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A collection of solved physics problems focusing on mechanics. the exercises cover various concepts, including center of mass, momentum, torque, work, energy, and centripetal acceleration. solutions are detailed, making it a valuable resource for students to practice and understand these fundamental physics principles. The problems are suitable for university-level introductory physics courses.
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You and a friend are moving a very heavy and irregular piece of furniture across a room. You are lifting it to prevent it from scratching your wooden floor. Your friend lets you pick where you are going to hold it and your friend will hold it at the other end (or some other place you tell your friend to hold it). To make it easier on yourself, you would: A.Hold the end closer to the center of mass (your friend holds the other end). B.Hold the end farther from the center of mass (your friend holds the other end). C.Hold it at the center of mass and have your friend hold it from one of the other ends. D.It doesn't matter where you pick - you'll both have to exert the same force no matter where you hold it. E.Hold either end since you have to exert the same force no matter which end you pick. - ANSWERB.Hold the end farther from the center of mass (your friend holds the other end). Two acrobats flying through the air grab and hold onto each other in midair as part of a circus act. One acrobat has a mass of 60 kg and has a horizontal velocity of 5 m/s just before the grab.Another acrobat has a mass of 50 kg and has a horizontal velocity of -3 m/s just before the grab. Their horizontal velocity immediately after they grab onto each other is: - ANSWERm1iv1i + m2iv2i = (m1 + m2) v2f (605) + (50-3) = (60 +50) v2f v2f = 1.4 m/s Your kid sister is making a mobile representing the earth, moon, and sun for her grade school science fair. The ruler is provided below to help you determine positions of the three hanging balls, of mass 15 g, 5 g, and 30 g, respectively. Of the five options provided, where is the horizontal center of mass at which would you connect a string to this mobile so that it would remain balanced when you hung it from the string?(The rods and strings all have negligible mass compared to the balls.) - ANSWERCoM = (m1r1 + m2r2 + m3r3)/ (m1 + m2 + m3) CoM = 7.15 cm An 60-kg diver stands at the edge of a lightweight diving board, which is supported at two locations, as shown in the figure below. Determine the strength and direction of the force exerted on the diving board by the right-most support. - ANSWER0 = -2Fgd
Swimmers at a water park have a choice of two frictionless water slides (see figure). Although both slides drop over the same height h, slide 1 is straight while slide 2 is curved, dropping quickly at first and then leveling out. How does the speed v1 of a swimmer reaching the end of slide 1 compare with v2, the speed of a swimmer reaching the end of slide 2? - ANSWERv1 = v An object of mass 10.0 kg is initially at rest. A 100 N force causes it to move horizontally through a distance of 6.00 m along a frictionless surface. What is the change in the kinetic energy of this object? - ANSWERdelta KE = W W = Fdcos(theta) W= 100 (6) cos (180) = 600 J Two children are riding on a merry-go-round. Child A is at a greater distance from the axis of rotation than child B. Which child has the larger tangential speed? - ANSWERlarger radius = larger tangential speed ----> child A A karate student throws a round kick to a target pad during her workout in the dojo. Her foot moves at 15 m/s just before landing the kick and is in contact with the pad for 0.02 seconds until it comes to rest on the pad. If the effective combined mass of her foot & lower leg is 8 kg, with what average force does she hit the pad? - ANSWERF = m (delta v/ delta t) F = 8 (0-15/ 0.02) = 6000N A constant force is applied to an object. If the angle between the force and the displacement is 90°, the work done by this force is: - ANSWERW = Fdcos(theta) cos(90) = 0 0 J = no work is done You are sitting on the left side of a slippery car seat as the car makes a circular turn to the left. As the car turns left you slide toward the right side of the car seat. How do you explain this observation? A. The seat is moving to the left underneath your booty and you tend to move in a straight line, thus you and the seat are moving with respect to each other. B.There is a net force being exerted on you directed radially away from the turn's center. C.The force of motion propels you radially away from the turn's center. D.The car seat pushes you forward. - ANSWERA. The seat is moving to the left underneath your booty and you tend to move in a straight line, thus you and the seat are moving with respect to each other. A piece of dirt (0.01 kg) is stuck in the tread of a spinning bicycle wheel. If the wheel is spinning with a frequency of 1/s and the wheel has a radius of 0.35 meters, what is the magnitude of centripetal acceleration of the piece of dirt? - ANSWERf = 1/T T = (2pir)/ v Ac = v^2/r 1 = (2 * pi * 0.35)/v v= 2. Ac = 2.2^2/0. Ac = 13.8 m/s^
A 1400 kg car is traveling on a level road at a constant speed of 26.8 m/s (60 miles per hour.) The drag force exerted by air on the car and the frictional force exerted by the road on the car's tires add to give a net force of 680N pointing opposite to the direction of the car's motion. What is the rate of work done (power) by the air and the road on the car? - ANSWERPower = work/time P = (Fdcos(theta))/delta t P= (680(26.8)cos(180)) = 18224 W = 18 kW Two cars (with masses 2000 kg and 1000 kg) collide head on an icy road. Before the collision, the more massive vehicle was moving at 10 m/s to the right and the less massive vehicle was moving at 15 m/s to the left. Immediately after the collision, the more massive vehicle was moving at 7.0 m/s to the left. How fast was the less massive vehicle immediately after the collision? - ANSWERelastic collision: mi1vi1 + mi2vi2 = m1fv1f + m2fv2f 2000(10) + 1000(-15) = 2000(-7) + 1000v2f v2f= 19 m/s A rabbit runs in a circle of radius r at a constant speed of v. A squirrel runs in a circle of radius r/3 at a constant speed of v/3. Which of the following statements is correct? I. The magnitude of the centripetal acceleration of the rabbit is three times the magnitude of the centripetal acceleration of the squirrel. II. The rabbit and the squirrel have centripetal accelerations of the same size. III. The rabbit and the squirrel complete one full revolution in the same amount of time. A)Only I B)Only II C)Only III D)II and III E)I and III - ANSWERE) I and III A hammock on earth is tied with ropes between two trees. A person lies init. Under what circumstances are its ropes more likely to break?A.If the ropes are stretched tightly between the trees and the hammock doesn't sag. B.If the ropes are stretched loosely between the trees and the hammock sags. C.The ropes have equal likelihood of breaking in cases A & B. - ANSWERA.If the ropes are stretched tightly between the trees and the hammock doesn't sag. Choose which statement describes a process in which an external force does negative work on the system. All processes occur on earth and the person is not part of the system. A)A person slowly lifts a box from the floor to a tabletop. B)A person slowly lowers a box from a tabletop to the floor. C)A person carries a bag of groceries horizontally from one counter to another. D)A person holds a heavy suitcase at rest while they yodel. - ANSWERB)A person slowly lowers a box from a tabletop to the floor. An object of mass 10.0 kg is initially at rest. A 100 N force causes it to move horizontally through a distance of 6.00 m along a frictionless surface. What is the change in the kinetic energy of this object? - ANSWERdelta KE = Fdcos(theta) delta KE = 100(6)cos(0) = 600 J
Two acrobats flying through the air grab and hold onto each other in midair as part of a circus act. One acrobat has a mass of 60 kg and has a horizontal velocity of 5 m/s just before the grab. Another acrobat has a mass of 50 kg and has a horizontal velocity of-3 m/s just before the grab. Their horizontal velocity immediately after they grab onto each other is: - ANSWERinelastic collision m1iv1i +m2iv2i = (m1 + m2) v2f 60(5) = 50(-3) = (60 + 50) v2f v2f = 1.36 m/s You need to load a crate of mass m onto the bed of a truck on earth. One possibility is just to lift the crate straight up over a height h, equal to height of the truck's bed. The force exert in this case is F1and the work done in this case is W1. The other possibility is to slide the crate up the frictionless ramp of length L as shown in the figure. In this case you exert force F2 and perform work W2. Which statement is true? A)F1> F2and W1= W B)F1=F2and W1> W C)F1= F2and W1= W D)F1> F2and W1< W E)F1> F2and W1> W2 - ANSWERA)F1> F2and W1= W As the figure below shows, a 500 kg wrecking ball hangs vertically from the end of a crane on earth. The boom of the crane is L = 7 m long and makes an angle of theta= 60 to the horizontal. The driver of the crane faces the wrecking ball. What is the torque on the crane with respect to the base of the boom due to the weight of the wrecking ball? - ANSWERT = rFsin(theta) T = 7 (500-9.8) sin (30) = -1750Nm 1750 Nm clockwise A roller coaster on earth includes a circular loop on which the seat of the car is farther from the center of the loop than the rider is. If the loop's radius is 6.00 m, what is the magnitude of the vertical force which the car exerts on a 60.0 kg rider at the bottom where the car travels at 12.0 m/s? - ANSWERFc = m (vt^2/r) + mg Fc = 60 (12^2/6) + (60 9.8) = 2028N =2030N An inelastic collision between two objects is characterized by the following A)Total momentum of the system is conserved B)Total energy of the system is conserved C)Total kinetic energy of the system remains constant D)Both A and B are true E)Both A and C are true - ANSWERD)Both A and B are true Tommy and his skateboard have a combined mass of 50 kg. Joe and and his skateboard have a combined mass of 100 kg. You push both of them with the same force-Tommy for two seconds and Joe for 1 second. After the pushes, A)Tommy's change in speed is 4 times greater than Joe's B)Joe's change in speed is 4 times greater than Tommy's