Name PRE-TEST. Directions: Circle the letter indicating whether the following statements are either true ("T") or false ("F").

Transcription

1 1 PRE-TEST Directions: Circle the letter indicating whether the following statements are either true ("T") or false ("F"). T F 1. An object's energy due to its motion is kinetic energy. T F 2. We can calculate an object's kinetic energy using the relationship: "energy is equal to mass times the speed of the object squared." T F 3. The energy due to position or condition of an object is its potential energy. T F 4. Glucose and oxygen are products of cellular respiration. T F 5. Work is the transfer of energy form one object or system to another when a force is applied over a distance. T F 6. Energy is defined as the ability to do work. T F 7. The energy stored in grain, such as wheat, is chemical potential energy. T F 8. The product of an object's mass times the acceleration of gravity is equal to the gravitational potential energy of the object. T F 9. Resistive forces, friction and air resistance for example, are always undesirable. T F 10. The formula used to calculate the work done is W = Fd.

2 2 GLOSSARY First law of thermodynamics energy cannot be created or destroyed, only converted from one form to another Force a push or a pull Kinetic energy the energy an object or system has due to its motion Potential energy the energy of an object or system due to its position or condition, e.g., gravitational potential energy, chemical potential energy Resistive force a force which acts against the motion of an object; friction and air resistance are common examples of resistive forces Slope the ratio of the vertical change (rise) divided by the horizontal change (run) of a line on a graph Work the transfer of energy from one object or system to another when a force is applied over a distance

3 3 WORK Work is a transfer of energy from one object or system to another. This transfer occurs when a force is applied over a distance. We can identify situations in which work has been done by looking for different energy forms at the beginning and at the end of an event. We also determine which object is doing the work and which object is having work done on it. Examples 1. What is the evidence that work is done when grain is lifted from the boot to the top of a grain elevator? bucket belt boot There are two pieces of evidence. First, although the grain in the boot is not moving, the elevator puts it in motion, and anything in motion has kinetic energy. Second, the grain at the top of the elevator has more gravitational potential energy than it had in the boot. This means the work done by the elevator on the grain has increased the grain s gravitational potential energy. The change in energy indicates work was done. 2. An ice skater on frictionless, horizontal ice glides at a constant speed across the ice. There is no evidence of work here. While gliding, the ice skater has kinetic energy. But because the speed remains constant the kinetic energy does not change. And, while moving horizontally, there is no change in gravitational potential energy. If there is no change in energy, no work is done. Check your understanding of this segment by completing the following. Use the back of the sheet if necessary. 1. In which of these situations is work done? a. a pitcher throws a baseball towards home base b. a hot air balloon rises from the ground c. a comet travels at a constant speed through deep space 2. Define the term force. 3. Define the term work.

4 4 GRAVITY WORKS We calculate the amount of work done by multiplying the force acting on the object by the distance the object moves in the same direction as the force acts. The equation is W = Fd, where F is force in newtons and d is distance in meters. In the special case where an object is moving vertically downward, the force required to cause the motion is the weight of the object. This is the force of gravity acting. To find the force due to gravity we multiply mass by the acceleration due to gravity (9.81 m/s 2 ). The equation is F g = mg, where m is mass in kilograms and g is the acceleration due to gravity in meters per second squared. Examples 1. Crystal has a mass of 47.7 kg; how much work does she do climbing the 5.0 m dive tower? given: m = 47.7 kg d = 5.0 m Crystal is moving vertically up, so she is doing work against gravity. In order for Crystal to climb the tower at a constant speed she must apply a force equal (and opposite) to the force of gravity acting on her. Crystal s weight is the force of gravity acting upon her, and we calculate it by multiplying her mass times the acceleration due to gravity. solution: F g = mg F g = 47.7 kg (9.81 m/s 2 ) F g = N F g = 468 N Now this value can be substituted into the work formula. W = Fd W = (467.9 N)(5.0 m) W = 2340 N m W = 2.3 x 10 3 J Note: The units newton meter are identical to the joule which is consistent with our description of work as a transfer of energy. Work is measured in energy units. 2. How much work is done to carry a 2.0 kg bowling ball horizontally at a constant 1.3 m/s? While moving horizontally there is no change in gravitational potential energy. As the speed is constant, there is also no change in kinetic energy. There is no work done in this case. Note: Work is done when a force acts and an object moves in the same direction. In this case the force is applied vertically (to hold the ball up), but since the direction in which the ball moves is horizontal, no work is done. Check your understanding of this segment by completing the following. Use the back of the sheet if necessary. 4. Find the force required to raise 250 kg of grain against gravity at a constant speed. 5. Find the work done to raise 250 kg of grain 29 m to the top of a grain elevator. 6. A teenager applies an average force of 40 N on the pedals of her bicycle. If this force is applied over a distance of 60 cm, how much work is done? 7. A 0.40 kg hawk dives vertically downward for a distance of 200 m. How much work does gravity do on the hawk?

5 5 REALIZING YOUR POTENTIAL Compare the amount of work done when a diver climbs from the swimming pool up to the five-metre platform with the work done when he or she dives from the platform and returns to the pool. Identify what does the work on the way up and on the way down. The amount of work done on the climb up is equal to the work done on the dive down. While climbing up the diver works against gravity. On the dive down, gravity works on the diver. The law of conservation of energy states energy can never be created nor destroyed, only converted from one form to another. When Crystal is on the platform she has gravitational potential energy. The moment before she enters the water that potential energy has been converted to kinetic energy Crystal is moving. The law of conservation of energy tells us that Crystal s initial gravitational potential energy is equal to her final kinetic energy. Example Find Crystal s speed the moment before she enters the water as she dives from the five-metre platform. From the law of conservation of energy we predict that gravitational potential energy is converted to kinetic energy. E p = E k 1 mgh = 2 mv 2 1 gh = v 2 2 2gh = v 2 divide both sides by m multiply both sides by 2 take the square root of both sides v = 2gh After isolating the variable, substitute the given values and calculate the answer. Measure from a reference level in this case from the pool surface, so the height, h, is 5.0 m, and the acceleration due to gravity, g, is 9.81 m. v = 2gh v = 2(9.81 m )(5.0 m) v = 9.9 Note: This calculation assumes no energy loss due to air resistance. s 2 Check your understanding of this segment by completing the following. Use the back of the sheet if necessary. 8. Starting from E p = E k, find an expression for the height in terms of speed and the acceleration due to gravity (h =?). 9. If an egg were dropped from 1.5 m above the ground, would it survive the fall? How fast is it travelling when it reaches the ground? 10. A volleyball is set at the net, travelling straight up at a speed of 7.2 m/s. How high above its original position will it reach? s 2

6 6 WHERE WILL IT STOP? A car travelling down a level street at a constant speed does no apparent work. There is no gain in gravitational potential energy, and there is no change in kinetic energy. But with the engine running, obviously energy is being converted. Where does it go? The engine is doing work against two main resistive forces the force of friction acting on all parts of the car, where the tire meets the road, in the engine itself and in all the moving parts of the car; and the force necessary to move the air out of the way (air resistance). Resistive forces cause the car to use more fuel. That s why car designers use wind tunnels and computer models to investigate methods of reducing these forces. But not all resistance forces are undesirable. The friction between the tire and the road, for instance, is essential to keeping the car on the road. Turning and stopping would be very difficult if friction forces were not significant. Check your understanding of this segment by completing the following. Use the back of the sheet if necessary. 11. The space shuttle uses air resistance to slow its descent to earth. Describe the energy conversion happening in this case and any design features the shuttle incorporates to deal with it.

7 7a A GRAPHIC ILLUSTRATION We draw graphs to aid our analysis of data we have collected. In general, graphs will have a title, labelled axes, an appropriate scale and a best-fit line drawn through the data points. The following graph is created from the bucket-belt data shown in this segment. Calculating slope requires two points from the best-fit line. Choose two that are far apart. This point is at 295 cm and 30 s. Distance (cm) Points from the best-fit line where it crosses a grid line of the graph are easiest to use. This point is at 50 cm and 5.0 s Distance vs. Time of a Bucket Time (s) Graphing Guidelines 1. In general the manipulated, or independent, variable is plotted on the horizontal axis. 2. Axes should be labelled including the units of measure in brackets, e.g., Time (s). 3. Title should follow the standard form of the label of the vertical axis versus the label of the horizontal axis; if necessary it can be followed with some words of description. 4. Determine the scale you will use: make good use of the graph space; don t crowd your data points in one corner the scale must be sufficient to include all data points the scales of the vertical and horizontal axis are not usually the same 5. Plot the points accurately. 6. Draw a best-fit line. Usually data points are not in a perfectly straight line. If they appear to be close to a straight line, use a straight edge and draw a single straight line such that about equal numbers of points lie above and below the line.

8 7b A GRAPHIC ILLUSTRATION Slope of a Line The slope of the best-fit line on a distance-versus-time graph tells us information about the object. Slope is defined as rise divided by run: rise slope = = distance Note: The symbol (called delta ) means change in. run time As you can see, slope is change in distance divided by change in time which is speed. slope = speed Example From the graph on the previous page find the speed of the bucket. We read two points from the best-fit line and substitute those values into the slope equation. When possible, choose points that are far apart on the line and on one of the grid lines. This will reduce error. The two points used in the calculation that follows are indicated on the graph: at 5.0 s and 50 cm, and at 30 s and 295 cm. distance slope = = time slope = slope = slope = 9.8 The speed of the bucket is 9.8 cm/s. 295 cm - 50 cm 30 s s 245 cm 25 s d 2 - d 1 Check your understanding of this segment by completing the following. Use the back of the sheet if necessary. t 2 - t Graph the distance-versus-time data in the table below. Place time on them horizontal axis. Include a title and labels, use appropriate scales and draw a best-fit line. 13. Calculate the speed of the object using the slope of the best-fit line. Distance (cm) Time (s)

9 8a POST-TEST MULTIPLE CHOICE Directions: Decide which of the choices best completes the statement or answers the question, then circle the letter that corresponds to your choice. (3 marks each) 1. The chemical potential energy in grain is stored a. carbon b. solar energy c. kinetic energy d. gravitational energy 2. A person climbing a flight of stairs increases her a. kinetic energy b. potential energy c. chemical potential energy d. gravitational potential energy 3. The slope of a distance versus time graph is equal to a. work b. speed c. acceleration d. distance traveled LONG ANSWER Directions: Answer the following questions in the spaces provided. Use the back of the sheet if necessary. 1. In order for stored, potential, energy to be useful it first has to be. (3 marks) 2. Scientists define a force as a or. (3 marks) 3. The scientific definition of work is. (4 marks) 4. The gravitational potential energy of an object is always described relative to a. (3 marks)

10 8b POST-TEST 5. The formula used to calculate work done is. (4 marks) 6. Having run out of fuel, a driver pushes his car with a constant force of 1000 N over 150 m toward a service station. Calculate the amount of work done by the driver on the car. (8 marks) 7. The force of gravity acting on an object is equal to the of that object. (3 marks) 8. To calculate your weight in newtons you multiply your mass in by the. (6 marks) 9. Whenever work is done on an object its total increases, and when an object or system does work its. (6 marks) 10. A spring is used to close some screen doors automatically. When a spring is stretched we say it has potential energy due to. (3 marks) 11. In preparation for a dive, a diver stands motionless on the edge of the 10-m platform. If the diver's mass is 65 kg, what is his gravitational potential energy relative to the surface of the water? (8 marks) 12. What happens to the diver's gravitational potential energy on the way toward the surface of the water? (4 marks)

11 8c POST-TEST 13. A diver, with a mass of 60.0 kg, has 2.94 kj of gravitational potential energy on top of the 5-m platform. How much work did the diver do an her body to get up to the 5.00 m level? (3 marks) Calculate her speed just before she enters the water. (Ignore air resistance.) (8 marks) 14. Prior to serving, a tennis player tosses the ball vertically up. If the ball leaves the player's hand with a speed of 5.50 m/s, calculate the maximum height above the player's hand the ball will reach before coming back down. (Ignore air resistance.) (8 marks) 15. The ratio change in distance to change in time defines. (3 marks) 16. Drawing the best-fit line for data plotted on a graph averages. (3 marks) 17. The ratio of the change in the vertical variable, the rise, to the change in the horizontal variable, the run, of a graph is equal to the. (3 marks)

12 8d POST-TEST 18. Use the following data to plot a distance versus time graph on the grid provided. Calculate the speed of the object. (8 marks) Time (s) Distance (m)