If the height of the track was increased to 40.00 cm, what changes, if any, would there be in the following:

 Gravitational Potential Energy at the top of the ramp: Increased (increased height)

 Final speed of the car at the bottom of the ramp: Increased (decreased time)

 Kinetic energy at the bottom of the ramp: Increased (increased final speed)

 The acceleration of the car: Increased (increased speed and decreased time)

 The accelerating force for the car: Increased (increased acceleration)

POSTLAB CALCULATIONS

1. The calories that we watch in our diet are actually kilocalories, or 1000 calories (usually designated as 1 C "big calories"). If a "Snickers" bar has 250 Calories (big calories), how many of stairs would you need to climb to burn off the energy from the candy bar? Show your work.

Conversions:

250 Calories = 250,000 calories 4.18 joules = 1 calorie 250,000 calories = 1,045,000 joules

From page 2: 1 flight of stairs = 1350 joules

1,045,000 joules / 1350 joules/flight = 774 flights

2. Consider the following: You are holding a small (about 100 g) rubber ball held at arm’s length in front of you and you drop it (you decide on the height). It hits the floor and bounces to the height of your waist (you decide on the height) and you catch it.

What is the potential energy of the ball before you drop it?

0.100 kg x 9.80 m/s2 x 1.80 m = 1.76 joules

What is the kinetic energy of the ball at the instant it hits the floor?

The same: 1.76 joules

What is the potential energy of the ball where you catch it?

0.100 kg x 9.80 m/s2 x 1.00 m = 0.980 joules

How much energy is unaccounted for from the point of dropping it and the point of catching it after it bounces? 1.76 joules – 0.98 joules = 0.78 joules unaccounted for in the experiment. This amount of energy has been converted to heat. An instant after the ball hits the floor and before the ball begins to bounce, the ball has stopped moving. Therefore the potential energy is zero (its height above the floor is zero) and its kinetic energy is zero (its velocity is zero). If the Law of Conservation of Energy is true, how is the energy stored in the ball? (Hint: Read page one of this lab manual!)

When the ball and the floor come in contact, the of the ball and the floor results in less elastic potential energy to propel the ball upward after it hits the floor. Elastic potential energy is how the energy is stored in the ball that causes the bounce. The more elastic potential energy stored, the higher the ball bounces.

3. A 100.0 g ball is placed on top of a 2.0 meter wall (Diagram 1), ramp (Diagram 2) and staircase (Diagram 3). Calculate the potential energy of the ball at each location illustrated below.

Diagram 1 Diagram 2 Diagram 3

1.96 joules 1.96 joules 1.96 joules

1.31 joules

0.66 joules Kinetic energy at 0 joules impact______1.96 joules 0 joules 0 joules

Work, Power & Energy 5