(5.2 m/s 2 up; 0.0m/s 2 ; 5.0 m/s 2 down)

Transcription

1 Exercises 1. A rope is attached to a 2.0 kg rock and pulled. Write a net force equation if the mass is a) accelerating up ( T - mg = ma) b) accelerating down (mg - T = ma) c) Find the cord tension if the mass is accelerating at i) 0.0 m/s 2 (20. N) ii) 1.0 m/s 2 UP ( 22 N) iii) 2.0 m/s 2 DOWN (16 N) iv) 9.8 m/s 2 DOWN (0.0 N) T 2 kg Fg 2. Find the acceleration of the mass if the cord tension is a) 30. N b) 19.6 N c) 9.6 N string 2 kg (5.2 m/s 2 up; 0.0m/s 2 ; 5.0 m/s 2 down) 3. In the diagrams below, assume the force F is the only horizontal force on the block. If the first block accelerates at rate a, then find an expression for the unknown acceleration. (a/2,2a) acceleration = a acceleration =? F M F 2M frictionless surface acceleration = a acceleration =? 2F F M M frictionless surface Physics 12 Student Workbook 80

2 4. A parachutist free-falls for a while and then opens their parachute. If the force of air resistance from the parachute is equal to the weight of the person, then which of the following is true? a) the person slows down b) the person speeds up c) the person moves at a steady speed explain your answer using principles of physics 5. A cyclist is moving to the right steadily at 8.2 m/s. If the force of air drag is 130 N, then what is the force of propulsion from the road? (130 N right) 6. A mass is being pulled up by a cable. If the mass is moving up and slowing down, compare the forces that act on the mass and write a net force equation (mg>t ; mg- T = ma) T Fg 7. Find the weight of a 80.0 kg person a) on the Earth b) on the Moon c) km above the surface of the Earth, where g= 5.70 N/kg (784 N; 128 N; 456 N) 8. An object in free-fall experiences only the force of gravity. for such an object a) draw a force diagram b) write a net force equation (mg = ma) c) solve for the acceleration (a= g) 9. A 75 kg mountain climber free-falls for 10.0 metres, then reaches the end of his safety rope. The rope stretches and stops the climber with 1.25 seconds. a) find the speed of the climber when the rope begins to stretch (14.0 m/s) b) write a net force equation for the 'slow down' by the rope (T-mg = ma) c) find the force from the rope (1580 N) 10. Add the force vectors to find the net force and direction: 6250 N North and N, 30.0 S of West (5420 N; 56.0 N of W) Physics 12 Student Workbook 81

3 Exercises 1. A 25.0 kg child is standing on a bathroom scale which reads in kg. The scale reads 32.0 kg. Describe the motion of the child. (2.74 m/s 2 acceleration up) 2. A person stands in an elevator. Write a net force equation in each case a) elevator at rest b) elevator accelerates up c) elevator moves up at constant speed d) elevator moves down at constant speed e) elevator accelerates down (F N =mg; F N -mg=ma; F N =mg; F N =mg; mg-f N =ma) 3. A 55.0 kg student is in an elevator accelerating up at 2.50 m/s 2. a) write a net force equation (F N -mg=ma) b) what would a force scale placed under their feet read? (676 N) 4. A 25 kg mass is falling and accelerating downwards a) write a force equation (mg-f air = ma; 65 N) b) What is the force of air resistance if the acc'n is 7.2 m/s 2 DOWN 5. a) A 5.00 kg rock is moving upwards on the earth and it experiences 5.00 N of air drag. Find its acceleration. b) A 5.00 kg rock is moving downwards on the earth and it experiences 5.00 N of air drag. Find its acceleration. c) The same rock is thrown downwards on the moon. Find its acceleration. (10.8 m/s 2 down; 8.8 m/s 2 down; 1.6 m/s 2 down... no air on moon!) 6. Find the acceleration if the applied force is a) 5 N (0.5 m/s 2 LEFT) b) 10 N (0 m/s 2 ) c) 20 N (1 m/s 2 right) 10 N applied Force friction 10 kg rock 7. A 200. kg spaceship speeds up from rest to 250. m/s in seconds. Assume there is no air friction and find a) the acceleration using kinematics (1250 m/s 2 ) b) the force from the engines ( N ) 8. A 250. gram ball is moving to the left at 25.0 m/s. A person catches it and stops it in seconds. Find the horizontal force and direction exerted on the ball by the person's hand. (19.5 N right) Physics 12 Student Workbook 87

4 9. A 55.0 kg parachutist is falling at constant speed. What force of air resistance acts on the person? (539 N up) 10. A 10. kg mass (initially at rest) is pulled with a force of 30. N across a 8.0 m long rough surface. The force of friction from the surface is 10. N. a) given that the mass accelerates right, write a net force equation b) Find the acceleration of the mass. c) find the final speed of the mass (T-Ff=ma; 2.0m/s 2 ;5.6 m/s) 10 kg rope rough surface 11. A plane flies north at 700. kph. The wind blows towards the East such that the resultant motion of the plane is along the line 20 E of N. Find the resultant speed of the plane. (745 kph) 12. A kg rocket accelerates straight upwards from the surface of the Earth. Find the thrust force from its engines if it is accelerating at 24.0 m/s 2. ( N) 13. A mass is thrown at an angle on flat ground. Sketch a graph showing the a) vertical velocity as a function of time b) horizontal velocity as a function of time 14. A parachutist jumps out of a plane and free falls. They reach terminal speed and maintain that speed for a while. Then they open their parachute. They quickly reach a different terminal speed and descend to the ground. Sketch a force- time graph. Explain for each section of the graph in a few words what is happening to the object. Physics 12 Student Workbook 88

5 Exercises 1. A force of 400. N is required to start a box moving across the floor (so friction must be about 400 N). If the box has mass 40.0 kg, find the friction coefficient (1.02) 2. A 20.kg box sits on a floor with µ=0.30. What force is required to move the box across the floor a) at steady speed (58.8 N ) b) accelerating at 1 m/s 2 (78.8 N) 3. A mass of 125 kg is being pulled to the right across a rough floor with an applied force of 200. N. Find the coefficient of friction if the acceleration of the mass is a) 0.0 m/s 2 (0.163) b) 1.50 m/s 2 right/speeding up (0.0102) c) 2.20 m/s 2 left/slowing down (0.388) 4. Find the acceleration of a 100. kg dragster if its tires have µ=0.80. (7.8 m/s 2 ) 5. A 50.0 kg rollerblader moving at 3.00m/s drags a foot on the ground to stop. If µ= 0.300, how far does the rollerblader go before stopping? (1.53 m) 6. A car is moving at speed v on a road with friction coefficient µ. Show that the stopping distance is given by d = v2 2µg 7. A 10. kg box sits on a floor with µ s =0.25 and µ k =0.20. Find the acceleration if the box is pulled with a) 15 N b) 22 N c) 30. N ( 0m/s 2 ; 0 m/s 2 ; 1.0 m/s 2 ) 8.. A 50.0 kg block is pushed with a force of 60.0 N across a 20.0 metre long floor. The first 10.0 metres of the floor are frictionless, but the last 10.0 metres have µ= Describe the motion of the block (4.90 m/s after 10m, then goes 5.38 m further and stops) 9. A 50.0 kg person falling at 8.00 m/s hits the floor and stops in seconds. Find the force that the floor exerts on this person. (8490 N) 10. A 55.0 kg person stands on a newton scale. Find the scale reading in each case a) elevator at rest b) elevator accelerates up at 1.00m/s 2 c) elevator moves up at constant speed d) elevator accelerates down at 1.00 m/s 2 e) elevator accelerates down at 9.80 m/s 2 (free fall) (539N; 594 N; 539 N; 484 N; 0N ) 11. Find the speed when this projectile hits the ground (17.9 m/s) 15.0 m 5.00 m/s Physics 12 Student Workbook 95

6 Exercises: 1. Find acceleration and cord tension (2m/s 2, 8 N) 12 N 4 kg 2 kg µ = 0 2. Find acceleration and cord tension (4.0 m/s 2 ; 48 N) 60. N 12 kg 3 kg µ = 0 3. Find acceleration (1.5 m/s 2 ) 21. N 8.0 kg 6.0 kg µ = 0 4. Find acceleration and cord tensions (3.0 m/s 2 ; 12 N; 18 N) 4.0 kg 2.0 kg 6.0 kg 36 N µ = 0 5. Find acceleration and cord tension (3.3 m/s 2 ; 13 N) 4.0 kg µ = kg 6. Find acceleration and cord tension (8.2 m/s 2 ; 33 N) µ = kg 20. kg Physics 12 Student Workbook 101

7 7. Write force equations for each mass (T = 6a; 30 - T = 3a) 6.00 kg 3.00 kg 30.0 N µ = Write force equations for each mass (T = 6a; T 1 = 3a) 6.00 kg µ= kg 9. a) write force equations for each mass (T = 12a; T 1 = 4a) b) find acceleration and cord tension (1.72 m/s 2 ; 32.3 N) 12.0 kg µ= kg 10. a) write force equation for each mass (30-T -3.92=4a; T-19.6 = 20a) b) find acceleration and cord tension (0.27 m/s 2 ; 25 N) 20. kg 4.0 kg 30. N µ = Find the acceleration of the system (4.1m/s 2 ) 3.0 kg 2.0 kg µ= kg Physics 12 Student Workbook 102

8 12. The blocks below are made of different materials and have different coefficients of friction. a) write force equation for each mass (T = 3a; T 2 -T =4a;117.6-T 2 =12a) b) solve for acc'n and tensions (4.4 m/s 2 ; 16 N; 65 N) 3.0 kg 4.0 kg µ=0.10 µ= kg 13. In the system below, the 2.0 kg moves with the 12 kg, ie. they accelerate as a system. Find the acceleration of the system and then find the coefficient of friction of the 2.0 kg. (3.6 m/s 2 ; 0.36) 2.0 kg 12 kg µ= kg 14. If the mass system below is accelerating upwards at 1.75 m/s 2, find the tension in the two cords. (upper:80.8 N; lower: 57.8 N) 2.00 kg 5.00 kg 15. A person (M) sits in a platform chair (m) and pulls themselves up using the rope. Write force equations for the person, chair and system fixed pulley person M platform chair m {T+F N -Mg=Ma; T-F N -mg=ma: 2T-(M+m)g=(M+m)a } Physics 12 Student Workbook 103

9 Exercises 1. The same water bottle from example #6 is now filled and thrown upwards. What will happen as the bottle is rising? leaky water bottle leaky water bottle after being thrown upwards. what happens as it rises? A) the water stops leaking out B) the water leaks out at the same rate C) the water leaks out faster Using principles of physics explain your answer. explanation: 2. Find the acceleration of these systems (2.3 m/s 2 ; 4.9 m/s 2 ) 3.5 kg 3M 5.7 kg M 3. Find the acceleration and the tensions (1.96 m/s 2 ; 39.2 N; 3.92 N) 5 kg 3 kg 2 kg frictionless surface Physics 12 Student Workbook 109

10 4. A 55 kg person pushes on the floor with 800. N of force for 0.25 seconds. How high do they jump off the ground? (7.2 cm) 5. A 40.0 kg table is on a floor with µk=0.270 and µs= Find a) the force required to move the desk (121 N) b) the acc'n of the desk if it is pushed with 150. N (1.10 m/s 2 ) 6. A diver jumps from a height of 24.0 metres into a swimming pool a) find her speed when she enters the water (21.7 m/s) b) if the diver stops after sinking 3.00 metres into the water, find the acc'n in the water (78.4 m/s 2 ) 7. Two rocks are dropped off a cliff, the second seconds after the first. How far below the cliff is the second stone when the rocks are m apart? (10.97 m) 8. The system shown below is at rest. Find the normal force exerted by the table (18N) 5.0 kg table 3.2 kg 9. There is humourous tale told of a worker who is caught in a pulley system, and pulled to the top of the system. The impact of the load stops the system within 0.15 seconds, but it causes half of the load to break off. The worker is then heavier and falls. The worker hits the ground, and stops within 0.50 seconds. Then he lets go of the rope and remaining load falls onto his head. Find the total time for this accident to occur. (7.42 sec) 80.0 kg load 60.0 kg worker 6.50 m 60.0 kg worker 40.0 kg load lets go of rope 40 kg breaks off 60.0 kg worker Physics 12 Student Workbook 110

11 Exercises 1. Consider a 10. kg mass on a 20. incline plane that is not moving. a) draw force diagram and write force equations b) find normal force, friction force and µ (F N =mgcos(θ); mgsin(θ)-f f =ma; 92 N; 33 N; 0.36) 10. kg A 5.00 kg mass slides down a 20.0 incline with µk= a) write force equations (F N =mgcos(θ); mgsin(θ)-f f =ma) b) Find the acc'n (1.97 m/s 2 ) 3. A 8.0 kg mass is on a 12 metre long 35 slope with µk=0.20. Find a) acc'n b) time to slide down slope c) speed at bottom of slope (4.0 m/s 2 ; 2.4 s; 9.8 m/s) 4. A mass m is sliding down a slope of angle θ with no friction. a) write a force equation (F N =mgcos(θ); mgsin(θ)=ma) b) find an expression for the acceleration. (gsin(θ)) 5. How long does it take a 20.0 kg mass to slide down a 13.0 m long, frictionless ramp inclined at 8.50? (4.24 sec) 6. A skater slides down an icy straight ramp. The ramp is 8 metres long, and it takes the skater 5.6 seconds to move down the ramp (assume frictionless). Find the angle of the ramp. (3 ) 7. A mass m is sliding down a slope of angle θ with friction coefficient µk. a) write a force equation using these variables b) find an expression for the acceleration. (F N =mgcos(θ); mgsin(θ)-µf N =ma ; a=gsin(θ) - µk g cos(θ)) 8. A 10. kg mass slides up a 30. incline with an initial speed of 10. m/s. The incline has friction coefficient µk=0.15. Find a) force equations b) F f & direction b) acc'n c) time to stop ( F N =mgcos(θ); mgsin(θ)+f f =ma; 13 N down slope; 6.2 m/s 2 ; 1.6 sec) 9. A 10 kg mass slides up a ramp inclined at 10.0 and stops after 4.06 metres. If the mass was initially moving at 4.00 m/s, find the coefficient of friction. (0.0278) 10. A mass m is sliding UP a slope of angle θ with friction coefficient µk. a) write force equations ( F N =mgcos(θ); mgsin(θ)+ µf N =ma) b) find an expression for the acceleration. (a= gsin(θ) + µk g cos(θ) Physics 12 Student Workbook 117

12 11. A 5.0 kg mass is at rest on a 15 slope. Find the value of µs. (0.27) 12. The friction of rubber soles on asphalt shingles is µs,max = What is the maximum angle roof at which a 55 kg roofer can walk without slipping? (35 ) 13. A mass m is at rest on a slope of angle θ with friction coefficient µs. a) write force equations (F N =mgcos(θ); mgsin(θ)=f f ) b) Find an expression for µs. (µs= tan(θ) ) 14. The table below has leg separation L= 1.25 metres. A textbook placed on it starts to slide when the table is lifted to a height of H= 45.0 cm. Find the friction coefficient between the book and table. (0.386) L H 15. A 2.2 kg mass moving at 20.0 m/s starts up a 25.0 slope that has µk= It slows down, stops, and then remains held in place by static friction. Find a) how far it slides b) µs (36.5 m; 0.466) 16. If the mass shown below is to remain stationary, then find a) the maximum value of F b) the minimum value of F (1660 N; 416 N) 150. kg F 45.0 µ -s-max=0.600 (hint: if F is large, which way would the mass tend to slide? and so what will be the direction of friction?) Physics 12 Student Workbook 118

13 Exercises 1. For the system below, find a) direction of motion (4.0 kg goes up, 10. kg slides down) b) friction & direction (7.51 N up ramp) c) acc'n (1.16m/s 2 ) d) cord tension (43.8 N) mu-k=0.100 mu-s-max= kg 10.0 kg A cart is given a push, so that it travels up a frictionless ramp. The cart slows to a stop and then rolls back down the ramp. What can be said about the acceleration of the cart as it is going up the ramp and as it is going down? A) the acceleration is greater when the cart is going up B) the acceleration is greater when the cart is going down C) the acceleration is the same when the cart is going up and down push rises falls 3. In the diagram below, the surfaces are frictionless and the system is at rest. How large is the mass M? (7.66 kg) M 5.00 kg Physics 12 Student Workbook 122

14 4. The system shown is at rest, but if pushed slightly, it will begin sliding. Find a) friction force b) direction system will move c) coefficient of maximum static friction (4.90 N; 3kg down; 0.115) 5.00 kg 3.00 kg Find the direction of motion and the acceleration µ=0 10. kg 120 N 32 (up ramp; 5.0m/s 2 ) 6. If the surface shown below is frictionless and the system moves at constant speed, find the value of θ. (58 ) 5.0 kg 6.0 kg θ A mass is initially sliding down a rough (µ=0.700) 8.00 ramp at 2.50 m/s. How far does it slide before stopping? (0.576 m) Physics 12 Student Workbook 123

15 8. For the system below, find a) direction of motion b) acceleration c) speed of system after 3 seconds (to right; m/s 2, m/s) 5.00 kg mu= kg A 50.0kg water skier initially moving at 18.0 m/s slides up a 7.00m long frictionless ramp inclined at Find a) acc'n on ramp b) speed when leaving ramp c) height of ramp at end d) flight time of skier e) range of skier (4.90 m/s 2 ; 16.0 m/s; 3.50 m; 1.99 sec; 27.5 m) 18.0 m/s v=? A 50. kg box is on a truck that is moving East at 15 m/s î. The truck slows quickly to a stop, accelerating at (-6.2 î) m/s 2. The box remains at rest on the back of the truck, but just barely. a) discuss the direction of the friction force on the box b) write force equations for the box (F f =ma) c) find the coefficient of friction between the box and the truck. (0.63) box truck 15 m/s box truck rest 11. Draw force diagrams for each of the masses and write force equations m1 upwards acc'n m2 (T 1 -m 1 g-t 2 =m 1 a T 2 -m 2 g = m 2 a) Physics 12 Student Workbook 124

16 Exercises 1. A 25.0 kg lawn mower is pushed with 500. N of force. The handle angle is 45.0 and the friction coefficient is µk= Find the acceleration (10.6 m/s 2 ) 2. A 50.0 kg mower is PULLED with a 300. N force along its handle, which is at If µk=0.100, find the normal force, friction force and acceleration (297 N, 29.7 N, 4.00 m/s 2 ) 3. Find the normal force, the friction force and the acceleration for this system. (87.7 N, 8.77 N, 1.44 m/s 2 ) 12.0 N 8.00 kg µ= Which direction will this system move? (down the ramp) 60.0 N kg In #4, assume that µk=0.100 and find the normal force, net force down the ramp and the acceleration (200. N; 26.1 N; 1.30 m/s 2 ) 6. If the boat shown below goes straight East then find the force F and the acceleration (150. N, 2.60 m/s 2 ) F 100. kg 300. N 30.0 S of E 7. Linda pulls on a sled with a force of N at 30.0 E of N. Elaine pulls with N at 5.00 W of N. Find the resultant force & direction (149 N, 15.0 EofN) 8. Find the net force & direction by adding the two force vectors graphically F 1 = 30.0 N East F 2 = 45.0 N at 20.0 E of N (62.0 N, 43.0 N of E) Physics 12 Student Workbook 129

17 9. Find the net force (and direction) in each case 4.0 N 4 N 3 N 4.0 N 4 N 4 N 3.0 N 3.0 N 4.0 N 4.0 N 2.0 N 7 N 3 N 7 N 2.0 N 7 N 5.0 N 7 N 5.0 N 7 N 7 N 10. N (0N, 1 N East, 5.0 N 53 N of E, 5.0 N 37 S of W, 5.0 N 53 N of E, 5.0 N 37 S of W, 10 N NE, 10 N NE, 0 N, 7 N S) 10 N, SW 10 N, SW 10. Find the tension in the two strings if the mass is at rest (30.4 N; 7.90 N) kg 11. Find the cord tension (note since the angles are the same, the tension will be the same in both cords) (115 N) kg 12. If in question 11, we make both of the angles smaller, what will happen to the tension? a) increase b) decrease c) remain the same Using principles of physics, explain your answer Physics 12 Student Workbook 130

18 Exercises and Review 1. a) write force equations b) find the tension in the two cords supporting the load kg (187 N; 99.5 N) 2. Two force scales are set up as shown below and they measure 40 N of tension in the cord. If another force scale is then attached and we exert 10 N of sideways force on the cord, then which of the following could be the readings on the force scales at the end of the cord? Note that the cord has been deflected by a very small angle (< 5 ) a) 45 N b) 41 N c) 40 N d) 50 N e) more than 50 N scale scale 40 N 40 N scale?? scale scale 10 N Using principles of physics explain your answer. 3. A wedge is an inclined plane that can be used to amplify forces. Consider the wedge below which is begin pushed downwards and is in equilibrium. Find the normal force on the sides of the wedge (ignore friction and the mass of the wedge) 120. N 120. N axe FN 10.0 FN block of wood (688 N) 4. Find the force required to maintain equilibrium if a 20.0 N force acts east and a 40.0 N force acts South (44.7 N; 63.4 N of W) Physics 12 Student Workbook 135

19 5. Draw a force diagram and write net force equations a) θ 1 static b) static 2 c) falling no air resistance d) θ static θ static static e) θ 1 2 φ f) static g) frictionless θ frictionless h) θ static i) rough j) sliding at constant speed θ frictionless k) accelerating up l) sliding right and slowing down rough Physics 12 Student Workbook 136

20 m) accelerating down n) accelerating right θ a) T1sin(θ) = mg; T1cos(θ) = T2 b) T=mg c) mg = ma d)tcos(θ)=t cos(θ) ; 2T sin(θ) = mg e) T1cos(θ) = T2cos(φ) ; T1sin(θ) + T2sin(φ) = mg f) FN=mg g) FN=mgcos(θ); T=mgsin(θ) h) mgsin(θ) = ma i) FN=mgcos(θ); Ff=mgsin(θ) j) FN=mg k) FN - mg = ma l) FN=mg; Ff= ma m) mg- T = ma n) T sin(θ) = mg; T cos(θ) = ma) 7. If a railcar (with pendulum) is given an initial velocity so that it moves up a frictionless ramp a certain distance before stopping, which diagram shows the correct position of the pendulum as the cart is rising up the ramp a) b) c) d) Using principles of physics explain your answer. 8. Solve for the tension in the cords using graphical addition of vectors 55.0 cable 1 cable kg (598 N; 343 N) 9. A kg rocket car is placed at the bottom of a 100. metre long ramp inclined at The rocket is turned on and it exerts a force of 8300 N for 5.70 seconds, and then it shuts down. Find the speed with which the rocket car leaves the ramp (assume frictionless) (28.8 m/s) 10. An object moves for 2.00 hours at 120. kph NorthEast, then travels 220. km at 30.0 S of E at a constant 80.0kph, then moves at 100. kph for a distance of 75.0 km to the West. Find a) the displacement vector (285î j^= 291 km, 11.8 NE) b) the average velocity vector (53.0 kph, 11.8 N of E) c) the average speed (97.3 kph) Physics 12 Student Workbook 137

21 Lesson 10: Practice Exam Section I. Multiple Choice. 1 mark each, 30 marks total 1) A 15 kg block rests on a level, frictionless surface and is attached via a string and pulley to a 5.0 kg overhanging mass. The system is released. Find the tension in the string a) 65 N b) 17 N c) 49 N d) 37 N e) 24.5 N 15 kg 5 kg 2) A 2.00 kg block is placed on a frictionless incline of What is the acceleration once the mass is released? a= m/s 2 a) 7.50 b) 3.14 c) 6.30 d) 12.6 e) 0 3) Two forces act on a 35 kg object: a 30. N force due North and a 40. N force due East. What is the acceleration of the object? a= m/s 2 a) 1.4 b) 155 c) 3.5 d) 0.7 e) 2 4) A mass m is placed on a frictionless 30. incline. If the incline is 10. metres long, how long does it take the mass to reach the bottom? a) 1.5 s b) 1.4 s c) 4.1 s d) 2.4 s e) 2.0 s 5) A kg sailboat experiences two forces: N towards the East and N towards the NorthWest. What is the direction of the acceleration? a) 60. N of W b) 30. N of W c) 30. N of E d) 74 N of W e) 52 N of W 6) A 5.00 kg block is moving upwards along a 30.0 incline with µ k = What is its acceleration? a = m/s 2 a) 4.90 b) 1.51 c) 9.80 d) 3.39 e) ) A person pushes a 20.0 kg lawnmower with a 100. N force along a 30.0 handle. What is the normal force acting on the mower? a) 98.0 N b) 198 N c) 196 N d) 246 N e) 282 N kg 8) What is the acceleration of the following Atwood machine? a= m/s 2 a) 4.2 b) 3.0 c) 2.8 d) 9.8 e) kg 5.0 kg Physics 12 Student Workbook 138

22 9) This system is at rest. How much friction is there on the incline mass and in what direction does friction act? (up or down the ramp) 4 kg 3 kg 40 friction direction a 10 N up b 4 N down c 4 N up d 0.4 N up e 0.4 N down ****10 and 11******************* A 250 kg crate rests on a level surface with µ k = ) If a horizontal force of N is needed to overcome the static friction on a 250. kg crate, what is µ s,max? a) 3.0 b) 0.15 c) 0.28 d) 0.31 e) ) If the object begins to slide under a N force, what is the acceleration of the block? a= m/s 2 a) 2.5 b) 1.8 c) 3.0 d) 3.8 e) 0 12) A soccer player kicks a 0.40 kg ball from rest to 9.0 m/s in 0.15 s. What is the average force exerted on the ball? a) 48 N b) 72 N c) 24 N d) 60 N ****13 and 14************************* A hockey puck initially moving at 8.0 m/s travels across rough ice and stops in 16 m. 13) Find the acceleration of the puck: a= - m/s 2 a) 1.0 b) 2.0 c) 2.4 d) 3.2 e) ) What is µ k? a) 0.05 b) 0.10 c) 0.20 d) e) 0.25 ****15 and 16************************ A 300. kg crate rests on an adjustable inclined plane. 15) If the crate starts to slide when the angle of the incline is 25, what is the maximum coefficient of static friction? a) 0.42 b) 0.47 c) 0.90 d) 0.12 e) 2.14 Physics 12 Student Workbook 139

23 16) If the incline is oiled so that an incline of 25 produces an acceleration of 0.70 m/s 2 then what is the coefficient of kinetic friction? a) 0.47 b) 0.42 c) 0.32 d) 0.12 e) 0.39 ****17 and 18************************* An elevator weighing N is supported by a cable. The maximum tension the cable can support is N. 17) What is the cable tension if the elevator accelerates upwards at 3.00 m/s 2? a) N b) N c) N d) N e) N 18) What is the maximum safe acceleration of the elevator? a= m/s 2 a) 3.50 b) 2.50 c) 4.90 d) e) ) You are in an elevator accelerating downwards at 1.0 m/s 2. If your mass is 100. kg, what is your apparent weight? a) 980 N b) 880 N c) 970 N d) 1080N e) 100 N 20) A skydiver is falling through the air. If he adjusts his parachute so that the force of air resistance from his chute balances the force of gravity, what will happen? a) he will stop b) he will slow down c) he will fall at constant velocity d) the chute will break e) he will continue to speed up 21. A car accelerates from rest up a hill. Which is the best force diagram? Note that the car is rolling and not sliding. A B C D 22. Select the best response: In order to start an object moving on a rough surface, a) you must have maximum static friction b) you pull with a force slightly larger than the force of kinetic friction c) the force you pull with must exceed the force of friction d) your maximum force must pull with more friction e) the applied force must be larger than maximum static friction Physics 12 Student Workbook 140

24 *********23, 24 and 25********** Consider the two masses m1 and m2 which are supported by strings string 1 m1 string 2 m2 23. What forces act on mass m1? a) gravity, applied force, tension b) upwards tension, applied force, gravity c) upwards tension, downwards tension, net force d) downwards tension, upwards tension, applied force e) downwards tension, upwards tension, gravity 24. What is the tension in string 1 if the system is at rest? T = a) weight of m1 b) weight of m1 and m2 c) weight of m2 d) zero e) 9.8 N 25. If string 1 is cut and the two masses free-fall, what will be the tension in string 2? a) zero b) weight of m1 and m2 c) weight of m2 only d) weight of m1 only e) What is the net force on this mass? 6.0 N 8.0 N a) 2.0 N b) 14 N c) 7.0 N d) 10. N e) 20. N 27. A mass M sits on a flat surface. If the surface is accelerating upwards, which equation is true? a) F = ma b) T - mg = ma c) mg = ma d) T - F f = ma e) F N - mg = ma Physics 12 Student Workbook 141

25 28. What is the angle of a ramp if a rollerblader rolls from rest 6.0 metres in 2.5 seconds? a) 29 b) 14 c) 11 d) 5.6 e) 1.9 *******29 and 30 ****************** frictionless 2.0 kg 7.0 kg 3.0 kg 29. What is the acceleration of this system? a = m/s 2 a) 3.9 b) 3.3 c) 5.7 d) 2.5 e) What is the correct force diagram (arrows to scale) for the 2 kg mass? A B C D d c a e d e d a b d b c b c b e d c b c a e e b a d e c b c Section II: Problems. Answer in the space provided. (20 marks total) 1. (5 marks) A 3 kg object is placed on a 35 incline where µ = 0.25 and then released. Write force equations and find the acceleration. (3.6 m/s 2 ) 2. (5 marks) A student of mass M puts a bathroom scale on a skateboard and then rolls down a ramp which in inclined at angle θ. What will the scale read? a) M b) less than M c) more than M Using principles of physics explain your answer. explanation: Physics 12 Student Workbook 142

26 3. (5 marks) A person holds a book against a wall by pushing on an 50.0 angle as shown below with a force of 27.0 N. The friction constant for the book on the wall is µ= The book is barely held in place by the 27.0 N force, ie it is tending to fall. a) draw a force diagram for the book; clearly label all forces acting on it b) write vertical and horizontal force equations c) find the book mass bonus) find the maximum force the person could exert on this book (at the angle shown below) and still have it remain at rest. vertical book 50 horizontal push wall (F sin(50) = F N ; F cos(50) + F f = mg ; 2.24 kg; 46.2 N) 4. (5 marks) An object on an incline is acted upon by a horizontal force F. If the friction coefficient is µ, write the force equations for the system. F θ θ (F sin(θ) + mg cos(θ) =F N ; F cos(θ) -F f - mgsin(θ) = ma OR mgsin(θ) -F cos(θ) -F f - = ma ) Physics 12 Student Workbook 143

27 other (hard) practice exam problems 1. What is the minimum force F required to keep the mass at rest on the incline if the coefficient of friction is µ = 0.270? The force is perpendicular to the incline and the mass is 10.0 kg. F 10.0 kg 20.0 (32.0 N) 2. A 10.0 kg object on an 32.0 incline is acted upon by a horizontal force (F). If the friction coefficient is µ = 0.150, find the maximum and minimum force for which the object will not move. F (83.8 N; 42.5 N) 3. Find the smallest value of the mass M for which the system will remain at rest given that the coefficient of static friction is kg µ=0.100 M 25.0 (4.98 kg) Physics 12 Student Workbook 144

28 4. Find the tension in the cord connecting the 6.00 kg and 2.00 kg masses. Assume all surfaces are frictionless. (1.96 N) 2.00 kg 6.00 kg kg A person holds a 6.00 kg book against a wall by pushing on an 50.0 angle as shown below. The friction constant for the book on the wall is µ=0.220 a) draw a force diagram for the book b) write vertical and horizontal force equations c) find the minimum push force required to keep the book at rest. bonus) why does the word 'minimum' need to be specified in this problem? Your answer should include a calculation (its up to you to decide what to calculate) vertical 6 kg book 50 horizontal wall push (F sin(50) = F N ; F cos(50) + F f = mg ;72.5 N ; at rest for any force 72.5 N to 124 N) 6. For the system below, find the maximum and minimum value of the mass M for which the system will remain at rest. mu-s-max=0.300 mu-k=0.200 M kg 20.0 (16.3 kg; 119 kg) Physics 12 Student Workbook 145