Physics Final Exam Review
The center of mass (or center of gravity) of a two-particle system is at the origin. One particle is located at (3.0 m, 0.0 m) and has a mass of 2.0 kg. The other particle has a mass of 3.0 kg. What is the location of the 3.0-kg particle? (-3.0 m, 0.0 m) (3.0 m, 0.0 m) (-2.0 m, 0.0 m) (2.0 m, 0.0 m)
(-2.0 m, 0.0 m)
Three masses are located in the x-y plane as follows: a mass of 6 kg is at (0 m, 0 m), a mass of 4 kg is at (3 m, 0 m), and a mass of 2 kg is at (0 m, 3 m). Where is the center of mass (or center of gravity) of the system? (1 m, 1 m) (1 m, 0.5 m) (0.5 m, 1 m) (2 m, 1 m) (1 m, 2 m)
(1 m, 0.5 m)
Three forces F 1→, F2→, and F 3→, each of magnitude 70 N, all act on an object as shown in the figure. The magnitude of the resultant force acting on the object is 140 N 210 N 70 N 35 N 0 N
0 N
A 20-g bead is attached to a light 120-cm-long string as shown in the figure. This bead moves in a horizontal circle with a constant speed of 1.5 m/s. What is the tension in the string if the angle α is measured to be 25°? 0.46 N 0.089 N 0.20 N 0.22 N 0.041 N
0.22 N
A 5.0-m radius playground merry-go-round with a moment of inertia of 2000 kg • m2 is rotating freely with an angular speed of 1.0 rad/s. Two people, each of mass 60 kg, are standing right outside the edge of the merry-go-round and suddenly step onto the edge with negligible speed relative to the ground. What is the angular speed of the merry-go-round right after the two people have stepped on? 0.80 rad/s 0.20 rad/s 0.60 rad/s 0.40 rad/s 0.67 rad/s
0.40 rad/s
A 50.0-kg block is being pulled up a 16.0° slope by a force of 250 N that is parallel to the slope. The coefficient of kinetic friction between the block and the slope is 0.200. What is the acceleration of the block? 0.260 m/s^2 0.412 m/s^2 0.528 m/s^2 0.983 m/s^2 0.158 m/s2
0.412 m/s^2
In the figure, block A has a mass of 3.00 kg. It rests on a smooth horizontal table and is connected by a very light horizontal string over an ideal pulley to block B, which has a mass of 2.00 kg. When block B is gently released from rest, how long does it take block B to travel 80.0 cm? 0.785 s 0.404 s 0.639 s 0.494 s 0.935 s
0.639 s
When a fan is turned off, its angular speed decreases from 10 rad/s to 6.3 rad/s in 5.0 s. What is the magnitude of the average angular acceleration of the fan? 1.2 rad/s^2 11 rad/s^2 0.86 rad/s^2 0.37 rad/s^2 0.74 rad/s^2
0.74 rad/s^2
A 3.0-kg mass and a 5.0-kg mass hang vertically at the opposite ends of a rope that goes over an ideal pulley. If the masses are gently released from rest, how long does it take for the 3.0-kg mass to rise by 1.0 m? 0.82 s 0.90 s 0.74 s 1.8 s 0.41 s
0.90 s
The mass of the Moon is 7.4× 10^22 kg, its radius is 1.74× 10^3 km, and it has no atmosphere. What is the acceleration due to gravity at the surface of the Moon? (G = 6.67× 10^−11 N⋅m^2/kg^2) 2.8× 10^6 m/s^2 0.80 m/s^2 4.9 m/s^2 9.8 m/s^2 1.6 m/s^2
1.6 m/s^2
To determine the location of the center of mass (or center of gravity) of a car, the car is driven over a scale on a horizontal floor. When the front wheels are over the scale, the weight recorded by the scale is 5800 N, and when the rear wheels are over the scale, the scale reads 6500 N. The distance between the front and rear wheels is measured to be 3.20 m. How far behind the front wheels is the center of mass located? 1.59 m 0.845 m 1.72 m 1.50 m 1.69 m
1.69 m
The innermost satellite of Jupiter orbits the planet with a radius of 422 × 103 km and a period of 1.77 days. What is the mass of Jupiter? (G = 6.67 × 10-11 N • m2/kg2) 1.33 × 10^27 kg 1.50 × 10^27 kg 1.89 × 10^27 kg 1.72 × 10^27 kg 3.08 × 10^27 kg
1.89 x 10^27 kg If you are on Pearson, you will likely be given a guide for constants. If you don't want to do the math, the mass of Jupiter is listed in the constants page.
Europa, a satellite of Jupiter, has an orbital diameter of 1.34 × 10^9 m and a period of 3.55 days. What is the mass of Jupiter? (G = 6.67 × 10^-11 N • m^2/kg^2) 1.53 × 10^27 kg 1.89 × 10^27 kg 1.65 × 10^27 kg 3.08 × 10^27 kg 1.07 × 10^27 kg
1.89 × 10^27 kg Again, if you are given a constants sheet to look at, the mass of Jupiter is likely to be on there.
If a net force accelerates a 4.5-kg tool at 40 m/s^2, what acceleration would that same net force give to an 18-kg tool? 160 m/s^2 9.8 m/s^2 10 m/s^2 32 m/s^2 180 m/s^2
10 m/s^2
An athlete holds a 7.5-kg shot put in his hand with his lower arm horizontal, as shown in the figure. His lower arm has a mass of 2.8 kg and its center of gravity (or center of mass) is 12 cm from the elbow-joint pivot. How much force must the extensor muscle (which is FM→ in the figure) in the upper arm exert on the lower arm? 500 N 100 N 1000 N 1500 N
1000 N
A ball is thrown with an initial velocity of 20 m/s at an angle of 60° above the horizontal. If we can neglect air resistance, what is the horizontal component of its instantaneous velocity at the exact top of its trajectory? zero 20 m/s 10 m/s 17 m/s
10m/s
A spaceship with a mass of 2.8 × 106 kg is traveling toward two spherical asteroids, each with a mass of 5.0 × 1016 kg, that are 40 km apart center-to-center. Its path is perpendicular to the line joining the asteroids and is aimed at the midpoint of that line. What is the net gravitational force exerted by the asteroids on the spaceship when the spaceship is 30 km away from that midpoint? (G = 6.67 × 10-11 N • m2/kg2) 6,200 N 18,000 N 16,000 N 8,000 N 12,000 N
12,000 N
A 900-kg car traveling east at 15.0 m/s suddenly collides with a 750-kg car traveling north at 20.0 m/s. The cars stick together after the collision. What is the speed of the wreckage just after the collision? 35.0 m/s 17.3 m/s 6.10 m/s 25.0 m/s 12.2 m/s
12.2 m/s
A certain aircraft has a mass of 300,000 kg. At a certain instant during its landing, its speed is 27.0 m/s. If the braking force is a constant 445,000 N, what is the speed of the airplane 10.0 s later? 12.2 m/s 14.0 m/s 20.0 m/s 10.0 m/s 18.0 m/s
12.2 m/s
A 55-kg box rests on a horizontal surface. The coefficient of static friction between the box and the surface is 0.30. A horizontal 140-N force is applied to the box. What is the friction force on the box? 42 N 140 N 16.5 N 0.00 N 160 N
140 N
An object starts from rest and undergoes uniform acceleration. During the first second it travels 5.0 m. How far will it travel during the third second? 15 m 5.0 m 25 m 45 m
15 m
A load is being lifted vertically upwards by means of two cables attached to it. The first cable exerts a force of 600 N at an angle of 35.0° to the left of the vertical. The second cable exerts a force of 1300 N. At what angle to the right of the vertical is the second cable pulling? 30.8° 67.8° 16.2° 15.4° 75.8°
15.4°
When a 125-kg piece of equipment is hung from a steel wire of diameter 6.00 mm, it stretches the wire by 4.00 mm. If instead the wire had a diameter of 3.00 mm, but all else were the same, by what distance would the same equipment stretch the wire? 4.00 mm 8.00 mm 16.0 mm 1.00 mm 2.00 mm
16.0 mm
A fisherman casts his bait toward the river at an angle of 25° above the horizontal. As the line unravels, he notices that the bait and hook reach a maximum height of 2.9 m. What was the initial velocity he launched the bait with? Assume that the line exerts no appreciable drag force on the bait and hook and that air resistance is negligible. 7.6 m/s 7.9 m/s 18 m/s 6.3 m/s
18 m/s
Find the orbital speed of an ice cube in the rings of Saturn. The mass of Saturn is 5.68 x 10^26 kg, and use an orbital radius of 1.00 x 10^5 km. (G = 6.67 × 10^-11 N • m^2/kg^2) 13.8 km/s 27.5 km/s 19.5 km/s
19.5 km/s
An ideal spring stretches by 21.0 cm when a 135-N object is hung from it. If instead you hang a fish from this spring, what is the weight of a fish that would stretch the spring by 31.0 cm? 279 N 199 N 91 N 145 N
199 N
You go to the playground and slide down the slide, a 4.0-m-long ramp at an angle of 34∘ with respect to horizontal. The pants that you've worn aren't very slippery; the coefficient of kinetic friction between your pants and the slide is μk = 0.37. A friend gives you a very slight push to get you started. How long does it take you to reach the bottom of the slide? Express your answer with the appropriate units.
2.07 seconds
In a certain cyclotron, a proton of mass 1.67 × 10^-27 kg moves in a circle of diameter 1.6 m with an angular speed of 2.0 × 10^6 rad/s. What is the angular momentum of the proton? 1.3 × 10^-21 kg • m^2/s 1.8 × 10^-21 kg • m^2/s 3.2 × 10^-21 kg • m^2/s 2.1 × 10^-21 kg • m^2/s
2.1 x 10^-27 kg • m^2/s
How many joules of energy are used by a 1.0-hp motor that runs for 1.0 hour? (1 hp = 746 W) 45 kJ 4.8 J 2.7 MJ 3.6 kJ
2.7 MJ
A 5.0-N projectile leaves the ground with a kinetic energy of 220 J. At the highest point in its trajectory, its kinetic energy is 120 J. To what vertical height, relative to its launch point, did it rise if there was no air resistance? 24 m 44 m 10 m 20 m It is impossible to determine the height without knowing the angle of launch.
20 m
An object with a mass of 10 kg is initially at rest at the top of a frictionless inclined plane that rises at 30° above the horizontal. At the top, the object is initially 8.0 m from the bottom of the incline, as shown in the figure. When the object is released from this position, it eventually stops at a distance d from the bottom of the inclined plane along a horizontal surface, as shown. The coefficient of kinetic friction between the horizontal surface and the object is 0.20, and air resistance is negligible. Find the distance d. 25 m 20 m 10 m 5.0 m 15 m
20 m
A 50-kg box is resting on a horizontal floor. A force of 250 N directed at an angle of 30.0° below the horizontal is applied to the box. The coefficient of static friction between the box and the surface is 0.40, and the coefficient of kinetic friction is 0.30. What is the force of friction on the box? 250 N 220 N 200 N 32 N 620 N
220 N
A 0.50-kg toy is attached to the end of a 1.0-m very light string. The toy is whirled in a horizontal circular path on a frictionless tabletop. If the maximum tension that the string can withstand without breaking is 350 N. What is the maximum speed the mass can have without breaking the string? 19 m/s 26 m/s 700 m/s 13 m/s
26 m/s
A thick-walled metal pipe of length 20.0 cm has an inside diameter of 2.00 cm and an outside diameter of 2.40 cm. What is the total surface area of the pipe, counting the ends, in square centimeters? 276 cm^2 277 cm^2 278 cm^2 279 cm^2
279 cm^2
A 30-kg child stands at one end of a floating 20-kg canoe that is 5.0-m long and initially at rest in the water. The child then slowly walks to the other end of the canoe. How far does the canoe move in the water, assuming water friction is negligible? 4.0 m 1.0 m 5.0 m 3.0 m 2.0 m
3.0 m
A solid steel column is 4.0 m long and 0.20 m in diameter. Young's modulus for this steel is 2.0 × 1011 N/m2. By what distance does the column shrink when a 5000-kg truck is supported by it? 3.2 × 10^6 m 7.8 × 10^6 m 8.0 × 10^7 m 3.1 × 10^5 m
3.1 x 10^5 m
A particular motor can provide a maximum torque of 110 N • m. Assuming that all of this torque is used to accelerate a solid, uniform, cylindrical flywheel of mass 10.0 kg and radius 3.00 m, how long will it take for the flywheel to accelerate from rest to 8.13 rad/s? 2.83 s 4.36 s 3.33 s 4.03 s
3.33 s
A flatbed truck is carrying a 20.0-kg crate along a level road. The coefficient of static friction between the crate and the bed is 0.400, and the coefficient of kinetic friction is 0.300. What is the maximum acceleration that the truck can have if the crate is to stay in place relative to the truck? 196 m/s^2 7.84 m/s^2 8.00 m/s^2 3.92 m/s^2 78.5 m/s^2
3.92 m/s^2
The lug nuts on a car wheel require tightening to a torque of 90 N • m. If a 30-cm long wrench is used, what is the magnitude of the minimum force required using the wrench? 150 N 300 N 15 N 30 N
300 N
What magnitude net force is required to accelerate a 1200-kg car uniformly from 0 m/s to 27.0 m/s in 10.0 s? 11800 N 444 N 1620 N 4360 N 3240 N
3240 N
The curved section of a speedway is a circular arc having a radius of 190 m. This curve is properly banked for racecars moving at 34 m/s. At what angle with the horizontal is the curved part of the speedway banked? 28° 30° 34° 32° 26°
32°
A man in a gym is holding an 8.0-kg weight at arm's length, a distance of 0.55 m from his shoulder joint. What is the torque about his shoulder joint due to the weight if his arm is held at 30° below the horizontal? 2.2 N • m 22 N • m 4.4 N • m 13 N • m 37 N • m
37 N • m
An object is moving in a straight line with constant acceleration. Initially it is traveling at 16 m/s. Three seconds later it is traveling at 10 m/s. How far does it move during this time? 57 m 48 m 30 m 39 m
39 m
Jason takes off across level water on his jet-powered skis. The combined mass of Jason and his skis is 75 kg (the mass of the fuel is negligible). The skis produce a forward thrust of 200 N and have a coefficient of kinetic friction with water of 0.10. Unfortunately, the skis run out of fuel after only 41 s. How far from his starting point has Jason traveled when he finally coasts to a stop? 2900 m 2000 m 3900 m 1400 m
3900 m
A small 1.4-N stone slides down a frictionless bowl, starting from rest at the rim. The bowl itself is a hemisphere of radius 75 cm. Just as the stone reaches the bottom of the bowl, how hard is the bowl pushing on it? 4.2 N 1.4 N 2.8 N 5.6 N 0.70 N
4.2 N
A 5.00-m-long uniform ladder, weighing 200 N, rests against a smooth vertical wall with its base on a horizontal rough floor, a distance of 1.20 m away from the wall. The coefficient of static friction between the ladder and the floor is 0.200. How far up the ladder, measured along the ladder, can a 600-N person climb before the ladder begins to slip? 4.56 m 1.50 m 1.05 m 3.95 m 1.26 m
4.56 s
A 0.24 kg blob of clay is thrown at a wall with an initial horizontal velocity of 16 m/s. If the clay comes to a stop in 91 ms, what is the average horizontal force on the clay due to the wall? 42 N 51 N 35 N 26 N
42 N
A jet plane is launched from a catapult on an aircraft carrier. In 2.0 s it reaches a speed of 42 m/s at the end of the catapult. Assuming the acceleration is constant, how far did it travel during those 2.0 s? 24 m 84 m 16 m 42 m
42 m
A prankster drops a water balloon from the top of a building. If the balloon is traveling at 29.1 m/s when it strikes a window ledge that is 1.5 m above the ground, how tall is the building? Neglect air resistance. 43 m 47 m 46 m 45 m
45 m
A car travels at 15 m/s for 10 s. It then speeds up with a constant acceleration of 2.0 m/s2 for 15 s. At the end of this time, what is its velocity? 45 m/s 375 m/s 15 m/s 30 m/s
45 m/s
A stone is moving on a rough level surface. It has 24 J of kinetic energy, and the friction force on it is a constant 0.50 N. What is the maximum distance it can slide? 2.0 m 24 m 12 m 48 m
48 m
Which of the following is the most reasonable estimate of the number of characters (typed letters or numbers) in a 609-page book? Assume an average of 194 words per page and a reasonable average number of letters per word. 5 × 10^7 char 5 × 10^6 char 5 × 10^5 char 5 × 10^4 char
5 × 10^5 char
Vector A has a magnitude of 8.0 m and points 30° north of east; vector B has a magnitude of 6.0 m and points 30° west of north; and vector C has a magnitude of 5.0 m and points 30° west of south. The resultant vector A+B+C is given by 2.7 m at an angle 74° north of east. 2.1 m at an angle 66° east of north. 5.9 m at an angle 74° north of east. 5.1 m at an angle 74° north of east. 4.8 m at an angle 74° east of north.
5.1 m at an angle 74° north of east.
The average density of blood is 1.06 × 10^3 kg/m^3. If you donate a pint of blood to the Red Cross, how many grams of blood have you donated? (2.00 pt = 1.00 qt, 1.00 L = 1000 cm^3, 1.00 qt = 0.947 L, and density is mass per unit volume.) 5020 g 5.02 × 10^5 g 0.502 g 5.02 g 502 g
502 g
An electrical motor spins at a constant 2695.0 rpm. If the rotor radius is 7.165 cm, what is the linear acceleration of the edge of the rotor? 5707 m/s^2 28.20 m/s^2 281.6 m/s^2 572,400 m/s^2
5707 m/s^2
A sled having a certain initial speed on a horizontal surface comes to rest after traveling 10 m. If the coefficient of kinetic friction between the object and the surface is 0.20, what was the initial speed of the object? 8.9 m/s 6.3 m/s 7.2 m/s 9.8 m/s 3.6 m/s
6.3 m/s
A batter hits a foul ball. The 0.14-kg baseball that was approaching him at 40 m/s leaves the bat at 30 m/s in a direction perpendicular to the line between the batter and the pitcher. What is the magnitude of the impulse delivered to the baseball? 1.4 N • s 5.6 N • s 7.0 N • s 3.5 N • s 9.8 N • s
7.0 N • s
An ice skater has a moment of inertia of 5.0 kg • m^2 when her arms are outstretched, and at this time she is spinning at 3.0 rev/s. If she pulls in her arms and decreases her moment of inertia to 2.0 kg • m^2, how fast will she be spinning? 7.5 rev/s 2.0 rev/s 3.3 rev/s 10 rev/s
7.5 rev/s
A cinder block of mass m = 4.0 kg is hung from a nylon string that is wrapped around a frictionless pulley having the shape of a cylindrical shell, as shown in the figure. If the cinder block accelerates downward at 4.90 m/s^2 when it is released, what is the mass M of the pulley? 4.0 kg 2.0 kg 6.0 kg 8.0 kg 10 kg
8.0 kg
As shown in the figure, a 10-kg block on a perfectly smooth horizontal table is connected by a horizontal string to a 63-kg block that is hanging over the edge of the table. What is the magnitude of the acceleration of the 10-kg block when the other block is gently released? 8.5 m/s^2 9.0 m/s^2 8.1 m/s^2 7.5 m/s^2
8.5 m/s^2
You push downward on a trunk at an angle 25° below the horizontal with a force of 750 N. If the trunk is on a flat surface and the coefficient of static friction between the surface and the trunk is 0.61, what is the most massive trunk you will be able to move? 112 kg 93 kg 73 kg 81 kg
81 kg
A 100-kg nonuniform boom that is 6.0 m long is loosely pinned at the pivot at P. A 600-kg concrete block is suspended from the end of the boom at A, as shown in the figure. The boom forms a 30° angle above the horizontal, and is supported by a 4.0-m cable between points D and B. Point B is 4.0 m from P, and point D is 4.0 m above P. The center of mass of the boom is at point C, which is 2.0 m from P. Assume that all the quantities shown in the figure are accurate to two significant figures. What is the tension in the cable connected between points B and D? 8100 N 7500 N 8400 N 9300 N 6900 N
9300 N
Scallops use jet propulsion to move from one place to another. Their shells make them denser than water, so they normally rest on the ocean floor. If a scallop wishes to remain stationary, hovering a fixed distance above the ocean floor, it must eject water _____ so that the thrust force on the scallop is _____. A)downward, upward B)upward, upward C)downward, downward D)upward, downward
A) downward, upward
Two vehicles approach a right angle intersection and then suddenly collide. After the collision, they become entangled. If their mass ratios were 1:4 and their respective speeds as they approached the intersection were both 13 m/s, find the magnitude and direction of the final velocity of the wreck. A)16 m/s at 76° with respect to the original direction of the lighter car B)11 m/s at 76° with respect to the original direction of the lighter car C)11 m/s at 14° with respect to the original direction of the lighter car D)16 m/s at 14° with respect to the original direction of the lighter car
B)11 m/s at 76° with respect to the original direction of the lighter car
Dave pushes his four-year-old son Thomas across the snow on a sled. As Dave pushes, Thomas speeds up. Which statement is true? A)Both forces have the same magnitude. B)The force of Dave on Thomas is larger than the force of Thomas on Dave. C)The force of Thomas on Dave is larger than the force of Dave on Thomas. D)It depends on how hard Dave pushes on Thomas.
Both forces have the same magnitude
Part A As noted in the passage, our solar system orbits the center of the Milky Way galaxy in about 200 million years. If there were no dark matter in our galaxy, this period would be A)shorter. B)the same. C)longer. Part B Saturn is approximately 10 times as far away from the sun as the earth. This means that its orbital acceleration is __________ that of the earth. 1/10 1/100 1/1000 1/10,000 Part C Saturn is approximately 10 times as far away from the sun as the earth. If dark matter changed the orbital properties of the planets so that Saturn had the same orbital speed as the earth, Saturn's orbital acceleration would be ________ that of the earth. 1/10 1/100 1/1000 1/10,000 Part D Which of the following might you expect to be an additional consequence of the fact that galaxies contain more mass than expected? A)The gravitational force between galaxies is greater than expected. B)There are more galaxies than expected. C)Galaxies are farther away than expected. D)Galaxies appear less bright than expected.
Part A C) longer Part B 1/100 Part C 1/10 Part D A)The gravitational force between galaxies is greater than expected.
Two ice skaters, Megan and Jason, push off from each other on frictionless ice. Jason's mass is twice that of Megan
Short Answer
Two horizontal curves on a bobsled run are banked at the same angle, but one has twice the radius of the other. The safe speed (for which no friction is needed to stay on the run) for the smaller radius curve is νν. What is the safe speed on the larger-radius curve? ν/2 ν/√2 ν√2 2ν
ν√2 ??
