ACTIVITY BASED PHYSICS MECHANICS RACTICE ROBLEM SETS

MECHANICS PRACTICE PROBLEM SETS2.312KINEMATICS TEST REVIEW PROBLEMS2.3.1Kinematics and Freefall1. An object with an initial velocity of 47.0 m/s accelerates uniformly at 2.0 m/s2 for9.0 s. Calculate the displacement of the object after 9.0 s. Answer: 504 m2. A driver of a car going 25 m/s suddenly sees the lights of a barrier 40.0 m ahead.It takes the driver 0.75 s before he applies the brakes, and the average accelerationduring braking is -10.0 m/s2. Does the car hit the barrier? Answer: Yes, x 50 m3. Highway safety engineers build soft barriers so that cars hitting them will slowdown at a safe rate. A person wearing a safety belt can withstand an accelerationof – 300 m/s2. How thick should barriers be to safely stop a car that hits a barrierat 30.56 m/s?Answer: x 1.6 m4. A weather balloon is floating at a constant height above Earth when it releases apack of instruments.a. If the pack hits the ground with a velocity of 73.5 m/s, how far does thepack fall?Answer: y 276 m downb. How long does the pack fall?Answer: t 7.5 sec5. Kyle is flying a helicopter that is rising at 5.0 m/s when he releases a bag of tools.After 2.0 s a. What is the bag's velocity?Answer: vf -14.6 m/sb. How far has the bag fallen?Answer: y -9.6 mc. How far below the helicopter is the bag?Answer: 19.6 m apart2.3.2Projectile Motion6. An auto, moving too fast on a horizontal stretch of mountain road, slides off theroad, falling into deep snow 43.9m below the road and 87.7 m beyond the edge ofthe road.a. How long did the auto take to fall?Answer: 2.99 secb. How fast was it going when it left the road?Answer: 29.3 m/s7. A player kicks a football from ground level with a velocity of magnitude 27 m/sat an angle of 30 degrees above the horizontal. Find:c. The time it is in the air.Answer: t 2.8 sd. The maximum height it reaches.Answer: y 9.3 me. Its distance from the player when it lands.Answer: x 66 m8. Jane jumps off a high-diving platform with a horizontal velocity of 2.8 m/s andlands in the water 2.6 s later. How high is the platform, and how far from the baseof the platform does she land? Answer: y 33 m, x 7.3 m9. A bullet is shot at an angle of 15 degrees with an initial velocity of 200. m/s. Find:Gamzon & Gregorian-Michaelsen6/13/12

MECHANICS PRACTICE PROBLEM SETSf. How long is it in the air.g. The maximum height it reaches.h. How far from the player does it land?13Answer: t 10.6 sAnswer: y 137 mAnswer: x 2050 m10. (G19) A tiger leaps horizontally from a 7.5 m high rock with a speed of 4.5m/s. How far from the base of the rock will she land? Answer: 5.6 m11. (G27) A ball thrown horizontally at 22.2 m/s from the roof of a buildinglands 36.0 m from the base of the building. How high is the building?Answer: 12.9 m12. (G31) A pilot of an airplane traveling 160 km/hr wants to drop supplies toflood victims isolated on a patch of land 160 m below. The supplies shouldbe dropped how many seconds before the plane is directly overhead?Answer: 5.71 sec13. (G35) A projectile is fired with an initial speed of 75.2 m/s at an angle of34.5 above the horizontal on a long flat firing range. Determine:a.b.c.d.The maximum height reached by the projectile. Answer: 92.6 mThe total time in the air.Answer: 8.69 secThe total horizontal distance covered.Answer: 539 mThe velocity of the projectile 1.50 sec after firing.Answer: 68.0 m/s, 24.2 Gamzon & Gregorian-Michaelsen6/13/12

MECHANICS PRACTICE PROBLEM SETS14Unit 3 DYNAMICS3.1NEWTON’S FIRST AND SECOND LAWS1. If a net horizontal force of 132 N is applied to a person with a mass of 60 kg whois resting on the edge of a swimming pool, what horizontal and verticalacceleration is produced?Answer: ax 2.2 m/s2ay 0 m/s22. A 61.0 kg object is to be given a horizontal acceleration of 0.70 m/s2. How largean unbalanced force must act upon it?Answer: 43 N3. A child pulls a wagon with a force of 77 N by a handle making an angle of 10 with the horizontal. If the wagon has a mass of 4.2 kg and we ignore friction,what is the horizontal acceleration of the wagon?Answer: 18 m/s24. A towrope will break if the tension in it exceeds 1500 N. It is used to tow a 700kg car along level ground. What is the maximum acceleration of the car if thewind resistance results in an opposing force of 25 N?Answer: 2.1 m/s2a. If the car is going to be towed onto the highway, it needs to reach a speedof 30 km/hr. How long will it take to get to this speed?Answer: 4.0 secb. How much distance is covered in this time?Answer: 17 m5. What average force is needed to accelerate a 7.00-gram pellet from rest to 175m/s over a distance of 0.700 m along the barrel of a rifle?Answer: 153 N6. A box rests on a frozen pond, which serves as a frictionless horizontal surface. Afisherman applies a horizontal force with a magnitude of 48.0 N at an angle of 30 to the horizontal produces an acceleration of 3.00 m/s2, what is the mass of thebox?Answer: 13.9 kg7. Both Suzy and Maria both want to pull their little sister, Michelle, on a sled. Suzygrabs hold of the rope attached to the front of the sled and pulls on it with a forceof 25.0 N at an angle of 45 . Maria grabs hold of the rope on the back of the sledand pulls in the opposite direction with a force of 21.0 N also at an angle. Thetotal mass of the sled and Michelle is 70 kg. At what angle must Maria pull if thesled is to remain stationary?Answer: 33 a. At what angle must she pull if Michelle is to move at a constant velocityof 5 m/s to the right?b. At what angle must she pull if Michelle is to move at a constant velocityof 2 m/s to the left?Gamzon & Gregorian-Michaelsen6/13/12

MECHANICS PRACTICE PROBLEM SETS158. An advertisement claims that their car can “stop on a dime.” What net forcewould actually be necessary to stop an 850-kg automobile traveling initially at45.0 km/hr in a distance that is equal to the diameter of a dime, which is 1.8 cm?Answer: 3.7 x 106 N9. An 875-kg car starts from rest and attains a speed of 26.3 m/s in 0.59 seconds.What is the magnitude of the average net force on the dragster during this time?Answer: 3.9 x 104 Na. Assuming the driver has a mass of 68 kg, how many times larger is theforce on the car than the horizontal force exerted on the driver by the seat?Answer: 13xGamzon & Gregorian-Michaelsen6/13/12

MECHANICS PRACTICE PROBLEM SETS3.216TENSION, FRICTION & VECTORS1. A cord supports an object with a mass of 10 kg. Find the tension in the cord if theobject is:a. At rest.Answer: T 98 Nb. Moving at constant velocity upward. Answer: T 98 Nc. Moving at constant velocity downward. Answer: T 98 Nd. Accelerating upward with at a 4.7 m/s2. Answer: T 145 Ne. Accelerating downward with at a 2.4 m/s2. Answer: T 74 N2. An object with a weight of 600 N is given a horizontal acceleration of 0.70 m/s2.How large an unbalanced force must act upon it? Answer: Fnet 43 N3. A 2.0 x 10-4 kg spider is suspended from a thin strand of spider web. The greatesttension the strand can withstand without breaking is 2.0 x 10-3 N. What is themaximum acceleration with which the spider can safely ascend the strand?Answer: a 0.20 m/s24. When a 0.40 kg apple is dropped, the earth exerts a force on it, giving it anacceleration of 9.8 m/s2. If the Earth’s mass is 5.98 x 1024 kg, what is the Earth’sacceleration?Answer: a 6.6 x 10-25 m/s25. A 20 kg block of wood is at rest on an ice-covered lake. You attach a rope to itand pull on it with a constant force at an angle of 30 . After 3.5 seconds it has aspeed of 5 m/s. Ignoring friction, with what magnitude of the force you pulled onthe block?Answer: F 32 Na. What is the magnitude of the normal force on the box by the ground?Answer: F 180 N6. A waitress shoves a ketchup bottle with a mass 0.45 kg toward the right along asmooth, level lunch counter. As the bottle leaves her hand, it has an initialvelocity of 2.8 m/s. As it slides, it slows down because of the constant horizontalfriction force exerted on it by the countertop. It slides a distance of 1.0 m beforecoming to rest. What are the magnitude and direction of the friction force?Answer: -1.76 N7. If you use a horizontal force of 30.0 N to slide a 12.0 kg wooden crate across afloor at a constant velocity, what is the coefficient of kinetic friction between thecrate and the floor?Answer: µ k 0.268. Suppose a delivery company has just unloaded a 51 kg crate full of home exerciseequipment on the sidewalk in front of your house. To get it into your house, youtie a rope to it and pull horizontally with a constant force of 125 N. If the crateaccelerates at 0.5 m/s2, what is the coefficient of friction between the crate and thesidewalk?Answer: µ 0.20Gamzon & Gregorian-Michaelsen6/13/12

MECHANICS PRACTICE PROBLEM SETS179. A cart is released at the top of an inclined plane that is elevated 20.0 from thehorizontal. The cart has a mass of 1.12 kg and reaches a velocity of 1.2 m/s after3.0 seconds. What is the coefficient of kinetic friction between the incline and theblock?Answer: µ 0.3210. Add the following vectors both graphically and analytically. Your answer foreach method must include the both the magnitude and the angle.A 2.5 cm at 40 Gamzon & Gregorian-MichaelsenB 6.0 cm at 150 Answer: R 5.7 cm at 125 6/13/12

MECHANICS PRACTICE PROBLEM SETS3.318DYNAMICS REVIEW PROBLEMS1. A large motorcycle weighs 2450 N. Calculate its mass in kilograms.Answer: m 250 kg2. A car with a mass of 700-kg changes its speed from 10.0 m/s to 30.0 m/s in adisplacement of 50.0 meters. Calculate the net force acting on the car during thistime.Answer: Fnet 5600 N3. A 5.0 kg object is to be given an upward acceleration of 0.30 m/s2 by pulling on arope straight upward. What must be the tension in the rope?Answer: T 51 N4. A horizontal force of 50 N is required to slide a 15 kg steel crate across the floorat a constant velocity. What is the coefficient of sliding friction between the crateand the floor?Answer: µ 0.345. Lucy is a 45.90 kg girl that is sitting on a tire swing. Schroeder pulls backhorizontally on the swing. This causes the rope of tire swing to make a 30 anglewith the horizontal. With what force must Schroeder pull back with and what isthe tension in the rope to keep Lucy at rest?Answer: T 899.6 N, FLS 779.1 N6. A 0.30 kg mass hangs at the end of a string. A second string hangs from thebottom of this mass and supports a 0.90 kg mass. Find the tension in each stringwhen the masses are accelerating upward at 0.70 m/s2. Ignore air resistance.Answer: T1 13 N, T2 9.5 N7. A small block with a mass of 300 grams and a large block with a mass of 500grams are pushed by a force F as shown below. The blocks accelerate togetherwith an acceleration of 200 cm/s2. The frictional forces are 1.2 N on the smallblock and 2.0 N on the large block. Watch your units!!a. How large a force does the 300-gram block exert on the 500-gram blockduring this motion.Answer: FLS 3.0 Nb. What must be the value of FSP be to get this acceleration?Answer: F 4.8 NF300 gm8.500 gm(G5) What is the weight of a 66-kg astronaut on Earth? Answer: 6.5 x 102 Na. On the moon (g 1.6 m/s2)?Answer: 1.1 x 102 NGamzon & Gregorian-Michaelsen6/13/12

MECHANICS PRACTICE PROBLEM SETS19b. On Mars (g 3.7 m/s2)?Answer: 2.4 x 102 Nc. In outer space traveling at constant velocity? Answer: 0 N9. (G7) What average force is required to stop an 1100-kg car in 8.0 seconds if it istraveling at 90 km/hr? Answer: 3.4 x 103 N opposite direction10. (G11) What is the average force exerted by a shot-putter on a 7.0 kg shot if theshot is moved through a distance of 2.8 m and is released with a speed of 1.3 m/s?Answer: 2.1 x 102 N11. (G13) A 10-kg bucket is lowered by a rope in which there is 63 N of tension.What is the acceleration of the bucket? Is it up or down? Answer: 3.5 m/s2 down12. (G17) The cable supporting a 2100-kg elevator has a maximum strength of 21,750N. What maximum upward acceleration can it give the elevator without breaking?Answer: 0.557 m/s213. (G19) A Saturn V rocket has a mass of 2.75 x 106 kg and exerts a force of 33 x106 N on the gases it expels. Ignoring the mass of the gases expelled andassuming that g remains constant, determine:a. The initial vertical acceleration of the rocket. Answer: 2.2 m/s2b. Its velocity after 8.0 sec.Answer: 18 m/sc. How long it takes to reach an altitude of 9500 m. Answer: 93 sec14. (G39) A ball thrown horizontally at 22.2 m/s from the roof of a building lands36.0 m from the base of the building. How high is the building?Answer: µ s 0.82, µ k 0.7415. (G41) A pilot of an airplane traveling 160 km/hr wants to drop supplies to floodvictims isolated on a patch of land 160 m below. The supplies should be droppedhow many seconds before the plane is directly overhead?Answer: µ s 0.8216. (G43) A pilot of an airplane traveling 160 km/hr wants to drop supplies to floodvictims isolated on a patch of land 160 m below. The supplies should be droppedhow many seconds before the plane is directly overhead?Answer: 5.71 sec17. G45) A pilot of an airplane traveling 160 km/hr wants to drop supplies to floodvictims isolated on a patch of land 160 m below. The supplies should be droppedhow many seconds before the plane is directly overhead?Answer: 5.71 sec18. (G47) A projectile is fired with an initial speed of 75.2 m/s at an angle of 34.5 above the horizontal on a long flat firing range. Determine:a. The maximum height reached by the projectile. Answer: 92.6 mGamzon & Gregorian-Michaelsen6/13/12

MECHANICS PRACTICE PROBLEM SETS20b. The total time in the air.Answer: 8.69 secc. The total horizontal distance covered. Answer: 539 md. The velocity of the projectile 1.50 sec after firing. Answer: 68.0 m/s, 24.2 Gamzon & Gregorian-Michaelsen6/13/12

MECHANICS PRACTICE PROBLEM SETS21Unit 4 WORK AND ENERGY4.1WORK, KINETIC ENERGY AND POTENTIAL ENERGY1. A rope is used to pull 255 N on a boat along side a pier. If the rope is held at aconstant 60 angle, with the horizontal, and the sailor pulls the boat 30 m, how muchwork is done by the sailor?Answer: 3825 J2. The dinosaur Tyrannosaurus rex is thought to have had a mass of about 7000 kg.a. How much kinetic energy would it have if its walking speed were about 4.0km/hr?Answer: 4320 Jb. How fast would a 70.0 kg person have to walk to have the same kinetic energyas the walking T. rex?Answer: 11.1 m/s3. How large a force is required to accelerate a 1300 kg car from rest to a speed of 20m/s in a distance of 80 m?Answer: 3250 N4. An 875-kg compact car is driving at 44.0 m/s when he sees a police car up ahead.Trying to avoid another speeding ticket, the driver slows down to 22.0 m/s.a. If it takes 250 meters to slow the car down, what is the average breaking forceon the car?Answer: -2540 Nb. The police officer caught the driver with his radar gun and decides to pull himover. Assuming the same breaking force from part a, how much distance willthe driver require slow down from 22.0 m/s to rest?Answer: 83.4 m5. A 0.50 kg block slides across a tabletop with an initial velocity of 20 cm/s and comesto rest in a distance of 0.70 m.a. Find the average friction force acting on the block.Answer: -1.4 Nb. Find the coefficient of friction between the block and the tabletop.Answer: 0.296. A 12-pack of cola with a mass of 4.30 kg is initially at rest on a horizontal floor. It isthen pushed in a straight line for 1.2 m by a horizontal force of 36.0 N. What is thefinal speed of the 12-pack if a. There is no friction between the 12-pack and the floor?Answer: 4.5 m/sb. The coefficient of kinetic friction between the 12-pack and the floor is 0.30.Answer: 3.6 m/s7. A comet with a mass of 7.85 x 1011 kg strikes Earth at a speed of 25.0 km/s.a. How much kinetic energy does the comet have? Answer: 2.45x1020 Jb. How much work is done to stop the comet?Answer: -2.45x1020 Jc. How many times larger (or smaller) is the work done than the energy releasedby the largest nuclear weapon ever built with an energy release of 4.2 x 1015 J?Answer: 58,000xGamzon & Gregorian-Michaelsen6/13/12

MECHANICS PRACTICE PROBLEM SETS228. A 66 kg rock climber first climbs 45 m upward to the top edgeof a quarry. Then he descends 85 m to the bottom of the quarry.Using the initial height as a reference, find the potential energyof the rock climber at a. The top of the quarry.Answer: 29,100 Jb. The bottom of the quarry.Answer: -25,900 JStartBottom9. A spring of negligible mass has a spring constant (K) of 1600 N/m.a. How much potential energy (PE) will be stored at equilibrium?Answer: 0 Jb. How much PE will be stored if it is extended 0.15 meters away fromequilibrium?Answer: 18.0 Jc. How far must the spring be compressed to store 3.20 J of potential energy?Answer: 0.06 mGamzon & Gregorian-Michaelsen6/13/12

MECHANICS PRACTICE PROBLEM SETS4.223WORK, CONSERVATION OF ENERGY AND POWER1. How much work does an 825 N force that pushes a car 35 meters do?Answer: 28,900 Ja. Would more, less, or the same amount of work be done if this 825 N forcewas applied at an angle of 45 ? Use calculations to support your answer.Answer: 8500 J less2. A compact car of 875-kg is driving with a velocity of 20.0 m/s?a. How much kinetic energy does it have?Answer: 175,000 Jb. What height above the ground would this car need to

MECHANICS PRACTICE PROBLEM SETS 8 Gamzon & Gregorian-Michaelsen 6/13/12 20. (G27) Determine the stopping distance for an automobile with an initial speed of 90 km/hr and human reaction time o