PHY 1401 – General Physics I Final Review Questions Useful Information: g = 9.81 m/s/s, G = 6.67 × 10-11 Nm2/kg2, Me = 5.98 × 1024 kg, Re = 6.37 × 106 m, 1 kg = 1000 g, 1 km = 1000 m, 1mm = .001 m Ch. 1 1. (15 points) a) Explain how you have to do unit conversions which include exponents on the units. b) Convert 27 yd3 to ft3. c) Write a problem for the following unit conversion. m 1km 3600s 15 s 1000m 1hr Ch. 2 2. (10 points) Consider the motion diagram shown below. a) Describe the type of motion shown. b) Explain your reasoning.

3. (15 points) Consider the graph shown below. a) Find the average velocity for the time intervals 0 to 30 minutes, 30 to 50 minutes, and 50 to 120 minutes. b) What is the acceleration for each of the intervals? Explain you reasoning. c) What is the meaning of the distance being negative on the time interval form 110 to 120 minutes?

Distance (km)

Distance vs. Time 70 60 50 40 30 20 10 0 -10 0 -20

20

40

60

80

100

120

140

Time (minutes)

4. (15 points) A car sits at a stoplight. When the light turns green the car accelerates uniformly at 3 m/s/s for a distance of 65 m. a) Sketch the situation. b) What is the speed of the car after it has traveled 65 m? c) How long does it take the car to travel the 65 m? Ch. 3 5. (10 pts) A hiker walks 4.5 miles at an angle of 20° S of E and then hikes 3.5 miles at an angle of 60° S of E. a) Sketch a vector diagram showing the net displacement of the hiker. b) Find the magnitude and direction of the hiker’s net displacement.

6. (15 points) A student stands at the edge of a 75 m tall building and tosses a ball horizontally with an initial velocity of 22 m/s. a) Sketch the situation. b) Sketch the trajectory of the ball. c) Find the time the ball is in the air. d) Find the horizontal distance from the edge of the building at which the ball lands. 7. (10 points) A student is moving in a slow cart. She tosses a ball up into the air. a) Neglecting air resistance, describe the path of the ball as seen by the student in the cart? b) A second student watches the cart go by. Describe the path of the ball as seen by the observer on the ground. c) Draw a vector diagram relating the velocity of the ball as it is going up as seen by the observer in the cart and the observer on the ground. Ch. 4 8. (15 pts) An 1100 kg car travels 10 m in 5.0 s and then another 10 m in the next 5.0 s. a) What is the net force acting on the car? Explain your reasoning. b) Find the average velocity of the car? c) Find the car’s average acceleration. 9. (20 pts) A block is sliding with an initial velocity of 5.0 m/s across a rough surface with a coefficient of kinetic friction μk = .20. a) Sketch the situation. b) Draw a free body diagram for the block. c) Find the acceleration of the block. d) Find the distance traveled by the block before it comes to rest and the time it takes the block to come to rest. 10. (10 points) One block sits on top of a second which in turn sits on a table. a) Sketch the situation. b) Draw a free body diagram for each of the blocks. c) Indicate the action/reaction pair by placing an x on each of the forces. 11. (15 pts) A 1.25 kg mass sits on a horizontal frictionless table. A cord runs over a pulley connecting the 1.25 kg mass to a .500 kg mass which is suspended vertically off the end of the table. a) Draw free body diagrams. b) Find the tension in the cord and the acceleration. c) Find the work done on the 1.25 kg mass after it moves 3.00 m. d) What force does the work? e) If the masses start form rest, how long will it take to travel 3.00 m? Ch. 6 12. (10 pts) A student carries around a 5 kg bowling ball horizontally a distance of 10 m. a) Draw a free body diagram for the bowling ball. b) What is the work done by the student against gravity? c) How does your answer change if instead of walking, the student runs the 10 m? 13. In the high jump, the kinetic energy of an athlete is transformed into gravitational potential energy. a) Sketch a before and after picture of the athlete at the beginning and at the top of the jump. b) What conservation law holds and why? c) With what minimum speed must the athlete leave the ground in order to lift his center of mass 2.10 m and cross the bar with a speed of .700 m/s?

14. (8 pts) A student asserts that “When I drop a ball from a height of 3.0 m, I measure the speed of the ball to be less at the bottom than predicted. Thus the law of conservation of energy doesn’t hold.” What if anything is wrong with the student’s statement? If it is correct, state why it is correct. If it is wrong, correct the student’s statement. 15. (10 pts) A 15.0 g ball, initially at rest, is pressed against a horizontal spring with spring constant k = 250 N/m compressing the spring by 2.0 cm. a) Draw before after pictures of the situation. b) Find the speed of the ball when it is released. c) Explain your reasoning Ch. 7 16. (30 pts) A 6500 kg railroad car moving at 4.0 m/s couples with a second 7500 kg car initially at rest. a) Sketch before and after pictures of the situation. b) What assumptions do you need to make so that conservation of momentum holds? c) Find the final velocity of both cars. d) Find the ratio of final to initial kinetic energy? Explain why this ratio should be less than 1. e) What is the change in momentum of the second car? f) If the collision lasted for 0.2 s, what is the average force exerted on the second car? g) How does it compare to the average force exerted on the first car. Explain your answer. 17. A 15.0 g bullet strikes and becomes embedded in a 1.10 kg block of wood placed on a horizontal surface just in front of the gun. If the coefficient of kinetic friction between the block and the surface is .250 and the impact drives the block a distance of 9.50 m before it comes to rest, what was the initial speed of the bullet? 18. (10 pts) A small cart of mass 125 g is traveling west at 2.0 m/s. It is tapped by a hammer and ends up traveling west at 3.0 m/s. a) If the length of the tap was .20 s, find the average force exerted on the cart. b) On the axes below sketch graphs of the force vs. time and velocity vs. time. Use the same time scale for both. Force

time V

time

Ch. 5 and 8 19. (10 pts) A 1200 kg satellite is in a circular orbit 500 km above the earth. a) Sketch the situation. b) Draw a free body diagram for the satellite. c) Find the speed of the satellite. 20. (10 pts) Pluto orbits the sun with a period of 249 years. a) Find its mean distance from the sun in units of au. b) What fraction of the area of its orbit has Pluto swept out in the lifetime of a 25 year old student? c) Does this mean that Pluto has traveled through that fraction of the distance of its orbit in the lifetime of the student? 21. (20 pts) A disk of mass 2.5 kg and radius .50 m rolls down a plane of height 5.0 m. a) Sketch before and after pictures of the situation. b) What assumptions do you need to make to use conservation of mechanical energy? c) If the disk rolls without slipping, what is its speed at the bottom of the hill. d) What is the ratio of translational to rotational kinetic energy? 22. (20 pts) Two forces are applied to a disk of mass 1.5 kg and radius .65 m which rotates on a frictionless pivot located at the center of mass of the disk. a) Find the net torque on the disk. b) Find the angular acceleration of the disk. c) If the disk starts from rest, find its angular velocity after 5 s. d) Find the angle through which it turns during the 5 s.

5N

10 N 23. (15 pts) A hoop of mass 2.0 kg and radius 1.5 m is rotating at an initial angular velocity of 5.4 s-1. A disk with the same mass and radius is dropped onto the hoop so that the centers coincide. a) Draw before and after pictures of the situation. b) What conservation law applies here? What assumptions do you need to make to apply it? c) Find the final angular velocity.

24. A helicopter rotor blade can be considered a long thin rod as shown. a) If each of the three rotor helicopter blades is 3.75 m long and has a mass of 160 kg, calculate the total moment of inertia of the three rotor blades about the axis of rotation. b) How much torque must the motor supply to bring the blades to a speed of 5.0 rev/s in 8.0 s? (For a long thin rod rotating about one end, I = 1/3 ML2) c) Assuming constant angular acceleration, through what angle do the rotor blades turn as they go from rest to 5.0 rev/s?

3.75 m

25. A solid sphere of mass 2.50 kg and radius 10.5 cm starts from rest and rolls without slipping down a 4.50 m long plank inclined at an angle of 38.5. a) Draw a sketch. b) Find the speed of the sphere at the bottom of the plane. c) Find the ratio of rotational KE to translational KE at the bottom. (I= 2/5 MR2) 26. (15 pts) a) For the bar in static equilibrium shown below, how will the sum of F1 + F2 compare to the mass of the bar. Why? b) Will F1 and F2 be the same? Explain. c) If the bar is 2.0 m long, has a mass of 5.0 kg, and F2 is applied 1.7 m from the left end, find F1 and F2. F1

F2

Ch 9 28. A student makes the following statement. “If I double the amount of metal I have, the density will double.” Is the student correct? Explain 29. a) What is the difference in blood pressure between the top of the head and the bottom of the feet of a 1.60 m tall person standing vertically? b) Express your answer in mm–Hg. 30. a) Draw a picture and give a one sentence explanation of your reasoning for the following. b) How high would the atmosphere extend (assume P = 0 atm at the top) if it were of uniform density air = 1.29 kg/m3. (Patm = 1.013 x 105 Pa)

31. A .025 m3 block of steel is dropped into a beaker of water. a) Sketch the situation. b) Will the piece of steel sink or float? Explain. c) Sketch a free body diagram for the block. d) Find the buoyant force on the piece of steel? e) Find the acceleration of the block in the water. Ch. 10 27. (10 pts) A nylon tennis string on a racket is under tension of 250 N. a) Sketch the situation. b) If its diameter is 1.00 mm, by how much is it lengthened from its unstretched length of 30.0 cm? c) If the diameter of the string is increased, will the string stretch more, less, or the same. Explain your answer. Enylon = 5  109 N/m2 2. A 2.0 kg mass sits on a frictionless horizontal surface and is attached to the wall by an adjustable, pre-stretched string with a spring constant The mass is initially oscillating. a) For each of the following describe whether the frequency of oscillation will increase, remain the same, or decrease. Explain your reasoning. i) The mass is tapped in the direction of travel as it passes through the equilibrium point. ii) The amplitude is increased when the mass reaches a turning point. iii) An additional mass is added as the mass reaches the turning point. iv) The spring is stiffened as the mass passes through the equilibrium point. b) For the initially specified situation, find the frequency of oscillation of the spring. c) If the initial displacement is .05 m, find the speed of the oscillator as it passes through the equilibrium point. Ch. 13 32. A balmy spring day has a temperature of 85 °F. a) Convert that temperature to celsius and kelvin. b) What physical property of the gas in the atmosphere changes as the temperature cools off to 55 °F that night? 33. (5 pts) A student states, “If an object at a temperature of 75 °C has twice the mass of a second object at 75 °C, then it has twice the heat.” Explain what is wrong with the student’s statement. 37. A 10 m long steel beam is at a temperature of 10 °C. a) Sketch the situation and indicate the change of length. b) How much will the beam change in length if it is cooled to -10 °C. 38. (5 pts) Super Invar, an alloy of iron and nickel, is a strong material with a very low coefficient of thermal expansion ( = .20 x 10-6 /C. A 2.0 m long tabletop of this alloy is used for sensitive laser measurements where extremely high tolerances are required. How much will this alloy table expand along it length if the temperature increases by 5.0C? 39. Long steam pipes often have a section in the shape of a U. Why? Ch. 14 40. A 250 g block of metal at a temperature of 250 °C and with specific heat .081 cal/(g °C) is dropped into 100 g of water at an initial temperature of 25 °C.

a) Sketch the situation. b) Find the final temperature. 41. (10 pts) 195 g of a substance is heated to 330°C and then plunged into an insulating container holding 250 g of water at a temperature of 18 °C. If the final observed temperature is 38 °C, what is the specific heat of the substance? (c = 1 cal/(g°C) for water) 42. A 150 block of ice is initially at –10 C. Heat is added at a constant rate until eventually steam at 110 C is produced. a) Draw a heating curve for the process. b) Assuming no heat is lost to the environment, find the total heat added. 43. A cube of ice is taken from a freezer at –8.50C and dropped into 305 g of water initially at 25 C° in a well-insulated styrofoam container of negligible mass. The final situation is that the cup is filled with water a t 17.0C. What was the mass of the ice cube? 44. The air cools off at night more quickly when the weather is clear than when it is cloudy. Explain. 45. The red giant star Betelgeuse has a radius of r = 3.1 x 1011 m. Its surface temperature is 2800 K. Assuming it is a perfect emitter e = 1, what is the power output of the star. (Hint: A = 4πr2) 46. Explain using the concept of latent heat and internal energy why a hot pan of water cools as it evaporates? Ch. 15 47. A piston contains .020 m3 of an ideal gas at pressure of 1 atm. Heat is added isothermally so that the volume of the piston doubles. a) Sketch a PV diagram for the process. b) How much work is done by the piston? c What is the change in internal energy of the gas? Explain. d) How much heat was added? 48. An ideal gas has its pressure cut in half slowly, while being kept in a container with rigid walls. 265 kJ of heat left the gas during the process. a) What variable will remain constant? b) Draw a PV diagram for the process. c) How much work is done on the gas for this process? d) What is the change in internal energy of the gas? 51. A process is carried out on an ideal gas which has the PV diagram shown in duplicate below. a) On the first diagram, shade the area corresponding to the net work done in going from A to B. b) On the second diagram, shade the area corresponding to the net work done in going from A to B to C. c) For which process A to B or A to B to C is more net work done. Explain why.

A

P

A

P B

B

C

C

V

V

Ch. 11 and 12 52. A sonic motion detector emits a longitudinal pulse of sound at a frequency of 40 kHz. a) Sketch a picture of the pulse. b) What is the wavelength of the sound wave? c) The pulse is reflected from an object and the return pulse is detected .075 s after being emitted. What is the distance to the object? 53. (10 points) A transverse wave pulse is directed at a fixed boundary. a) Sketch the incident and reflected pulses. b) What is the phase relationship between the incident and reflected pulses? 54. (10 points) The sketches below each show two pulses directed at each other. a) For each, sketch diagrams showing the pulses when they interfere and after they interfere. b) For each indicate whether the interference is constructive or destructive and indicate the phase relationship between the pulses.

a)

b)

55. (15 pts) A string of length .60 m is fixed at both ends. a) Sketch the standing wave pattern for the first three harmonics. b) Find the wavelength of the first three harmonics. c) If the fundamental plays a note of at 500 Hz, find the speed of the wave on the string. 56. An organ pipe can be modeled as a tube closed on one end and open on the other. a) Sketch a picture of the fundamental standing wave. b) Express the wavelength of the fundamental in terms of the length of the column. c) If a set of organ pipes is to cover the frequency range from 20 Hz to 20,000 Hz, what must be the range of lengths? 57. The A string on a violin is 32 cm long and vibrates at 440 Hz. a) Draw a picture of the lowest frequency standing wave. b) What is the speed of sound in the string?