# ACTIVITY BASED PHYSICS

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1 ACTIVITY BASED PHYSICS MECHANICS PRACTICE PROBLEM SETS SOUTHINGTON HIGH SCHOOL CCP PHYSICS

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3 MECHANICS PRACTICE PROBLEM SET TABLE OF CONTENTS UNIT 2 KINEMATICS One Dimensional Motion Freefall Projectile Motion UNIT 3 DYNAMICS Newton s First and Second Laws Tension, Friction & Vectors Dynamics Review Problems UNIT 4 WORK AND ENERGY Work, Kinetic Energy and Potential Energy Work, Conservation of Energy and Power Work and Energy Review Problems UNIT 5 IMPULSE, MOMENTUM & CONSERVATION OF MOMENTUM Impulse and Momentum Conservation of Momentum Impulse, Momentum and Conservation Review UNIT 6 UNIFORM CIRCULAR MOTION Uniform Circular Motion & Gravity Circular Motion Review... 37

6 MECHANICS PRACTICE PROBLEM SETS (G27) Determine the stopping distance for an automobile with an initial speed of 90 km/hr and human reaction time of 1.0 sec for an acceleration of -4.0 m/s 2. Answer: 103 m g. Repeat this process for an acceleration of -8.0 m/s 2. Answer: 64 m 21. (G29) A speeding motorist traveling 120 km/hr passes a stationary police officer. The officer immediately begins pursuit at a constant acceleration of 2.78 m/s 2. How much time will it take for the police officer to reach the speeder, assuming that the speeder maintains a constant speed? Answer: 24.0 s h. How fast will the police officer be traveling at this time? Answer: 240 km/hr

9 MECHANICS PRACTICE PROBLEM SETS Highway safety engineers build soft barriers so that cars hitting them will slow down at a safe rate. A person wearing a safety belt can withstand an acceleration of 300 m/s 2. How thick should barriers be to safely stop a car that hits a barrier at m/s? Answer: x = 1.6 m 18. A weather balloon is floating at a constant height above Earth when it releases a pack of instruments. a. If the pack hits the ground with a velocity of 73.5 m/s, how far does the pack fall? b. How long does the pack fall? Answer: t = 7.5 sec Answer: y = 276 m down 19. Kyle is flying a helicopter that is rising at 5.0 m/s when he releases a bag of tools. After 2.0 s c. What is the bag's velocity? Answer: v f = m/s d. How far has the bag fallen? Answer: y = -9.6 m e. How far below the helicopter is the bag? Answer: 19.6 m apart

12 MECHANICS PRACTICE PROBLEM SETS 14 Unit 3 DYNAMICS 3.1 NEWTON S FIRST AND SECOND LAWS 1. If a net horizontal force of 132 N is applied to a person with a mass of 60 kg who is resting on the edge of a swimming pool, what horizontal and vertical acceleration is produced? Answer: a x = 2.2 m/s 2 a y =0 m/s 2 2. A 61.0 kg object is to be given a horizontal acceleration of m/s 2. How large an unbalanced force must act upon it? Answer: 43 N 3. 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/s 2 4. A towrope will break if the tension in it exceeds 1500 N. It is used to tow a 700 kg car along level ground. What is the maximum acceleration of the car if the wind resistance results in an opposing force of 25 N? Answer: 2.1 m/s 2 a. If the car is going to be towed onto the highway, it needs to reach a speed of 30 km/hr. How long will it take to get to this speed? Answer: 4.0 sec b. How much distance is covered in this time? Answer: 17 m 5. What average force is needed to accelerate a 7.00-gram pellet from rest to 175 m/s over a distance of m along the barrel of a rifle? Answer: 153 N 6. A box rests on a frozen pond, which serves as a frictionless horizontal surface. A fisherman 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/s 2, what is the mass of the box? Answer: 13.9 kg 7. Both Suzy and Maria both want to pull their little sister, Michelle, on a sled. Suzy grabs hold of the rope attached to the front of the sled and pulls on it with a force of 25.0 N at an angle of 45. Maria grabs hold of the rope on the back of the sled and pulls in the opposite direction with a force of 21.0 N also at an angle. The total mass of the sled and Michelle is 70 kg. At what angle must Maria pull if the sled is to remain stationary? Answer: 33 a. At what angle must she pull if Michelle is to move at a constant velocity of 5 m/s to the right? b. At what angle must she pull if Michelle is to move at a constant velocity of 2 m/s to the left?

13 MECHANICS PRACTICE PROBLEM SETS An advertisement claims that their car can stop on a dime. What net force would actually be necessary to stop an 850-kg automobile traveling initially at 45.0 km/hr in a distance that is equal to the diameter of a dime, which is 1.8 cm? Answer: 3.7 x 10 6 N 9. 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 10 4 N a. Assuming the driver has a mass of 68 kg, how many times larger is the force on the car than the horizontal force exerted on the driver by the seat? Answer: 13x

15 MECHANICS PRACTICE PROBLEM SETS A cart is released at the top of an inclined plane that is elevated 20.0 from the horizontal. The cart has a mass of 1.12 kg and reaches a velocity of 1.2 m/s after 3.0 seconds. What is the coefficient of kinetic friction between the incline and the block? Answer: µ = Add the following vectors both graphically and analytically. Your answer for each method must include the both the magnitude and the angle. A = 2.5 cm at 40 B = 6.0 cm at 150 Answer: R = 5.7 cm at 125

17 MECHANICS PRACTICE PROBLEM SETS 19 b. On Mars (g=3.7 m/s 2 )? Answer: 2.4 x 10 2 N c. In outer space traveling at constant velocity? Answer: 0 N 9. (G7) What average force is required to stop an 1100-kg car in 8.0 seconds if it is traveling at 90 km/hr? Answer: 3.4 x 10 3 N opposite direction 10. (G11) What is the average force exerted by a shot-putter on a 7.0 kg shot if the shot is moved through a distance of 2.8 m and is released with a speed of 13.0m/s? Answer: 2.1 x 10 2 N 11. (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/s 2 down 12. (G17) The cable supporting a 2100-kg elevator has a maximum strength of 21,750 N. What maximum upward acceleration can it give the elevator without breaking? Answer: m/s (G19) A Saturn V rocket has a mass of 2.75 x 10 6 kg and exerts a force of 33 x 10 6 N on the gases it expels. Ignoring the mass of the gases expelled and assuming that g remains constant, determine: a. The initial vertical acceleration of the rocket. Answer: 2.2 m/s 2 b. Its velocity after 8.0 sec. Answer: 18 m/s c. How long it takes to reach an altitude of 9500 m. Answer: 93 sec

19 MECHANICS PRACTICE PROBLEM SETS A 66 kg rock climber first climbs 45 m upward to the top edge of a quarry. Then he descends 85 m to the bottom of the quarry. Using the initial height as a reference, find the potential energy of the rock climber at a. The top of the quarry. Answer: 29,100 J b. The bottom of the quarry. Answer: -25,900 J Start Bottom 9. 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 J b. How much PE will be stored if it is extended 0.15 meters away from equilibrium? Answer: 18.0 J c. How far must the spring be compressed to store 3.20 J of potential energy? Answer: 0.06 m

24 MECHANICS PRACTICE PROBLEM SETS (G43) A vertical spring (ignore its mass) whose spring constant is 900 N/m is attached to a table and is compressed m. a. What speed can it give to a kg ball when released? Answer: 8.22 m/s b. How high above its original position (spring compressed) will the ball fly? Answer: 3.44 m 28. (G51) A ski starts from rest and slides down a 20 incline 100 m long. a. If the coefficient of friction is 0.090, what is the ski s speed at the base of the incline? Answer: 22 m/s b. If the snow is level at the foot of the incline and has the same coefficient of friction, how far will the ski travel along the level ground? Use energy methods! Answer: 274m 29. (G55) A kg block is firmly attached to a very light horizontal spring (k = 180 N/m). It is noted that the block-spring system, when compressed 5.0 cm and released, stretches out 2.3 cm beyond the equilibrium position before sopping and turning back. What is the coefficient of kinetic friction between the block and the table? Answer: (G65) A pump is to lift 8.00 kg of water per minute through a height of 3.50 m. What power rating should the pump motor have? Answer: 4.57 W

26 MECHANICS PRACTICE PROBLEM SETS 28 b. What is the change in momentum of the bullet if it ricochets in the opposite direction with a speed of 99 m/s? Answer: kg m/s 9. A kg freight car is rolling along a track at 3 m/s. Calculate the time needed for a 1000 N force to stop it. Answer: 30 sec 10. A kg hockey puck is moving to the right at 3.00 m/s. What is the velocity of the puck after a force directed to the right with a magnitude of 25.0 N is applied for s? Answer: 10.8 m/s

27 MECHANICS PRACTICE PROBLEM SETS CONSERVATION OF MOMENTUM 1. A 95-kg fullback running at 8.2 m/s collides in midair with a 128-kg defensive tackle moving in the opposite direction. After the collision, both players come to rest. How fast was the tackle moving initially? Answer: -6.1 m/s 2. A thread holds two carts together as shown in the diagram below. After the thread is cut, a compressed spring pushes the carts apart, giving the 1.5-kg car a speed of 27 cm/s to the left. What is the velocity of the 4.5-kg car? Answer: 9.0 cm/s to the right 3. Two campers dock a canoe. Once the canoe comes to rest, one camper with a mass of 80.0-kg gets off the canoe with a velocity of +4.0 m/s. The canoe and the other camper drift off in the opposite direction with a speed of 2.78 m/s. What is the combined mass of the canoe and the second camper? Answer: 115 kg 4. A spaceship with a mass of 2.0 x 10 6 kg is cruising at a speed of 5.0 x 10 6 m/s when it blows up into two pieces. One section, with a mass of 7.5 x 10 5 kg is blown straight backwards with a speed of 1.0 x 10 6 m/s. What is the magnitude and direction of the velocity of the second piece of the spaceship? Answer: 8.6 x 10 6 m/s 5. A ceramic penguin with a mass of 0.5 kg suddenly bursts apart into two pieces. One piece has a mass of 0.15 kg and has a velocity of -2.0 m/s. What is the velocity of the second piece? Answer: 0.86 m/s 6. The nucleus of an atom has a mass of 3.80 x kg and is at rest. The nucleus is radioactive and suddenly ejects a particle of mass 6.60 x kg at a speed of 1.50 x 10 7 m/s. Find the recoil speed of the nucleus that is left behind. Answer: x 10 5 m/s 7. A 0.2 kg plastic ball moves with a velocity of 0.3 m/s. It collides with a second plastic ball of mass 0.1 kg, moving along the same line at a velocity of 0.1 m/s. After the collision, the velocity of the 0.1 kg ball is 0.26 m/s. What is the new velocity of the first ball? Answer: 0.22 m/s

29 MECHANICS PRACTICE PROBLEM SETS 31 Answer: v 1f = -0.1 m/s, v 2f =.5 m/s 16. An 8.00g bullet is fired into a 250g block that is initially at rest on the edge of a table that is 1m tall. The bullet remains in the block and after the collision the block lands 2.00m from the base of the table. What is the initial velocity of the bullet? Hint: You will need to use projectile motion to solve this one! Answer: v b = 142.9m/s

32 MECHANICS PRACTICE PROBLEM SETS 34 Answer: 15 m/s 18. (G62) A 5800-kg open railroad car coasts along with a constant speed of 8.60 m/s on a level track. Snow begins to fall vertically and fills the car at a rate of 3.50 kg/min. Ignoring friction with the tracks, what is the speed of the car after 90.0 min? Answer: 8.16 m/s 19. (G66) A 140-kg astronaut (including space suit) acquires a speed of 2.50 m/s by pushing off with his legs from an 1800-kg space capsule. As the reference frame, use the position of the capsule before the push. a. What is the change in speed of the space capsule? Answer: m/s b. If the push lasts s, what is the average force exerted by each one the other? Answer: 700 N

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