Physics 20 Energy Worksheets

Transcription

1 Worksheet 1: Work = F x d 1) It is often possible to do work in pushing an object without transferring any energy to the object being pushed. What happens to the energy associated with the work done in this case? 2) A 20.0 N object is lifted at a constant velocity from the floor to a height of 1.50 m. How much work is done on the object? (30.0 J) 11) A 1165 kg car travelling at 55 km/h is brought to a stop while skidding 38 m. Calculate the work done on the car by the frictional forces. (-1.4 x 10 5 J) 12. How much work is done when an object is moved 3.8 m at 40 to a 6.2 N force and 35 to a 7.1 N force? [40 J] 3) A 15.0 N object is moved horizontally 3.00 m across a level floor using a horizontal force of 6.00 N. How much work is done on this object? (18.0 J) 4) A 2.20 N object is held 2.20 m above the floor for 10.0 s. How much work is done on the object? (0) 5) A 10.0 kg object is accelerated horizontally from rest to a velocity of 11.0 m/s in 5.00 s by a horizontal force. How much work is done on this object assuming the object is on a frictionless surface? (605 J) 6) A 90.0 N box is pulled 10.0 m along a level surface by a rope. If the rope makes an angle of 20.0 with the surface, and the force exerted through the rope is 75.0 N, how much work is done on the box? (705 J) 13) A student exerts a horizontal force of 225 N to push a heavy box along the school corridor at a constant speed of 2.00 m/s. How much work does she do in 15.0 s? (6.75 x 10 3 J) 14) If a 50.0 kg box is pushed 10.0 m at a constant speed along a horizontal surface by a force of 65.0 N acting at a 30.0 angle as shown in the diagram, how much work is done on the box? 7) A 60.0 kg student runs at a constant velocity up a flight of stairs. If the vertical distance of the stairs is 3.2 m, what is the work done against gravity?(1.9 x 10 3 J) 8) A 20.0 kg box is pulled horizontally 9.0 m along a level frictionless surface at a constant velocity. How much work is done on the box? (0) 9) An 80.0 kg box is pushed at a constant velocity along a frictionless incline as shown in the diagram. To find the work done, should you use the force of 65.0 N or should you find the horizontal component of 65.0 N? Why? (563 J) 15) Given the following force-displacement graph of an object being pulled along a level surface, determine the work done in moving the object 16.0 m.(56 J) How much work is done on the box in moving it from the bottom to the top of the incline? (5.5 x 10 3 J) 10) A 25.0 kg object is accelerated from rest through a distance of 6.0 m in 4.0 s across a level floor. If the force due to friction between the object and the floor is 3.8 N, what is the work done in moving the object?(1.4 x 10 2 J) 16) Given the following force-displacement graph of an object moving along a horizontal surface, determine the work done in moving the object 8.0 m. (-26 J) 1

2 Worksheet 2: Potential Energy 1) In which of the following cases does potential energy increase, and in which cases does potential energy decrease? a) A positive charge is brought closer to a negatively charged body. b) The South pole of a magnet is moved away from the South pole of a similar magnet. c) A body is raised further above the surface of the earth. d) A spring is stretched. e) The North pole of a magnet is brought closer to the South pole of a similar magnet. f) A weight is place on top of a large spring. g) A space capsule decreases the size of its orbit around the earth. h) A negatively charged body is moved in a circle around a positively charged body. 2) A 25.0 N object is held 2.10 m above the ground. What is the potential energy of the object with respect to the ground? (52.5 J) 3) An uncompressed spring is 20.0 cm in length. What is the potential energy of this spring when an average force of 65.0 N compresses it to a length of 13.5 cm? (4.2 J) 4) A 2.75 kg box is at the top of a frictionless incline as shown in the diagram. What is the potential energy of the box with respect to the bottom of the incline? (189 J) 5) The bob of a pendulum has a mass of 2.0 kg. This bob is pulled sideways so that it is 0.75 m above the table top. What is the potential energy of the bob with respect to the equilibrium position? (4.9 J) If the force applied along the incline is 6.00 x 10 2 N, what is the potential energy of the object when it is at the top of the incline with respect to the bottom of the incline? (1.2 x 10 4 J) Worksheet 3: Kinetic Energy 1) A 3.0 kg object is traveling at a constant speed of 7.5 m/s. What is the kinetic energy of this object? (84 J) 2) The kinetic energy of a 20.0 N object is 5.00 x 10 2 J. What is the speed of this object? (22.1 m/s) 3) A 10.0 N object is accelerated uniformly from rest at a rate of 2.5 m/s 2. What is the kinetic energy of this object after it has accelerated a distance of 15.0 m? (38 J) 4) An 8.0 kg object is dropped from a height of 7.0 m. What is the kinetic energy of this object as it hits the ground? (5.5 x 10 2 J) 5) A 10.0 N object has kinetic energy of 3.00 x 10 2 J. What is the speed of the object? (24.3 m/s) 6) By what factor must the kinetic energy of an object be increased to cause its speed to triple? (9 times) Worksheet 4: Elastic (Spring) Potential 1) List three common devices that, like a stretched or compressed spring, can store potential energy when temporarily deformed. 2) An engineer is designing the suspension system for a car. He decides that the coil spring used should compress 4.00 cm when a force of 1000 N is applied a) What is the spring constant of the spring b) If the spring is compressed a distance of 14.0 cm, what force was exerted on it? (2.50 x 10 4 N/m, 3.50 x 10 3 N) 3) The following data was generated from an experiment in which a spring was stretched to different lengths by hanging several masses on a spring: 6) A 2.00 x 10 2 kg object is pushed to me top of an incline as shown in the diagram. x (m) Force (N) a) Use your graphing calculator to determine the best approximation of the spring constant of the spring. (Plot Force as the responding variable) b) How much energy will be stored in the spring if it is stretched to a length of 37.0 cm? (352 N/m, 24 J) 2

3 4) The following data was generated from an experiment in which a spring was stretched by hanging several different masses on a spring: Mass (kg) Length of Spring (cm) a) Use your graphing calculator to determine the best approximation of the spring constant of the spring. b) How much energy will be stored in the spring if it is stretched to a length of cm? (55.1 N/m, J) 5) A 0.60 kg mass is vibrating at the end of a spring. If the spring constant is 26 N/m, and the maximum displacement of the mass is 0.15 m a) How much energy is stored in the spring? b) If the spring contracts to 0.03 m, what is the change in elastic potential of the spring? (2.93 x 10-1 J, x 10-1 J) 6) The elastic constant for a spring is 750 N/m a) How far must you stretch it from equilibrium in order to store 45.0 J of elastic potential in it? b) If you want to double the elastic potential of the spring, how much farther would you need to stretch it? (34.6 cm, 14.3 cm) 7) An object vibrates at the end of a horizontal spring (k = 32 N/m) along a frictionless surface. If the object's potential energy is 4.5 J, what is the displacement? (0.53 m) 8) An object vibrates at the end of a horizontal spring (k = 28 N/m). If the object's displacement is 0.18 m, what is its potential energy? (0.45 J) 9) A 0.46 kg object vibrates at the end of a horizontal spring (k = 12 N/m). If the object's kinetic energy is 7.3 J, what is its speed? (5.6 m/s) 10) How much work was done on a spring (k = 76.0 N/m) in stretching it 3.50 cm? ( J) 11) A force of 8.2 x 10 1 N is required to hold a Hooke's Law rubber band with a stretch of 2.7 cm. What is the potential energy stored in the band? (1.1 J) 12) A 75 g object vibrates at the end of a frictionless spring (k = 5.0 N/m). If the maximum displacement of the object is m, what is the maximum acceleration? (5.3 m/s 2 ) Worksheet 5: Work-Energy Theorem 1) How much work is required to accelerate a 1.10 x 10 3 kg car from rest to 5.00 km/h along a level frictionless surface? (1.06 x 10 3 J) 2) What was the average net force exerted on a 4.5 x 10-3 kg bullet by a gun while accelerating it from rest to a speed of 1.0 x 10 3 m/s through a displacement of 0.70 m? (3.2 x 10 3 N). 3) A student throws a 1.0 kg rock vertically into the air with an average force of 18 N. If this force was exerted through a displacement of 0.30 m, what was the speed of the rock as it left the student's hand? (2.2 m/s) 4) A spring exerts an average horizontal force of 23.0 N on a 0.12 kg pebble while acting through a displacement of 5.0 x 10-2 m. What is the speed of the pebble as it leaves the spring? (4.4 m/s) 5) A force of friction of 3.2 N acts on a 1.1 kg puck while it is sliding along a horizontal surface. If the initial velocity of the puck was 7.5 m/s, how far will the puck travel before coming to rest? (9.7 m) 6) A 0.65 kg puck is sliding along a horizontal surface at a speed of 2.0 m/s. If the puck comes to a stop in 5.5 m, what is the force of friction acting along the surface? (0.24 N) 7) A student throws a 1.1 kg rock vertically into the air while accelerating it through a displacement of 0.36 m. If the rock leaves the student's hand at a speed of 4.2 m/s, what was the average force exerted by the student on the rock while accelerating it? (38 N) 8) A 15 kg box is pulled along a horizontal frictionless surface by a horizontal force of 35 N. If the box accelerates uniformly from rest, how fast is it travelling after 3.5 m? (4.0 m/s) 9) How much energy is needed to accelerate a 1.1 x 10 3 kg object along a horizontal frictionless surface from 15 km/h to 25 km/h in 5.0 s? (1.7 x 10 4 J) Worksheet 6: Conservation of Energy 1) A heavy object is dropped. If this object reaches the floor at a speed of 3.2 m/s, from what height was it dropped? (0.52 m) 3

4 2) A heavy object is dropped from a vertical height of 8.0 m above the ground. What is the speed of this object as it hits the ground? (13 m/s) 3) A heavy object is dropped from the top of a building. If this object hits the ground with a speed of 37.0 m/s, how tall was the building? (69.8 m) What is the speed of the pendulum bob as it passes through the equilibrium position? (2.2 m/s) 10) A system containing a frictionless pulley is described in the diagram. If this system is released, at what speed does the 12.0 kg object hit the floor? (3.1 m/s) 4) A 4.0 N box slides along a frictionless surface, while travelling at a speed of 2.1 m/s. This object hits an ideal spring as shown in the diagram compressing it 2.3 x 10-2 m. What is the spring constant of the spring? (3.4 x 10 3 N/m) 5) A heavy object is thrown vertically down from the top of a 1.3 x 10 2 m building at a speed of 11.0 m/s. What is the velocity as it hits the ground? (52 m/s) 6) A 0.20 kg mass vibrates at the end of a horizontal spring (k = 15 N/m) along a frictionless surface. What is the maximum displacement of the mass if it reaches a maximum speed of 0.12 m/s? (1.4 x 10-2 m) 7) A 0.40 kg mass vibrates at the end of a horizontal spring along a frictionless surface reaching a maximum speed of 0.50 m/s. If the maximum displacement of the mass is 0.11 m, what is the spring constant? (8.3 N/m) 11) A heavy box slides down a frictionless incline as shown in the diagram. If the box starts from rest at the top of the incline, what is its speed at the bottom? (10.8 m/s) 12) A roller coaster car starts from rest at point A. 8) A heavy box slides down a frictionless incline as shown in the diagram. What is the speed of this car at point C, if the track is frictionless?(13 m/s) If the box starts from rest at the top of the incline, what is its speed at the bottom? (8.9 m/s) 9) A pendulum is dropped from the position as shown in the diagram 0.25 m above the equilibrium position. 13) A 2.5 kg object is dropped from a height of 10.0 m above the ground. Calculate the speed of the object as it hits the ground. (14 m/s) 14) A student is running at a speed of 3.5 m/s and grabs a long rope that is hanging vertically from a tree. How high can the student swing? (0.62 m) 4

5 15) A pendulum is 1.20 m long. What is the speed of the pendulum bob when it passes through its equilibrium position if it is pulled aside until it makes a 25.0 angle to the vertical? (1.49 m/s) 3) A constant force of 85 N accelerates a 12 kg box from a speed of 2.0 m/s to a speed of 8.0 m/s as it travels 15 m along a horizontal surface. What is the coefficient of friction between the two surfaces? (0.52) 4) A 1.50 x 10 2 N force is pulling a 50.0 kg box along a horizontal surface. The force acts at an angle of 25.0 as shown in the diagram. 16) A 45 kg student runs with a speed of 2.0 m/s off a horizontal ledge that is 5.0 m above a swimming pool. Calculate the speed of the student when she hits the water. (9.9 m/s) 17) A 1.0 kg box slides without friction around the loop-theloop apparatus as shown in the diagram. (*note that F N is not mg in this problem) If this force acts through a displacement of 12.0 m, and the coefficient of friction is 0.250, what is the speed of the box, assuming it started from rest? (3.74m/s) 5) If the object starts from rest at point A, and the radius of the loop is 0.75 m, what is the speed of the box at point B? 6.3 m/s) Worksheet 7: Energy Questions with Friction 1) A 12 kg box initially at rest slides from the top of an incline as described in the diagram. If the force of friction along the incline is 5.0 N, what is the speed of the object as it reaches the bottom of the incline? (1.0 x 10 1 m/s) 2) A 45.0 kg box initially at rest slides from the top of an incline as described in the diagram. If the box reaches the bottom of the incline at a speed of 5.0 m/s, what is the force of friction on the box along the incline? (1.3 x 10 2 N) Calculate the mechanical energy converted to thermal energy when a 8.0 kg box is pushed 5.0 m along a 30.0 incline at constant velocity by an average force of 75 N parallel to the incline. (1.8 x 10 2 J) 6) A 45.0 kg box is pulled across a horizontal surface by a constant horizontal force of 192 N. If the box starts from rest, and the coefficient of friction is 0.35, what is the final speed of the box when it has travelled 8.0 m? (3.7 m/s) 7) A 2.5 kg box slides from rest m down a 30.0 incline as shown in the diagram. If the force of friction acting along the incline is 3.2 N, what is the speed of the box when it reaches the bottom of the incline? (2.5 m/s) 8) An 18.0 N box slides from rest m down a 30.0 incline as shown in the diagram. If the box reaches the bottom of the incline with a speed of 1.30 m/s, what was the force of friction along the incline? (6.93 N) 9) A 115 N box slides 50.0 m along a 40.0 incline as shown in the diagram. If the force of friction along the incline is 35.0 N, what is the change in the box's gravitational potential energy? (3.70 x 10 3 J) 5

6 10) A 75.0 kg box, starting from rest, slides down the incline described in the diagram. If the force due to friction along the incline is 17.9 N, a) How much thermal energy was produced? HINT: When work is done to overcome friction, what happens to some of the mechanical energy? (1.4 x 10 2 J) b) What is the velocity of the box at the bottom? (9.7 m/s) 11) A 45.0 kg student starts from rest and slides 28.0 m down a water slide. What is the speed of the student at the bottom if the force of friction along the slide is 55.0 N and the vertical drop is 5.00 m? (5.45 m/s) Worksheet 8: Absolute Potential Energy Use the following information for the problems below mass of earth = 5.98 x kg mass of the sun = 1.99 x kg mass of the moon = 7.35 x kg radius of the earth = 6.37 x 10 6 m radius of the sun = 6.96 x 10 8 m radius of the moon = 1.74 x 10 6 m distance earth to moon = 3.84 x 10 8 m distance earth to sun = x m 1. What is the absolute potential energy of the moon with respect to the earth? (-7.63 x J) 2. What is the absolute potential energy of the sun with respect to the earth? (-5.31 x J) 3. Answer the following questions concerning absolute potential energy. a) What is the change in the absolute potential energy of a 1500 kg rocket as it rises from the earth s surface to a position 150 km above the earth's surface? ( 2.16 x 10 9 J) b) What value do you get if you use the formula E p = mgh? (2.21 x 10 9 J) c) Which of these values is more 'correct'. Explain your choice. d) The rocket drops from it s position in a) to a height of 25 km above the earth. By how much has its potential energy changed. (-1.79 x 10 9 J) 4. A 4.00 x 10 3 kg object is lifted from the earth's surface to an altitude of 3.2 x 10 5 m. How much work does this require? (1.2 x J) 5. A 50 kg object is 100 km above the earth's surface and moves to a position 50 km above the earth's surface. How much does its potential energy change? (-2.4 x 10 7 J) 6. A spacecraft of mass 470 kg rests on the surface of an asteroid of radius m and mass kg. How much energy must be expended so that the spacecraft may rise to a height of m above the surface of the asteroid? (30 J) 7. A kg rocket rests on the surface of the Earth. To what maximum distance from the Earth's centre would the rocket be lifted if 2.5 x J of work were done on it? (9.36 x 10 6 m) 8. What minimum energy is required to take a stationary kg satellite from the surface of the Earth and put it into a circular orbit with a radius of m and an orbital speed of m/s? (Ignore Earth's rotation.) (1.2 x J) 9. Show that the velocity of escape from a parking orbit 500 km above the earth is about 3.88 x 10 4 km/h. 10. Calculate the velocity of escape from an orbit 500 km above Jupiter. (6.01 x 10 4 m/s 11. Calculate the velocity of escape from an orbit 500 km above Mars. (4.70 x 10 3 m/s) 6

7 12. If a satellite is in geostationary orbit around the Earth, what is its escape velocity? (4.35 x 10 3 m/s) 13. A kg satellite travels around the earth in a stable orbit with a radius of 1. 3 x10 7 m a) What is the speed of the satellite in this orbit? (5.5 x 10 3 m/s) b) What is the value of the escape velocity from this orbit? (7.83 x 10 3 m/s) Worksheet 9: Power 1) What is the power output of a machine which applies a force of 2.50 x 10 4 N for 12.0 s in pulling a block through 60.0 m? (1.25 x 10 2 kw) 2) How much work can a 2.00 HP motor do in 2.00 h? (1.07 x 10 7 J) 3) A shot-putter accelerates a 7.30 kg shot from rest to 15.0 m/s. If this motion takes s, what average power was developed? ( 1.64 x 10 3 W ) 4) A truck gained a kinetic energy of 4.2 x 10 4 J in 14.0 s. What was its minimum power output? (3.0 kw) 5) What power is exerted by a weight lifter, who clean and jerks 350 kg from the floor to a height of 2.14 m in 1.5 s? How many horsepower has the weight lifter produced? ( 4.9 x 10 3 W or 6.6 HP) 6) The battery of your calculator can provide energy at the rate of J/s for 275 h. If this energy could be used to accelerate a kg baseball from rest, what speed would the ball reach? (629 m/s) 7) A winch of power output 5.0 kw can raise a crate with a steady maximum speed of 10.0 m/s. What is the mass of the crate? (51 kg) 8) A 70.0 kg hiker climbs to the top of a 4.20 x 10 3 m high mountain. The climb is made in 4.00 h starting at an elevation of 3.20 x 10 3 m. a) How much work is done against gravity? b) What is the average power output? (6.87 x 10 5 J) (47.7 W) 9) The maximum output power of an electric motor is W. It is used to operate a conveyer belt carrying sand. The belt is 12.0 m long and the sand is lifted 4.00 m by the belt. What mass of sand can be allowed to flow onto the conveyer belt every minute so that the motor will not be over - loaded. Ignore any friction of the conveyer belt. (612 kg) 10) An electric motor raises a 1.5 x 10 2 kg block at a steady speed of 2.0 m/s. Find the minimum power output of the motor. (2.9 x 10 3 W) 11) What is the shortest amount of time it could possibly Take an average horse, who can develop HP, to pull a kg weight up a frictionless incline plane if the rise of the plane is 3.00 m? (13.8 s.) Worksheet 10: Efficiency 1) A machine operates at a power consumption of 3.5 kw for 10.0 minutes. In the process it produces 5.0 x 10 5 J of heat energy. Estimate the machine's efficiency. (76 %) 2) An electric power saw operates at a power consumption of 0.77 kw for 3.6 h per day, 5 days per week. In the process, it produces 1.1 x 10 7 J of heat energy. Calculate the saw's mechanical efficiency. (78%) 3) A car in a long distance rally requires an average force of 5.15 x 10 3 N while travelling at 100 km/h and that the gasoline used over a 50.0 h period contains 1.3 x J of chemical energy, what's its efficiency of the car engine? (19.8 %) 4) Bill replaced a 60 W filament bulb with an energy efficient alternative rated at 11 W. Both bulbs give out 9.0 W of light. Find their efficiencies. (15 %, 82%) 5) A kg toy car is pushed back against a spring-based launcher as shown in Diagram 1. Diagram 2 shows a graph of the force required to compress the spring m a) What is the work done in compressing the spring? b) Assuming no losses due to heat, what maximum speed is reached by the toy car when it is released? c) If in fact, the maximum kinetic energy of the car is 0.78 J, what is the efficiency of the spring-based launcher? (0.90 J, 7.7 m/s, 87%) 6) An electric motor pumps water from the bottom of a 55.0 m well to a household reservoir where it enters the reservoir at 3.50 m/s. If the pump is 65% efficient and needs to pump 1.50 L/s, what is the minimal electrical power the pump must have. ( 1 L = 1 kg for water, 1.26 x 10 3 W) 7

8 7) The most efficient solar cells devised have an efficiency of 40.8%. If A 3.00 m 2 cell can produced a photocurrent of V, what solar energy must be falling on the cell each second? (441 J/s) Worksheet 11: Simple Harmonic Motion 1. A...B...C...D...E An object moves with a simple harmonic motion between the points marked A and E. 5. A ball is oscillating on a spring with a maximal displacement of 15 cm and a frequency of 13 Hz. a) What is the period of this motion? (0.077 s) b) What is the mass of the ball if the spring constant is 3.33 x 10 4 N/m (5.0 kg) 6. Ignoring the damping introduced by the shock absorbers, explain how the number of passengers in a car affects the vibration frequency of the car's suspension system. (as mass increases f decreases) a) What is its equilibrium position. b) At what point or points does it have a maximum speed? c) At what point or points does it have maximum acceleration? d) When the object moves from B toward A, is the direction of the acceleration positive (to the right) or negative (to the left)? e) At point E, is the force acting on the object positive, negative, or zero? f) If the distance between each two letters above is 1 cm, what is the amplitude of the vibration? g) What is the displacement at point D? h) If the object moves from A to E in 1 s, what is the period of vibration? i) What is the frequency of the vibration? a) C b) C c) A, E d) positive e) negative f) 2 cm g) 1 cm h) 2 s i) 0.5 Hz (a) the equilibrium position (b) the amplitude (c) the displacement when the object is at the 20 cm mark, the 24 cm mark, the 26 cm mark, and the 30 cm mark. (a) 26 cm b) 6 cm c) +6 cm, +2 cm, 0 cm, -4 cm) 3. The figures shows the shadow of an object in circular motion as the shadow moves in simple harmonic motion. Where on the shadow's path is : 7. A spring stretches by m when a 2.8 kg object is suspended from its end. How much mass should be attached to this spring so that its frequency of vibration is f = 3.0 Hz? (4.3 kg) 8. A 1.1 kg object is suspended from a vertical spring whose spring constant is 120 N/m. a) Find the amount by which the spring is stretched from its unstrained length. (9.0 x 10-2 m) b) The object is pulled straight down by an additional distance of 0.20 m and released from rest. Find the speed with which the object passes through its original position on the way up. (2.1 ms/) 9. If you double the amplitude of a simple harmonic motion, how does this change the frequency, maximum velocity, maximum acceleration and the total mechanical energy of the medium particles? (f = same, v max doubles a max doubles, E mech four times ) 2. A meter stick is held vertically behind an object on spring. The object vibrates from the 20. cm mark on the stick to 10. the What should be the length of 32 cm mark. Find : a pendulum for which the period is to be 1.00 s in a place where g = 9.81 m/s? (0.25 m) 11. A pendulum makes 200 complete swings in 2 min 30 sec. Find the period and frequency. (T = 0.8) (T = 0.8 s f = 1 Hz) 12. A pendulum with a length of 200 cm vibrates with a period of 2.82 s. What is the value of the acceleration of gravity in that location? (9.93 m/s 2 ) a) the velocity equal to zero b) the acceleration equal to zero? 4. A 2.0 N force was used to hold a 300 g object attached to a spring 10 cm from equilibrium. The object is then pulled down, released and allowed to vibrate. a) What is the spring constant? (20 N/m) b) What is the frequency and period of the object? (1.3 Hz) 13. A pendulum has a length of 150 cm and a bob of 100 g and vibrates with a period of T = 2.44 s. a) What is the value of the acceleration of gravity in that location? (9.93 m/s 2 ) b) The pendulum is displaced to the side through an angle of 10.0 o. What is the restoring force on the bob? (0.172 N) c) What is the velocity of the bob as it moves through the equilibrium point of its vibration? (0.673 m/s) 8