Slide 1 / 76 Slide 2 / 76 1 driver in a 2000 kg Porsche wishes to pass a slow moving school bus on a 4 lane road. What is the average power in watts required to accelerate the sports car from 30 m/s to 60 m/s in 9 seconds? Work & nergy Multiple hoice Problems 1,800 5,000 10,000 100,000 300,000 Slide 3 / 76 Slide 4 / 76 2 force F is at an angle θ above the horizontal is used to pull a heavy suitcase of weight mg a distance d along a level floor at constant velocity. The coefficient of friction between the floor and the suitcase is μ. The work done by the force F is: Fdcos θ - μ mgd Fdcos θ -μ mgd 2Fdsin θ - μ mgd Fdcos θ - 1 3 force of 20 N compresses a spring with spring constant 50 N/m. How much energy is stored in the spring? 2 J 5 J 4 J 6 J 8 J Slide 5 / 76 Slide 6 / 76 4 stone is dropped from the edge of a cliff. Which of the following graphs best represents the stone's kinetic energy K as a function of time t? 5 4 kg ball is attached to a 1.5 m long string and whirled in a horizontal circle at a constant speed of 5 m/s. How much work is done on the ball during one period 9 J 4.5 J zero 2 J 8 J
Slide 7 / 76 6 student pushes a box across a horizontal surface at a constant speed of 0.6 m/s. The box has a mass of 40 kg, and the coefficient of kinetic friction is 0.5. The power supplied to the box by the person is Slide 8 / 76 7 force F is applied in horizontal to a 10 kg block. The block moves at a constant speed 2 m/s across a horizontal surface. The coefficient of kinetic friction The work done by the force F in 1.5 minutes is: 40 W 60 W 150 W 120 W 200 W 9000 J 5000 J 3000 J 2000 J 1000 J Slide 9 / 76 8 ball swings from point 1 to point 3. ssuming the ball is in SHM and point 3 is 2 m above the lowest point 2. nswer the following questions. What happens to the kinetic energy of the ball when it moves from point 1 to point 2? Slide 10 / 76 9 ball swings from point 1 to point 3. ssuming the ball is in SHM and point 3 is 2 m above the lowest point 2. nswer the following questions. What is the velocity of the ball at the lowest point 2? increases decreases remains the same zero more information is required 2.2 m/s 3.5 m/s 4.7 m/s 5.1 m/s 6.3 m/s Slide 11 / 76 10 block with a mass of m slides at a constant velocity V 0 on a horizontal frictionless surface. The block collides with a spring and comes to rest when the spring is compressed to the maximum value. If the spring constant is K, what is the maximum compression in the spring? Slide 12 / 76 11 2 kg block released from rest from the top of an incline plane. There is no friction between the block and the surface. How much work is done by the gravitational force on the block? V 0 (m/k) 1/2 KmV 0 V 0 K/m m V 0 /K V 0 (K/m) 1/2 F (V 0 m/k) 1/2 80 J 60 J 50 J 40 J 30 J
Slide 13 / 76 12 2 kg block released from rest from the top of an incline plane. There is no friction between the block and the surface. What is the speed of the block when it reaches the horizontal surface? Slide 14 / 76 13 crane lifts a 300 kg load at a constant speed to the top of a building 60 m high in 15 s. The average power expended by the crane to overcome gravity is: 3.2 m/s 4.3 m/s 5.8 m/s 7.7 m/s 6.6 m/s 10,000 W 12,000 W 15,000 W 30,000 W 60,000 W Slide 15 / 76 14 satellite with a mass m revolves around arth in a circular orbit with a constant radius R. What is the kinetic energy of the satellite if arth s mass is M? Slide 16 / 76 15 n apple of mass m is thrown in horizontal from the edge of a cliff with a height of H. What is the total mechanical energy of the apple with respect to the ground when it is at the edge of the cliff? ½ mv mgh ½GMm/R 2 ½ GMm/R 2Mm/R 2 1/2mv 0 mgh ½ mv 2 0 - mgh 2 mgh - ½ mv 0 2 mgh + ½ mv 0 Slide 17 / 76 16 n apple of mass m is thrown in horizontal from the edge of a cliff with a height of H. What is the kinetic energy of the apple just before it hits the ground? Slide 18 / 76 17 500 kg roller coaster car starts from rest at point and moves down the curved track. Ignore any energy loss due to friction. Find the speed of the car at the lowest point. ½ mv 2 0 + mgh ½ mv 2 0 - mgh mgh 2 ½ mv 0 2 mgh - 1/2 mv 0 10 m/s 20 m/s 30 m/s 40 m/s 50 m/s
Slide 19 / 76 18 500 kg roller coaster car starts from rest at point and moves down the curved track. Ignore any energy loss due to friction. Find the speed of the car when it reaches point. 10 m/s 20 m/s 30 m/s 40 m/s 50 m/s Slide 20 / 76 19 Two projectiles and are launched from the ground with velocities of 50 m/s at 60 and 50 m/s at 30 with respect to the horizontal. ssuming there is no air resistance involved, which projectile has greater kinetic energy when it reaches the highest point? projectile projectile they both have the same none zero kinetic energy they both have zero kinetic energy at the highest point more information is required Slide 21 / 76 20 n object with a mass of 2 kg is initially at rest at a position x = 0. non-constant force F is applied to the object over 6 meters. What is the total work done on the object? Slide 22 / 76 21 n object with a mass of 2 kg is initially at rest at a position x=0. non-constant force F is applied to the object over 6 meters. What is the velocity of the object at 6 meters? 200 J 150 J 170 J 190 J 180 J 150 m/s 25 m/s 300 m/s 12.25 m/s not enough information Slide 23 / 76 22 metal ball is held stationary at a height h 0 above the floor and then thrown upward. ssuming the collision with the floor is elastic, which graph best shows the relationship between the total energy of the metal ball and its height h with respect to the floor? (2gH+1/2v o 2 ) 1/2 v o -2gH (2gH + v o 2 ) 1/2 2gH+(1/2v o 2 ) 1/2 v o +2gH Slide 24 / 76 23 toy car travels with speed v o at point x. Point Y is a height H below point x. ssuming there is no frictional losses and no work is done by a motor, what is the speed at point Y?
Slide 25 / 76 24 rocker is launched from the surface of a planet with mass M and radius R. What is the minimum velocity the rocket must be given to completely escape from the planet's gravitational field? (2GM/R) 1/2 (2GM/R) 1/2 (GM/R) 1/2 2GM/R 2GM/16R 2 Slide 26 / 76 25 block of mass m is placed on a frictionless inclined plane with an incline angle θ. The block is just in contact with a free end of an unstretched spring with a spring constant k. If the block is released from rest, what is the maximum compression in the spring? kmg sinθ kmg cosθ 2mg sinθ/k mg/k kmg Slide 27 / 76 26 In a physics lab a student uses three light frictionless PSO lab carts. ach cart is loaded with some blocks, each having the same mass. The same force F is applied to each cart and they move equal distances d. In which on of these three cases is more work done by force F? Slide 28 / 76 27 In a physics lab a student uses three light frictionless PSO lab carts. ach cart is loaded with some blocks, each having the same mass. The same force F is applied to each cart and they move equal distances d. Which cart will have more kinetic energy at the end of distance d? cart I cart II cart III the same work is done on each more information is required cart I cart II cart III all three will have the same kinetic energy more information is required Slide 29 / 76 Slide 30 / 76 28 In a physics lab a student uses three light frictionless PSO lab carts. ach cart is loaded with some blocks, each having the same mass. The same force F is applied to each cart and they move equal distances d. Which cart will move faster at the end of distance d? cart I cart II cart III all three will move with the same speed more information is required
Slide 31 / 76 30 ball of mass m is fastened to a string. The ball swings in a vertical circle of radius r with the other end of the string held fixed. Neglecting air resistance, the difference between the string's tension at the bottom of the circle and at the top of the circle is: mg 2mg 3mg 6mg 9mg Slide 32 / 76 Work & nergy Free Response Problems Slide 33 / 76 1. 50 kg block is pulled from rest by a force of 1000 Slide 34 / 76 1. 50 kg block is pulled from rest by a force of 1000 a. raw a free-body diagram and show all the applied forces. b. How much work is done by force F? c. How much work is done by the normal force? d. How much work is done by the gravitational force? e. How much work is done by the friction force? f. What is the net work done on the block? g. What is the change in kinetic energy of the block? a. raw a free-body diagram and show all the applied forces. f F N mg F Slide 35 / 76 1. 50 kg block is pulled from rest by a force of 1000 b. How much work is done by force F? W = FΔx(os θ) Slide 36 / 76 1. 50 kg block is pulled from rest by a force of 1000 c. How much work is done by the normal force? 0 J W = (1000 N)(5.6 m)(os37) W = 4472 J
Slide 37 / 76 1. 50 kg block is pulled from rest by a force of 1000 d. How much work is done by the gravitational force? 0 J Slide 38 / 76 1. 50 kg block is pulled from rest by a force of 1000 e. How much work is done by the friction force? ΣF = ma F N + FSinθ = mg F N = mg - FSinθ f = μfn f = μ(mg - FSinθ) f = (0.5)[(50kg)(9.8m/s 2 ) - 1000N Sin37 ] = 214.8 N W = FΔx = (214.8 N)(5.6 m) = 1203 J Slide 39 / 76 1. 50 kg block is pulled from rest by a force of 1000 f. What is the net work done on the block? Slide 40 / 76 1. 50 kg block is pulled from rest by a force of 1000 g. What is the change in kinetic energy of the block? W net = F netδx = (Fsinθ-fΔx) W net = [(1000 N)(sin37 ) - 214.8 N)](5.6 m) ΔK = W app - W f ΔK = 4,472J - 1,203J = 3,269J W net = 2167 J Slide 41 / 76 2. boy pushes a 10 kg sled at a constant speed by a. raw a free-body diagram and show all the applied forces. b. How much work is done by force F? c. How much work is done by the normal force? d. How much work is done by the gravitational force? Slide 42 / 76 2. boy pushes a 10 kg sled at a constant speed by a. raw a free-body diagram and show all the applied forces. F N e. How much work is done by the friction force? f. What is the coefficient of kinetic friction between the sled and the surface? g. How much work is done by the net force on the sled? mg F
Slide 43 / 76 2. boy pushes a 10 kg sled at a constant speed by b. How much work is done by force F? W = FΔx osθ Slide 44 / 76 2. boy pushes a 10 kg sled at a constant speed by c. How much work is done by the normal force? 0 J W = (75 N)(15 m)(os 30 ) W = 974 J Slide 45 / 76 2. boy pushes a 10 kg sled at a constant speed by d. How much work is done by the gravitational force? 0 J Slide 46 / 76 2. boy pushes a 10 kg sled at a constant speed by e. How much work is done by the friction force? W f = -974 J Slide 47 / 76 2. boy pushes a 10 kg sled at a constant speed by f. What is the coefficient of kinetic friction between the sled and the surface? W = fδx Slide 48 / 76 2. boy pushes a 10 kg sled at a constant speed by g. How much work is done by the net force on the sled? 0 J W = μ(mg + FSinθ) μ = W/(mg + FSinθ)Δx μ = 974J/[(10kg)(9.8m/s 2 ) + 75Sin30 ](15m) = 0.48
Slide 49 / 76 3. 5 kg block is released from rest at the top of a quarter-circle type curved frictionless surface. The radius of the curvature is 3.8 m. When the block reaches the bottom of the curvature it then slides on a rough horizontal surface until it comes to rest. The coefficient of kinetic friction on the horizontal surface is 0.02. a. What is the kinetic energy of the block at the bottom of the curved surface? b. What is the speed of the block at the bottom of the curved surface? c. Find the stopping distance of the block? d. Find the elapsed time of the block while it is moving on the horizontal part of the track. e. How much work is done by the friction force on the block on the horizontal part of the track? Slide 50 / 76 3. 5 kg block is released from rest at the top of a quarter-circle type curved frictionless surface. The radius of the curvature is 3.8 m. When the block reaches the bottom of the curvature it then slides on a rough horizontal surface until it comes to rest. The coefficient of kinetic friction on the horizontal surface is 0.02. a. What is the kinetic energy of the block at the bottom of the curved surface? 0 + W = f GP = K mgh = K K = mgh = (5kg)(9.8m/s 2 )(3.8m) K = 186J Slide 51 / 76 3. 5 kg block is released from rest at the top of a quarter-circle type curved frictionless surface. The radius of the curvature is 3.8 m. When the block reaches the bottom of the curvature it then slides on a rough horizontal surface until it comes to rest. The coefficient of kinetic friction on the horizontal surface is 0.02. b. What is the speed of the block at the bottom of the curved surface? K = ½mv 2 v = (2K/m) 1/2 v = (2)(186J)/5kg) 1/2 v = 8.6 m/s 2 Slide 52 / 76 3. 5 kg block is released from rest at the top of a quarter-circle type curved frictionless surface. The radius of the curvature is 3.8 m. When the block reaches the bottom of the curvature it then slides on a rough horizontal surface until it comes to rest. The coefficient of kinetic friction on the horizontal surface is 0.02. c. Find the stopping distance of the block? 0 + W = f K - W = 0 K = W K = fδx Δx = K/f = K/μmg Δx = 186J/(0.02)(5kg)(9.8m/s 2 ) = 190 m Slide 53 / 76 3. 5 kg block is released from rest at the top of a quarter-circle type curved frictionless surface. The radius of the curvature is 3.8 m. When the block reaches the bottom of the curvature it then slides on a rough horizontal surface until it comes to rest. The coefficient of kinetic friction on the horizontal surface is 0.02. d. Find the elapsed time of the block while it is moving on the horizontal part of the track. a = F/m = -f/m v = vo + at Slide 54 / 76 3. 5 kg block is released from rest at the top of a quarter-circle type curved frictionless surface. The radius of the curvature is 3.8 m. When the block reaches the bottom of the curvature it then slides on a rough horizontal surface until it comes to rest. The coefficient of kinetic friction on the horizontal surface is 0.02. e. How much work is done by the friction force on the block on the horizontal part of the track? 186 J -vo = at -vo = (- f/m)t t = vom/f t = vom/μmg t = vo/μg = (8.6m/s)/(0.2)(9.8m/s2) = 44s
Slide 55 / 76 a. How much work is done by the spring on the marble? b. What is the speed of the marble at the edge of the table? c. What is the total energy of the marble at the edge of the table with respect to floor level? d. How much time it will take the marble to reach the floor level from the table? e. What is the horizontal range of the marble? Slide 56 / 76 a. How much work is done by the spring on the marble? W = P = ½kx 2 f. What is the kinetic energy of the marble just before it strikes the floor? Slide 57 / 76 b. What is the speed of the marble at the edge of the table? Slide 58 / 76 c. What is the total energy of the marble at the edge of the table with respect to floor level? ½KX 2 = ½mv 2 v 2 = KX 2 /m v = X(K/m) 1/2 = ½mv 2 + mgh = ½m(KX 2 /m) + mgh = ½KX 2 + mgh Slide 59 / 76 d. How much time it will take the marble to reach the floor level from the table? Slide 60 / 76 e. What is the horizontal range of the marble? H = ½gt 2 t = (2H/g) 1/2 R = v o t R = x(k/m) 1/2 (2H/g) 1/2 R = (2HKx 2 /mg) 1/2
Slide 61 / 76 f. What is the kinetic energy of the marble just before it strikes the floor? K = ½KX 2 + mgh Slide 62 / 76 5. 5 kg object is initially at rest at x 0 = 0. nonconstant a. How much work is done on the object during first 12.5 m? b. What is the change is kinetic energy at the end of 12.5 m? c. What is the speed of the object at the end of 12.5 m? d. What is the total work done by the force for the entire trip? e. What is the change in kinetic energy for the entire trip? f. What is the speed of the object at the end of 20 m? Slide 63 / 76 5. 5 kg object is initially at rest at x 0 = 0. nonconstant a. How much work is done on the object during first 12.5 m? Slide 64 / 76 5. 5 kg object is initially at rest at x 0 = 0. nonconstant b. What is the change is kinetic energy at the end of 12.5 m? W = area under the F vs. x graph W =½bh W =½(12.5m)(40N) W = 250J ΔK = W = 250J Slide 65 / 76 5. 5 kg object is initially at rest at x 0 = 0. nonconstant c. What is the speed of the object at the end of 12.5 m? Slide 66 / 76 5. 5 kg object is initially at rest at x 0 = 0. nonconstant d. What is the total work done by the force for the entire trip? K = ½mv 2 2K/m = v 2 v = (2K/m) 1/2 v = (2(250J)/5kg) 1/2 W = area under the F vs. x graph W =½bh + ½bh W =½(12.5m)(40N) + ½(7.5m)(40N) W = 250J + 150J W = 400J v = 10 m/s
Slide 67 / 76 5. 5 kg object is initially at rest at x 0 = 0. nonconstant e. What is the change in kinetic energy for the entire trip? Slide 68 / 76 5. 5 kg object is initially at rest at x 0 = 0. nonconstant f. What is the speed of the object at the end of 20 m? ΔK = W = 400J K = ½mv 2 2K/m = v 2 v = (2K/m) 1/2 v = (2(400J)/5kg) 1/2 v = 12.6 m/s Slide 69 / 76 6. 900 kg roller coaster car starts from rest at point rolls the loop flies off the inclined part of the track. ll the dimensions are: H = 80 m, r = 15 m, h = 10 m, ϴ = 30. a. What is the speed of the car at point? b. What is the speed of the car at point? c. What is the speed of the car at point? d. What is the force applied by the surface on the car at point? e. What is the force applied by the surface on the car at point? f. How far from point will the car land? Slide 70 / 76 6. 900 kg roller coaster car starts from rest at point rolls the loop flies off the inclined part of the track. ll the dimensions are: H = 80 m, r = 15 m, h = 10 m, ϴ = 30. a. What is the speed of the car at point? GP = K mgh = ½mv 2 gh = ½v 2 v = (2gh) 1/2 v = (2(9.8m/s 2 )(80m)) 1/2 v = 39.6 m/s Slide 71 / 76 6. 900 kg roller coaster car starts from rest at point rolls the loop flies off the inclined part of the track. ll the dimensions are: H = 80 m, r = 15 m, h = 10 m, ϴ = 30. b. What is the speed of the car at point? GP = K + GP f mgh = ½mv 2 + mg2r gh = ½v 2 + g2r v 2 = 2g(H - 2r) v = (2g(H - 2r)) 1/2 v = (2(9.8m/s 2 )(80m-30m)) 1/2 v = 31.3 m/s Slide 72 / 76 6. 900 kg roller coaster car starts from rest at point rolls the loop flies off the inclined part of the track. ll the dimensions are: H = 80 m, r = 15 m, h = 10 m, ϴ = 30. c. What is the speed of the car at point? GP = K + GP f mgh = ½mv 2 + mgh gh = ½v 2 + gh v 2 = 2g(H - h) v = (2g(H - h)) 1/2 v = (2(9.8m/s 2 )(80m-10m)) 1/2 v = 37.0 m/s
Slide 73 / 76 6. 900 kg roller coaster car starts from rest at point rolls the loop flies off the inclined part of the track. ll the dimensions are: H = 80 m, r = 15 m, h = 10 m, ϴ = 30. d. What is the force applied by the surface on the car at point? Slide 74 / 76 6. 900 kg roller coaster car starts from rest at point rolls the loop flies off the inclined part of the track. ll the dimensions are: H = 80 m, r = 15 m, h = 10 m, ϴ = 30. e. What is the force applied by the surface on the car at point? F N - mg = mv 2 /r F N = mg + mv 2 /r F N = m(g + v 2 /r) F N = 900kg(9.8m/s 2 + (39.6m/s) 2 /15m) F N = 102,910N Slide 75 / 76 F N + mg = mv 2 /r F N = mv 2 /r - mg F N = m(v 2 /r - g) F N = 900kg((39.6m/s) 2 /15m - 9.8m/s 2 ) F N = 49,961N Slide 76 / 76 6. 900 kg roller coaster car starts from rest at point rolls the loop flies off the inclined part of the track. ll the dimensions are: H = 80 m, r = 15 m, h = 10 m, ϴ = 30. f. How far from point will the car land? v0 = 37.0m/s y0 = 10m Y-direction voy = v0sinθ = 37m/s(sin30) = 18.5m/s y = y0 +voyt + ½gt 2 y = 10m +(18.5m/s)t + (-4.9m/s 2 )t 2 t = 4.3s X-direction vox = 37m/s(cos30) = 32.2m/s x = x0 +voxt + ½at 2 x = voxt x = (32.2m/s)(4.3s) x = 138.5m