CHAPTER 4 NEWTON’S LAWS (DYNAMICS) HW 4a Fig Newton (read 4.1-4.3) 1. A rock is thrown at an angle of 35.0 to the horizontal with a speed of 11.5 m/s. How far does it travel? 2. How much does a 34.5 kg gymnast weigh? 3. A car is being pushed in a parking lot. Draw a FBD of the system. Label the vectors. 4. What is the mass of a 235 N acrobat? 5. A 25.6 kg rocket accelerates upward at 105 m/s2. What is the thrust pushing it up? 6. A ball is attached to a string and hangs from the ceiling. Draw a FBD of the system. Label the vectors. 7. The space shuttle has a mass of 2.0 x 106 kg. At lift off the engines generate an upward thrust of 1.3 x 108 N. (a) Draw a FBD of the space shuttle system. (b) What is the weight of the shuttle? (c) What is the acceleration of the shuttle when it is launched? (d) The average acceleration of the shuttle during its 7.5 minute run is 18 m/s2. What velocity does it theoretically achieve at the end of that time? 4b Force that Mass to Accelerate (read 4.4-4.5) 1. What net force is required to accelerate a 135 000 kg aircraft from rest to a speed of 35.0 m/s in 11.0 s? 2. A frog jumps at an angle of 42.5 to the horizontal with a speed of 13.5 m/s. How far does it travel? 3. A small weather rocket weighs 15.7 N. a. What is the rocket’s mass? b. The rocket fires its engine when it is dropped from a balloon at high altitude. If the rocket has a thrust of 109.2 N (straight up), what is the acceleration on the rocket? 4. A 2500 kg car is pushed with a 250 N force, (a) what is the acceleration acting on the car? (b) what is the acceleration if the mass is doubled? 5. A 450 kg mass is accelerated at 2.5 m/s2. (a) What is the force causing this acceleration? (b) how fast is the mass traveling at the end of 3.0 s? (c) much distance will have been covered after 3.5 s 6. A crate rests on very low friction wheels. The crate and the wheels and stuff have a weight of 865 N. You pull on the rope with a force of 145 N. What is the acceleration of the system? How far will it move in 2.00 s? 7. An artillery shell has a mass of 75 kg. The projectile is fired from the weapon and has a velocity of 670 m/s when it leaves the barrel. The gun barrel is 2.7 m long. Assuming the force and therefore the acceleration is constant while the projectile is in the barrel, what is the force that acted on the projectile? 4c Force is a Vector (Read 4.6)_ 1. A helicopter flying horizontally at a speed of 14.0 m/s drops a package. The package falls to the ground in 3.50 s. (a) How high was the helicopter flying? (b) how far horizontally does the package travel before it hits the ground? 2. A book sits on a table. The book has a mass of 1.25 kg. Draw a free body diagram. 3. A boy pushes a lawnmower. The handle of the lawn mower makes an angle of 22 with the horizontal. If the boy pushes with a force of 135 N, what are the horizontal and vertical components of 2250 N the force? 35.0 4. A sled is towed by two mules as shown in the drawing right. (a) What is the net 35.0 1250 N force acting on the barge if the frictional force that must be overcome is 1250 N? 2250 N (b) If the barge is moving at 2.5 km/h, what is the net force acting on it? 5. What acceleration will result when a 12-N net force applied to a 3-kg object? A 6-kg object? 6. A force of 16 N causes a mass to accelerate at a rate of 5 m/s2. Determine the mass. 7. An object is accelerating at 2 m/s2. If the net force is tripled and the mass is halved, then what is the new acceleration? 4d That Darn Light (Read 4.7)_ 1. A disturbing weight hangs suspended as shown in the drawing. Find the tensions in the two strings. 2. A 12 250 kg boulder hangs from two cables which are at the angles shown. Calculate T in the two cables. 3. A 46.5 kg traffic light hangs from two cables which are at the angles shown. Calculate T in the two cables. 4. A 50.5 kg traffic light hangs from two cables which are at the angles shown. Calculate T in the two cables. 1 2 3 4 20.3 23.8 79.0 81.8 52 52 119 kg 4f Rise Over Run (Read 4.8) 1. A 5.00 kg ball rolls down a 18.0° ramp. What is the acceleration of the ball? Ignore friction. If the ramp is 2.00 m long, how much time to reach the bottom? 2. An snowball is rolled down a snow bank of 30o. It is 300 m above the mountain base. If Mr C is standing at the bottom how much time does he have to get out of the way? 3. A bowling ball is pushed down a frictionless hill of 50o. It is pushed with an initial velocity of 5m/s how fast will it hit the pin that is 16m away? 4. A 7.00 kg ball rolls down a 17.5° ramp. (a) What is the acceleration of the ball? (Ignore friction) (b) If the ramp is 2.00 m long, how much time to reach the bottom? 5. A 3.0 m board has one end raised to a height of 60 cm to form an incline. A 4.0 kg mass is allowed to slide without friction down the entire length of the inclined plane. a. Draw the FBD b. What is the final speed when it reaches the bottom? 6. A 34.5 kg block rests on the ramp as shown in the drawing to the right. What is the tension in the line that is connected to the top of ramp? 4g Friction Stiction 1. A 250.0 kg crate is being pulled across the floor at a constant velocity with a rope that makes an angle of 22.0 to the horizontal. If the force applied is equal to 875 N, what is the coefficient of kinetic friction? 2. A boy pulls a 47.5 kg crate with a rope. The rope makes an angle of 28.0 to the horizontal. The coefficient of kinetic friction for the crate and the deck is 0.3. The boy exerts a force of 185 N. What is the a of the crate? 3. You pull on a 98.0 kg bag of seed and drag it across a warehouse. If the coefficient of kinetic friction for the bag on the floor is 0.445, what horizontal force must you apply to move the bag at a constant speed? 4. A police officer pushes a 77.2 kg crate across a floor with a pole. The pole makes an angle of 32.0. The coefficient of kinetic friction for the crate and the deck is 0.350. The officer exerts a force of 535 N. What is the acceleration of the crate? 5. A box is on a 45.0o incline where the coefficient of sliding friction is 0.2. Find the acceleration and the final velocity after 1 minute assuming a zero velocity at the start. 6. A 10.0 kg box is on a 48.0o incline where the coefficient of sliding friction is 0.482. Find the a) FBD b) normal force & parallel force, c) force due to kinetic friction, d) net force, e) acceleration, and f) the time when the box will be 15.0 m down the incline, all assuming a zero velocity at the start. 7. A 100kg sled (and slider) slides down a lightly snowy hill, starting from rest 150 meters up the hill. The hill has a slope of 15degrees, with a long level field at the bottom. The coeff of kinetic friction of snow is 0.1. It slides 130 meters on the grass before stopping. What was the coefficient of friction on the grass? 4h The Pulley Is Spinning 1. A pulley with weights of 89.94 g and 90.31g are suspended from a pulley that is 1.71m from the floor. A key is attached to the heavier mass. The weights are held evenly 77.5cm from the floor. When released it takes the heavier mass 2.20s to hit the floor. a)What is the weight of the key. b) What is the zenith of the lighter mass? 2. A 20.0 kg cart with very low friction wheels sits on a table. A light string is attached to it and runs over a low friction pulley to a 0.0150 kg water bottle that falls with gravity. What is the acceleration experienced by the cart? What is the fall time if table is 6m (assume it hits before cart launches.) What will be the horizontal velocity that the cart launches off the table? 4.50 kg 3. A 4.50 kg block rests on a frictionless ramp as shown. It is attached to a 4.20 kg block 4.20 kg by a very low mass string that is run over a low friction pulley. (a) In what direction will the blocks travel? And (b) What will be the acceleration of the blocks when the system is 35.0 released? 2 HW 4A 1) 12.7m/s 2) 338N 3) FBD 4) 24.0 kg 5) 2938N 6) FBD 7) a) FBD b) 2.0E7 N c) 55 m/s d) 8100m/s 2 2 2 HW 4B 1) 430000N 2) 18.5m 3 a) 1.6Kg b) 58.4 m/s 4 a) 0 .1 m/s b) 0 .050 m/s 5a) 1125N b) 7.5m/s c)15.3m 6a) 1.64 m/s2 b) 3.28m 7) F = 6.2E6 N 4 a) 2436 N HW 4C 1a) 60.0 m b) 49.0m 2) FBD 3) Fx = 125N Fy = -50.6N 2 2 2 4b) 0 (constant speed) 5a) 4 m/s b) 2 m/s 6) 3.2 Kg 7) 12 m/s HW 4D 1. T1 = 1100N T2 = 226N 2. T1 = 17800N T2 = 114000N 3. T1 = 290N T2 = 290N 4) T1 = 110N T2 = 445N 2 2 HW 4E 1. a=3.5 m/s , T2=17.6N, T1=53N 2) a=0.338 m/s 3) T1 and T2 = 118 and combined T2 = 118N, T1 and 236N 4. M2=3.49kg T=33N 2 5. a=0.239 m/s T=50.2N =11.5o a=1.95 m/s2 b) Vf=3.4m/s HW 4F 1) t=1.15s 2) t=ramp length 600m (t=15.6s) 3) Vf=16.3m/s 4) a=2.95m/s2 t=1.16s 5a) c) t=1.77s 6. T = 190N 2 2 2 HW 4G 1)M= 0.382 2)a=1.05 m/s 3)F=427N 4)a= 1.16 m/s 5a)a=5.54 m/s , vf=332m/s 6a) FBD b) Fn=65.6N Fp=72.8N c) Ff=31.6N 2 4e Pulley Me Up 1. A box is being pulled with another behind it (10Kg and 5 Kg) at 53N across ice. What is the acceleration, T1 & T2? 2. Two masses are connected by a light string that runs over a frictionless pulley as shown below. What is the acceleration of the system when the masses are released and allowed to move? 3. Two 10.0 kg masses are each hanging from the ceiling of an elevator that is accelerating upward at 2.00 m/s2. What is the tension in each rope? If one is cut down and then tied to the other what is the T1 and T2? 4. Two masses are connected by a very light weight string that passes over your basic very low friction pulley (below). The mass on the left is 3.25 kg. The 3.25 kg mass accelerates upward at 0.345 m/s2. (a) What is the mass on the other side of the pulley? (b) what is the tension in the string? 5. Two masses are connected by a light string which passes over a frictionless pulley as shown below. (a) What is the acceleration of the system? (b) What are the tensions in the string? 2. 4. 5. 2.25 kg 5.00 kg m1 2.10 kg m2 a 3.25 kg 5.25 kg 2 d)Fnet=41.2 e)a=4.12 m/s f)2.7s 7) a=1.59 m/s , Vf=21.8m/s = 0.187 HW 4H 1) Key weight = .00568kg y= 1.574m 2) time to fall 40.4s Vf = .296 m/s 2 3) 1.82 m/s

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