Assignment  Forces. Reading: Chapter 4. Objectives/HW


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1 Assignment  Forces Reading: Chapter 4 Objectives/HW The student will be able to: HW: 1 State Newton s 1 st and 2 nd Laws of Motion and apply these laws to 1 5 physical situations in order to determine what forces act on an object and to explain the object s resulting behavior. 2 Recognize and state the proper SI unit of force and give its 6 10 equivalence in fundamental units and use the relation F net = ma to solve problems. 3 Recognize the difference between weight and mass and convert from one to the other. 4 State and utilize Newton s 3 rd Law to solve related problems Understand and utilize the concept of the normal force to solve related problems. 6 Understand and utilize the relation between friction force, normal force, and coefficient of friction for both cases: static and kinetic. 7 State the factors which influence air resistance and describe qualitatively the effect of each factor on the magnitude of the frictional force. And explain what is meant by terminal velocity. 8 Resolve forces into components using trigonometry and use the results to solve related force problems. 9 Apply the concept of force components to objects on an incline and solve related problems Homework Problems 1. Using Newton s Laws explain why you must push harder on the pedals of a singlespeed bicycle to start it moving than to keep it moving with a constant velocity. 2. Suppose you have a nearly empty jar of salsa that you want to pour into a bowl. Of course you will turn the jar upside down but sometimes this is not enough to get the salsa out of the jar. Usually you will end up not only turning the jar over but also shaking it up and down. Using Newton s Laws explain why the salsa comes out of the jar. 3. The Pioneer 10 spacecraft has left our Solar System and is traveling at a speed of 29,000 mph (and has been doing so for years). Explain why this object is moving so fast although it ran out of fuel long ago. 4. If you are in a car that is struck from behind, you can receive a serious neck injury called whiplash. (a) Using Newton s Laws explain what happens to the person s head. (b) Using Newton s Laws explain how a headrest helps to reduce whiplash injuries.
2 5. When the space shuttle is launched from Earth, a constant force is applied and the shuttle accelerates upward. As the flight progresses, its rate of acceleration increases. Explain using Newton s Laws. 6. A net force of 150 N causes a certain person to accelerate 1.20 m/s 2. Determine the person s mass. 7. A racecar has a mass of 710 kg. It starts from rest and travels 40 m in 3.0 s. What magnitude is the net force on the car? 8. A net braking force of 9000 N is used to stop a 1500 kg car with initial speed 20 m/s. Determine the distance to bring the car to a complete halt. 9. Two forces act on a falling skydiver with mass 100 kg: a downward gravity force and an upward air resistance (friction) force. Suppose the net force on the skydiver is this means the gravity force is 670 N greater than the friction force. (a) Determine the resulting acceleration. After the parachute opens the acceleration is 5.0 m/s (b) Determine the net force at this point. (c) Which force is larger now and by how much? 10. Suppose you hook a 1.5 kg fish while using line that is rated at 38 N (it can only sustain that much force before breaking). If the fish fights back with 40 N of force, what is the minimum acceleration rate you must play out the line in order to keep it from breaking? 11. Compare the force needed to lift a 10 kg rock on the Earth and on the Moon. Now compare the force needed to throw the same rock horizontally at the same speed in the two locations. 12. A 95.0 kg (209 lb) boxer has matches in the Canal Zone (g = m/s 2 ) and in the Arctic Circle (g = m/s 2 ). (a) What is his mass in the Canal Zone? (b) What is his weight in the Canal Zone? (c) What is his mass in the Arctic Circle? (c) What is his weight in the Arctic Circle? (e)based on this, should a scale or a balance be used for the weighin? 13. Suppose a certain motorcycle weighs 2450 N. What is its mass in kilograms? 14. A 4500 kg helicopter accelerates upward at 2.0 m/s 2. What lift force is exerted on the propellers by the air? 15. Safety engineers estimate that an elevator can hold 20 persons of 75 kg average mass. The elevator itself has a mass of 500 kg. Tensile strength tests show that the cable supporting the elevator can tolerate a maximum force of 29.6 kn. What is the greatest acceleration that the elevator s motor can produce without breaking the cable?
3 16. An elevator car that weighs 3.0 kn is accelerated upward at 1.3 m/s 2. What force does the cable exert to give it this acceleration? 17. A rocket with a mass of 23.0 Mg is sitting vertically on a launch pad. The rocket s engine fires to produce a thrust of 680 kn. (a) What is the net force acting on the rocket just as it leaves the ground? (b) What is the acceleration of the rocket? 18. A person throws a ball with mass 175 g. If the person s hand exerts a force of , what will be the resulting acceleration of the ball? (You must include the effect of gravity.) 19. Mules are smart but stubborn. Once upon a time a particularly smart and particularly stubborn mule refused to pull its owner s cart and gave the following argument: I refuse to pull the cart because it is impossible to do so according to Newton s laws of motion. According to the 2 nd Law it is necessary to have a net force in order for the cart to accelerate. According to the 3 rd Law no matter how hard I pull the cart forward, the cart will pull an equal amount backward and therefore the net force will be zero and the cart will not move. Even if I could pull a million Newtons forward, the cart would pull a million Newtons backward and so I refuse to even try! What is the flaw in the mule s argument? 20. When you drop a 0.40 kg apple, Earth exerts a force on it that accelerates it toward the Earth s surface. Assuming Newton s Laws are true (and they are!) the Earth must also accelerate toward the apple. Given its mass is x kg, determine the rate at which the Earth accelerates upward toward the falling apple. 21. A 115 kg astronaut on a space walk pushes against her space capsule which has mass 2250 kg. The astronaut accelerates 1.50 m/s 0. (a) Find the force exerted on the astronaut. (b) Find the force exerted on the capsule. (c) Find the acceleration of the capsule. 22. Suppose a 100 g superball is in contact with the floor. Determine the normal force the floor exerts on the ball for the following situations: (a) The ball is at rest. (b) The ball is in the process of bouncing and it is accelerating 250 m/s (c) Determine the force the ball exerts on the floor as it is bouncing. 23. The maximum force a grocery sack can withstand and not rip is 250 N. If 20 kg of groceries are lifted from the floor to the table with an acceleration of 5.0 m/s 2, will the sack hold? 24. A person stands on a bathroom scale in an elevator at rest on the 64 th floor of a building. The scale then reads 836 N. (a) As the elevator begins to move upward the scale reading increases to 935 N, but then eventually returns to 836 N. Find the acceleration of the elevator. (b) As the elevator approaches the 74 th floor, the scale reading drops as low as 782 N. What is the
4 acceleration of the elevator? (c) Using your results from parts a and b, explain which change in velocity, starting or stopping, would take the longer time. (d) Describe how the readings of the scale would change if the person went back down to the 64 th floor. 25. A sled of mass 50 kg is pulled horizontally over flat ground. The static friction coefficient is 0.30, and the sliding friction coefficient is (a) What does the sled weigh? (b) What minimum amount of force must be applied to the sled in order to start it moving? (c) What amount of applied force will keep it moving at a constant velocity of 3.0 m/s? (d) What amount of applied force will accelerate the sled at 3.0 m/s 2? 26. A force of accelerates a 5.0 kg block at 6.0 m/s 180 along a horizontal surface. (a) Determine the force of friction acting on the block. (b) Determine the coefficient of friction. 27. A 20 kg wagon is rolling to the right across a floor. A person attempts to catch and stop the crate and applies a force of on it. If the coefficient of friction is 0.18, calculate the deceleration rate of the wagon as it is caught. 28. Two brothers are goofing around on the surface of a frozen lake where = The older brother weighs 825 N and the younger weighs 765 N. The older brother shoves the younger with a force of (a) Find the acceleration of the younger brother. (b) Find the acceleration of the older brother. 29. A truck 0.0. In the bed of the truck is a 15 kg crate for which static = 0.20 and sliding = (a) What is the maximum acceleration rate at which the crate will not slide across the bed? (b) If the truck exceeds this, what will be the acceleration of the crate? 30. A truck with mass 2000 kg tows a boat and trailer of total mass 500 kg. The rolling coefficient of friction for the truck is and for the trailer is The force of the truck s drive wheels pushing backward on the pavement is 3.0 kn. (a) Determine the acceleration rate of the truck and trailer moving forward together. (b) Determine the amount of force the truck s hitch exerts forward on the trailer. 31. A 275 kg mule pushes backward with its feet on the ground as it pulls a cart forward. The mule and the cart both accelerate forward m/s 0.0. (a) What force does the ground exert on the mule s feet? (b) What force does the cart exert on the mule? (c) What force does the mule exert on the cart? (d) Assuming the coefficient of friction for the cart is 0.25, what is its mass?
5 32. The terminal velocity of a baseball falling through air is 43 m/s. However a baseball batted through air can go well over 50 m/s. Explain. 33. Two pingpong balls are dropped from a very high bridge into a river. One is filled with air and the other with water. Both experience air resistance as they fall. Which ball has a greater terminal velocity? Which ball reaches terminal velocity first? Which ball goes into the river first? Explain. 34. A 40 kg crate is pulled across the ice with a rope. A force of is applied. Assume friction is negligible. (a) Determine the acceleration of the crate. (b) Determine the force that the crate exerts on the ice. 35. Three people haul a heavy sign to the roof of a building by using three ropes attached to the sign. Abby stands directly above the sign and pulls straight up on a rope. Eric and Kim stand on either side of Abby. Their ropes from 30.0 angles on either side of Abby s rope. A force of 102 N is applied to each rope. What is the net upward force acting on the sign? 36. A traffic signal weighs 150 N and hangs above an intersection. It is supported equally by wires on either side that form an angle of 120 with each other. (a) What is the tension in each of these wires? (b) If the angle between the wires is reduced to 90.0, what is the new tension? (c) As the angle between the wires decrease, what happens to the force in the wire? 37. Joe hangs a sign weighing 750 N with two cables. Cable A is directed toward Cable B is directed toward 0.0. Nothing but these two cables supports the sign. Calculate the tension in cable B. See figure 628, p. 131 for a diagram. 38. A suitcase with mass 18 kg is pulled at a constant speed by a handle that makes an angle with the horizontal. The frictional force on the suitcase is 27 N and the force applied on the handle is 43 N. (a) Determine the value of the angle,. (b) Determine the normal force exerted on the suitcase. 39. A person exerts a force of on a 20.0 kg crate which slides to the left across a level floor where = (a) Find the normal force on the crate. (b) Find the force of friction on the crate. (c) Find the acceleration of the crate. 40. You slide a 325 N trunk up a 20.0 inclined plane with a constant velocity by exerting a force of 211 N parallel to the inclined plane. (a) Determine the component of the trunk s weight parallel to the plane. (b) What would be the sum of your applied force, friction, and the parallel component of the trunk s weight and why? (c) Determine the friction acting on the trunk. (d) Determine the coefficient of friction.
6 41. A 475 gram box is given a push and it then slides up and back down a ramp with a 35.0 incline. The coefficient of friction is (a) Determine the rate of deceleration as the box slides up the ramp. (b) Determine the rate of acceleration as the box slides back down the ramp. (c) Determine the amount of applied force necessary to push the box up the ramp at a steady speed. 42. A snow skier of mass 85.0 kg slides with constant velocity down a slope which makes an angle of 10.0 with the horizontal. (a) What is the coefficient of sliding friction? (b) If the slope increases to 15.0 what will be the skier s rate of acceleration?
7 Answers to selected problems a. b kg N m 9. a m/s b c m/s a. b. 929 N c. d. 934 N e kg m/s a b m/s m/s m/s a b c mm/s a b N No, the sack will rip would need to withstand 300 N or not exceed 2.7 m/s a. 1.2 m/s 90 b c. d. 25. a. 490 N b. 150 N c. 49 N d. 200 N 26. a. 10 N b. 0.20
8 m/s a m/s 0.0 b m/s a. 2.0 m/s 2 b. 1.5 m/s a m/s 2 b. 480 N 31. a b c d. 462 kg a. 2.2 m/s 0.0 b N 36. a. 150 N b. 110 N c N 38. a. 51 b. 140 N 39. a b c. 1.9 m/s a. 111 N b. c. 100 N d a. 8.0 m/s 2 b. 3.2 m/s 2 c. 3.8 N 42. a b m/s 2
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