(b) Find the x and y components of this force. acceleration? (c) What is the net force on the sailboat

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1 1 Vectors and Net Forces (a) 1 The forces acting on a sailboat are 390 N north and 180 N east. If the boat (including crew) has a mass of 270 kg, 3 A dog pulls on a pillow with a force of 5 N at an angle of 37 0 above the horizontal. (a) Draw a free body diagram of the forces on the sailboat. (a) Draw a free body diagram of the forces on the pillow (b) What are the magnitude and direction of its (b) Find the x and y components of this force. acceleration? (c) What is the net force on the sailboat (a) Drawing (b) 4 N; 3 N (b) 1.6 m/s north of east or 24 0 east of north 4 Two forces are applied to a car in an effort to accelerate it, as shown in the figure below. (c) 429 N 65 0 north of east or 24 0 east of North (a) What is the net (resultant) force of these two forces? (b) If the car has a mass of 3200 kg, what acceleration does 2 Four forces act on a hot air balloon, shown from the side in the figure below. Find the magnitude and direction of the it have? Disregard friction. net (resultant) force on the balloon. (a) 780 N to the right of forward (b) 0.24 m/s to the right of forward 4305 N 15 0 above the 1520 N force

2 2 Vectors and Net Forces (a) 5 A man is pulling on his 20 kg dog with a force of 70.0 N directed at an angle of above the horizontal. 7 A 3.00 kg ball is dropped from the roof of a building m high. While the ball is falling to Earth, a horizontal wind (a) Draw a free body diagram of the forces on the dog. exerts a constant force of 12.0 N on it. (b) Find the x component of this force. (a) Draw the free body diagram. (c) Find the y component of this force. (b) How long does it take the ball to hit the ground? (d) Find the normal force on the dog. (c) How far from the building does the ball hit the ground? (d) What is its speed and angle when it hits the ground? (e) With what force and angle will the ball hit the ground? (a) Drawing (b) 60.6 N Good review problem of projectile motion (c) 35.0 N (d) N (a) (b) 72.0 m 6 A crate is pulled to the right with a force of 85 N, to the left with a force of 115 N, upward with a force of 565 N, and (c) 6.00 s (d) 63.6 m/s downward with a force of 236 N. (e) N (a) Draw a free body diagram of the forces on the crate. (b) Find the net external force in the x direction. (c) Find the net external force in the y direction. (d) Find the magnitude and direction of the net external force on the crate. (a) (b) -3.0 x 10 1 N left (c) 329 N up (d) 3.3 x 10 2 N clockwise from the positive x-axis

3 Pushing and Pulling (c) 8 Two men and a boy are pulling a boat along a canal. The two men pull with forces F 1 and F 2 whose magnitudes and 9 A gardener pushes a 10 kg lawn mower by applying a force of 150 N along the handle. directions are indicated in the figure. (a) Draw a free body diagram (a) Find the magnitude and direction of the smallest force (b) Find the horizontal component of this force when the which the boy could exert to keep the boat in the middle of lawn mower handle makes an angle of the canal. (c) Find the horizontal component of this force when the (b) If the boa has a mass of 400 kg what is the net force on lawn mower handle makes an angle of 45 0 the boat (d) Find the horizontal component of this force when the (c) What is the observed acceleration of the boat lawn mower handle makes an angle of 60 o with the horizontal. (a) (b) 130 N (c) 106 N (d) 75.0 N (Hard) 10 Two ropes are pulling on a log. Find the net (resultant) force on the log if F 1 is pulled with 12 N of force at 10 0 and F 2 is changed to 14.0 N at (a) 186 N 90 0 from the bank on the 320 N side (b) 477 N (c) 1.19 m/s N Three people are pulling on a tree. The first person pulls with 15 N at ; the second with 16 N at ; the third with 11 N at What is the magnitude and direction of the net (resultant) force on the tree? 27 N 125 0

4 Chapter 11: Planar Forces Pushing and Pulling (c) 12 Two men wish to pull down a tree by means of a rope fastened near the top. If they use only one rope the tree will 15 The rock shown below is acted on by one or more forces. Draw the free body diagram for the rock tied to a rope and come down on top of them. To prevent this, they tie two pulled so that the rock moves horizontally at constant ropes 10 meters long to the same point and stand on the velocity. Note: There must be air friction in this case. ground 10.0 meters apart when they pull. If each pulls with a force of 300 newtons, what is the net force exerted by the ropes on the tree? 520 newtons 13 Three people attempt to haul a heavy sign to the roof of a building by means of three ropes attached to the sign. Person A stands directly above the sign and pulls straight up on a rope. Person B and Person C stand on either side of person A. Their ropes form 30 degree angles with Person A's rope. A force of 10 2 newtons is applied on each rope. What is the net upward force acting on the sign? 16 Dan applies a force of 92 N on a heavy box by using a rope held at an angle of 45 0 with the horizontal. (a) What are the vertical and horizontal components of the 92-N force? (a) Draw the free body diagram (b) Calculate the upward force the ice exerts on the crate as 278 Newtons it is pulled. (c) Calculate the normal force on the crate. (d) Calculate the net force on the box 14 The rock shown below is acted on by one or more forces. Draw the free body diagram for the rock tied to a rope and pulled so that the rock accelerates horizontally at 2g. No air friction (a) F h = 65 N; F v = 65 N (b)

5 Pushing and Pulling (c) 17 Beth, a construction worker, attempts to pull a stake out of the ground by pulling on a rope that is attached to the stake. 19 Joe pushes on the handle of a 10-kg lawn spreader. The handle makes a 45 0 angle with the horizontal. Joe wishes to The rope makes an angle of with the horizontal. Beth accelerate the spreader from rest to 1.39 m/s in 1.5 s. exerts a force of 125 N on the rope. (a) Draw a free body diagram. (a) Draw a free body diagram of the forces on the stake (b) What is the normal force on the spreader? (b) What is the magnitude of the upward component of the (c) What force must Joe apply to the handle? Neglect force acting on the stake? friction. (class) (a) Drawing (b)108 N (a) (b) 107.2N 18 A 40-kg crate is pulled across the ice with a rope. A force of 100 N is applied at an angle of 30 o with the horizontal. (c) 13 N (a) Draw the free body diagram (b) Calculate the upward force the rope exerts on the ice 20 A water skier is towed by a speedboat. The skier moves to one side of the boat in such a way that the tow rope forms block as it is pulled. an angle of 55 o with the direction of the boat. The tension (c) Calculate the normal force on the crate. on the rope is 350 N. What would be the tension on the rope (d) Calculate the net force on the box if the skier were directly behind the boat? (e) What is the observed accleration of the ice block? (class) 200 N (a) picture (b) 50 N (c) 342 N, up Refer to Problems and Solutions Manual for diagram (d) 86.6 N (e) 2.2 m/s 2

6 Chapter 11: Planar Forces Pushing and Pulling (c) 21 Wendy pushes a 15 kg lawn spreader across a lawn by applying a force of 95 N along the handle that makes an 22 A student pulls a 125 kg box across a floor by means of a rope making an angle of 60 0 with the horizontal. He applies angle of with the horizontal. a 60 N force on the rope (a) Draw a free body diagram. (a) What is the component of the force in the horizontal (b) What are the horizontal and vertical components of the direction? force? (b) What is the component of the force in the vertical (c) What is the normal force on the spreader? direction? (d) The handle is lowered so it makes an angle of (c) What is the normal force on the box? with the horizontal. Now what are the horizontal and (d) If the angle of the rope is reduced to 30 0 and the same vertical components of the force? force applied, what will now be the magnitudes of the (e) What is the new normal force on the spreader? horizontal, vertical components and the normal force on the box? (a) (b) horizontal = 48 N, (a) H= 30 N vertical = 82 N (b) V= 52 N (c) (c) N (d) horizontal = 82 N, (d) Hcomp. 52 N vertical = 48 N Vcomp 30 N (e) Fnormal

7 Pushing and Pulling with Friction (d) 23 A 3.5 kg block is pushed along a horizontal floor by a force F = 15 N that makes an angle = 40 degrees with the 25 A box of mass m rests on a horizontal table. The box is pulled by a massless rope with a force F at an angle as horizontal, as shown in the figure below. The coefficient shown in the figure below. The coefficient of static friction of kinetic friction between the block and the floor is is 0.6. The minimum value of the force needed to move the (a) Calculate the frictional force exerted on the block box depends on the angle. (b) Calculate the acceleration of the block. (a) Discuss qualitatively how you would expect this force to depend on. (b) Compute the force for the angles = 0, 10, 20, 30, 40, 50, and 60 and make a plot of F versus for mg = 400 N. From your plot, at what angle is it most efficient to apply the force to move the box? (class0 (a) 11.0 N (b) 0.14 m/s 2 (a) The force initially decreases with 0 since the upward component of F will decrease the normal force exerted by the table, Fn. As q increases further, 24 A 5-kg block is held at rest against a vertical wall by a horizontal force of 100 N. however, the forward component of F decreases so much that F must become larger again in order to (a) What is the frictional force exerted by the wall on the move the box. block? (b) What is the minimum horizontal force needed to prevent the block from falling if the coefficient of friction between the wall and the block is s = 0.40? 26 A student moves a box of books by attaching a rope to the box and pulling with a force of N at an angle of The box of books has a mass of 20.0 kg and the coefficient of kinetic friction between the bottom of the box and the sidewalk is Find the acceleration of the box (a) N (b) 123 N 1.24 m/s 2 to the right

8 Chapter 11: Planar Forces Pushing and Pulling with Friction (d) 27 Two students are sliding a 225 kg sofa at a constant speed across the floor. The students carry the sofa, each exert a 30 A clerk moves a box of cans down an aisle by pulling on a rope attached to the box. The clerk pulls with a force of force equal to half the weight of the sofa N at an angle of with the horizontal. The box (a) Which would be an improvement over sliding the sofa has a mass of 35.0 kg, and the coefficient of kinetic friction (b) What other changes could be made to make moving the between box and floor is Find the acceleration of the sofa easier without lifting it off the floor? box. Change the angles or put the sofa on rollers 1.4 m/s 28 A box of books weighing 325 N moves with a constant velocity across the floor when it is pushed with a force of 425 N exerted downward at an angle of below the 31 A 4.00 kg block is pushed along the ceiling with a constant applied force of 85.0 N that acts at an angle of with horizontal. Find k between the box and the floor. the horizontal, as in the figure below. The block accelerates to the right at 6.00 m/s. Determine the coefficient of kinetic friction between the block and the ceiling A student moves a box of books down the hall by pulling on a rope attached to the box. The student pulls with a force of 185 N at an angle of 25 0 above the horizontal. The box has a mass of 35 kg, and µ k between box and floor is (challenge) Find the acceleration of the box m/s 2

9 Chapter 11: Planar Forces Pushing and Pulling with Friction (d) 32 A brick layer applies a force of 100 N to each of two handles of a wheelbarrow. Its mass is 20 kg and it is loaded 34 Suppose you put a wooden block against a wall and push horizontally to keep it from falling. Draw a diagram with 30 bricks, each of mass 1.5 kg. The handles of the showing the forces on the block and the causes of those wheelbarrow are 30 0 from the horizontal and the coefficient forces. Pay special attention to the normal force and the of friction is What initial acceleration is given the weight of the block. Are they in the same direction? Are wheelbarrow? they equal? 0.71 m/s Weight down, friction up; force of your hand onto wall; (normal) force of wallout. Normal force is perpendicualr to the weight. Weight is equal (and opposite to friction force, which is the coefficient of 33 Rachel pulls her 18-kg suitcase at a constant speed by pulling on a handle that makes an angle A with the friction times the normal force. horizontal. The frictional force on the suitcase is 27 N and Rachel exerts a 43-N force on the handle. (a) What angle does the handle make with the horizontal? 35 A giant crane in Washington, D. C., was tested by lifting a load with a mass of x 10 6 kg. (b) What is the normal force exerted on the suitcase? (a) Find the force needed to lift the load with an observed acceleration of m/s 2. (b) If the same force is applied to pull the load up a smooth slope that makes a angle with the horizontal, what (a) 51 0 would be the acceleration? (b) 143 N, up 2.19 x 10 7 N 4.90 m/s 2

10 3 Frictionless Inclined Planes (e) 36 A box is held in position by a cable along a smooth incline shown in the figure below. If = 60 0 and m = 50 kg, find 38 A horizontal force of 100 N pushes a 12-kg block up a frictionless incline that makes an angle of 25 0 with the the tension in the cable and the normal force exerted by the horizontal. incline. (a) What is the normal force that the incline exerts on the block? (b) What is the acceleration of the block? (Hard) (a) 149 N (b) 3.41 m/s 2 39 A 65-kg girl weighs herself by standing on a scale mounted on a skateboard that is rolling down an incline as shown in T = 425N, the picture. Assume there is no friction so that the force F n = 245N exerted by the incline on the skateboard is perpendicular to the incline. What is the reading on the scale if = 30 0? 37 A block is projected up a frictionless inclined plane with initial speed 3.5 m/s. The angle of incline is (a) How far up the plane does it go? (b) How long does it take to get there? (c) What is its speed when it gets back-to the bottom (a) 1.25 m (b).714 sec 552 N (c) 3.5 m/s since no friction

11 1 Frictionless Inclined Planes (e) 40 A 2.0 kg mass starts from rest at the top of an inclined plane 85 cm long and slides down to the bottom in 0.50 s. What 43 A 40.0 kg wagon is towed up a hill inclined at with respect to the horizontal. The tow rope is parallel to the net force acts on the mass along the incline? incline and exerts a force of 140 N on the wagon. Assume that the wagon starts from rest at the bottom of the hill, and disregard friction. (a) How fast is the wagon going after moving 30.0 m up 13.6 N the hill? (b) How fast is the wagon going after moving 80.0 m up the hill? 41 A block with a mass of 5.0 kg is held in equilibrium on an incline of angle = by the horizontal force, F, as shown in the figure. (a) Find the magnitude of F. (a) 4.9 m/s (b) Find the normal force exerted by the incline on the (b) 8.0 m/s block. 44 Suppose a 3.00 x 10 2 N force is used to pull an exceptionally large elephant with a mass of 1.22 x 10 4 kg up a frictionless slope. What is the maximum angle that the slope can make with the horizontal if the task is to be completed? (challenge) (a) 28 N (b) 56 N degrees 42 A laundry basket has a mass of 5.5 kg, find the magnitude of the normal force at rest on a ramp inclined 12 0 above the horizontal 53 N

12 3 Frictionless Inclined Planes (e) 45 The largest squash ever grown had a mass of 409 kg. Suppose you want to push a squash with this mass up a 47 A 3.00 kg block starts from rest at the top of a incline and slides 2.00 m down the incline in 1.50 s. smooth ramp that is 6.00 m long and that makes a (a) Find the acceleration of the block. angle with the horizontal. You push the squash with a force (b) Find the coefficient of kinetic friction between the of 2080 N. block and the incline. (a) Calculate the net force exerted on the squash (c) Find the frictional force acting on the block. (b) Calculate the observed acceleration of the squash (d) Find the speed of the block after it has slid a distance of (c) Calculate the time it will it take to reach the top of the 2.00 m. ramp (a) 1.78 m/s 2 (a) 76 N (b) 0.37 (b).19 m/s 2 (c) 9.4 N (c) 8.2 s (d) 2.67 m/s 46 The rock shown below is acted on by one or more forces. Draw the free body diagram for the rock. Sliding without 48 The coefficient of static friction between the 3.00 kg crate and the incline of the figure shown below is friction. What is the minimum force, F N that must be applied to the crate perpendicular to the incline to prevent the crate from sliding down the incline? (challenge) 32.1 N

13 2 Friction and Inclined Planes (f) 49 The most massive car ever built was the official car of the General Secretary of the Communist Party in the former 51 In 1994, a 3.00 x 10 3 kg pancake was cooked, and flipped, in Manchester, England. Soviet Union. The car had a mass of 3,335 kg. Suppose (a) If the pancake is placed on a surface that is inclined this car is moving down a slope when the driver with respect to the horizontal, what must the applies the brakes. The wheels stop rotating, and the car coefficient of kinetic friction be in order for the pancake to slides, decelerating at a rate of 6.00 m/s 2. slide down the surface with a constant velocity? (a) Calculate the force of kinetic friction acting on the car (b) What would be the frictional force acting on the as it decelerates. pancake? (b) Determine the coefficient of kinetic friction ,682 N 1.52 x 10 4 N Walter Arfeuille of Belgium lifted a kg load off the ground using his teeth. Suppose Arfeuille can hold three times that mass on a slope using the same force. What is the coefficient of static friction between the load and the slope? 0.2

14 Friction and Inclined Planes (f) 52 A 5.0 kg block on an inclined plane is acted upon by a horizontal force of 50 N shown in the figure below. The 53 You slide a 325-N trunk up a inclined plane with a constant velocity by exerting a force of 211 N parallel to coefficient of friction between block and plane is the inclined plane. (a) What is the acceleration of the block if it is moved up (a) What is the component of the trunk's weight parallel to the plane? the plane? (b) How far up the plane will the block go if it has an (b) What is the sum of your applied force, friction, and the initial upward speed of 4.0 m/s? parallel component of the trunk's weight? Why? (c) What happens to the block after it reaches the highest (c) What is the size and direction of the friction force? point? (d) What is the coefficient of friction? (a) 111 N; (b) zero, constant velocity; (c) 100 N, down plane; (d) A 91 kg refrigerator is placed on a ramp. The refrigerator begins to slide when the ramp is raised to an angle of (class Problem) What is the coefficient of static friction? (a) m/s 2 (b) 3.83 m (c) stops Two forces act on an object. A 36-N force acts at A 48-N force acts at What would be the magnitude and direction of their equilibrant? 60 N 99 0

15 Hanging Signs (h) 56 A weight of 50.0 newtons is hung from the center of a stretched horizontal wire 10.0 m long. It causes the wire to 60 A street lamp weighs 150 N. It is supported equally by two wires that form an angle of with each other. sag 1.0 meter at its center. What is the force exerted by (a) What is the tension of each of these wires? each half of the wire supporting the weight? (Hint: make a (b) If the angle is changed to 90 0, What is the new tension scale diagram of the wire with the weight hung from it.) on the string? 125 N (a) 150 newtons in each wire (b) 106 newtons in each wire 57 A person weighs 612 N. If the person sits in the middle of a hammock that is 3.0 m long and sags 1.0 m below the points of support, what force would be exerted by each of the two hammock ropes? 61 A sphere of mass 3.0 x 10-4 kg is suspended from a cord. A steady horizontal breeze pushes the sphere so that the cord makes an angle of 37 degrees with the vertical when at rest. (a) Draw a free body diagram. (b) Find the magnitude of the push. 460 N on each side (c) Find the tension in the cord. 58 A bell ringer decides to use a bowling ball to ring the bell. He hangs the 7.3-kg ball from the end of a 2.0 m long rope. He attaches another rope to the ball to pull the ball back, (a) and pulls it horizontally until the ball has moved 0.60 m (b) 2.22 x 10-3 N away from the vertical. How much force must he apply? (c) 3.69 x 10-3 N 22 N 59 An electric sign weighing 200 newtons is supported by two slanting cables. Each cable is attached to the same point of the sign and makes a 45 0 angle with the horizontal. What is the force exerted by the sign along each of its cables? 141 N.

16 5 Hanging Signs (h) 62 The largest toad ever caught had a mass of 2.65 kg. Suppose a toad with this mass is placed on a metal plate 64 Joe wishes to hang a sign weighing 750 N so that cable A attached to the store makes a angle as shown in the that is attached to two cables, as shown in the figure below. figure below. Cable B is attached to an adjoining building. If the plate is pulled upward so that it has an observed Calculate the necessary tension in cable B. acceleration of 2.55 m/s 2, what is the tension in the cables? 433 N, right 23 N -23 N 65 Two students are sliding a 225 kg sofa at a constant speed across the floor. One student pulls with a force of 225 N at an angle of 13 0 above the horizontal. The other student pushes with a force of 250 N at an angle of 230 below the horizontal. What is the coefficient of kinetic friction 63 A traffic light is supported by two cables that are apart. Each cable exerts a force of 150 newtons on the light. between the sofa and the floor? (a) Draw a free body diagram (b) How much does the light weigh? (Think of the weight of the light, the downward force, as the eqilibriant.) 0.20 (a) (b) net (resultant) 102 newtons 70 0 equilibriant 102 newtons down 66 A block of mass 8.0 kg, starting from rest, is pulled along a horizontal tabletop by a constant force of 2.0 Newtons at an angle of 35 0 from the horizontal. (a) Draw a picture of the situation. (b) What is the net force on the watermelon? (c) What is the acceleration of the body?

17 Chapter 5: Linear Forces Pushing and Pulling (c) 67 A 5.5 kg watermelon is pushed across a table at an angle of 47 0 from the horizontal. The acceleration of the watermelon 71 A person applies a 220 N force at 25 0 to the horizontal to push 55 kg crate across a level floor. If the coefficient of is 4.2 m/s 2 to the right. kinetic friction is (a) Draw a free body diagram of the situation. (a) Draw a picture of the horizontal (b) Find the net external force exerted on the watermelon. (b) What is the magnitude of the frictional force? (c) What is the applied force on the watermelon? (c) What is the acceleration of the crate? 68 A tow rope at a 50 0 angle with the ground is used to pull a 1,750-kg car, giving it an acceleration of 1.35 m/s In 1988, a 3,500 kg telephone constructed by a Dutch telecommunications company was demonstrated in the (a) Draw a free body diagram of the situation. Netherlands. Suppose this phone is towed horizontally by a (b) What is the net force on the car? force equal to 8,800 N and pulled at a 15 0 angle. Given that (c) What is the force applied to the rope? the coefficient of kinetic friction is 0.12; calculate the magnitude of the net acceleration of the telephone. 2,362.5 N in the direction of the acceleration 69 You give to a 24.3 kg box a push at an angle of 20 0 with the horizontal and a force of 85.5 N. (a) Draw a free body diagram of the motion. (b) What is the net force on the car? (b) What is the acceleration of the car? 73 A blue whale with a mass of 1.90 x 10 5 kg was caught in What minimum force pulled at an angle 10 0 would be needed to pull the whale at a constant velocity along a horizontal ramp if the coefficient of kinetic friction between the ramp's surface and the whale were 0.160? 70 A 5-kg object is pulled along a frictionless horizontal surface by a force of 10 N at 15 0 from the horizontal. (a) Draw a free body diagram of the situation. (b) What is the net force on the block? (c) What is the observed acceleration of the block? (d) If the object is at rest at t = 0, how fast is it moving after 3 s? (e) How far does it travel from t = 0 to t = 3 s? 74 Cleopatra's Needle, an obelisk given by the Egyptian government to Great Britain in the late nineteenth century, is more than 20 m tall and has a mass of roughly 1.89 x 10 5 kg. Suppose the monument is lowered onto its side and dragged horizontally to a new location. Given that the magnitude of the acceleration of the monument is m/s 2 and the coefficient of kinetic friction is 0.100, calculate the magnitude of the force applied at 10 0 that must be applied to the monument in order to move it.

18 Chapter 5: Linear Forces Pushing and Pulling with Friction (d) 75 Isaac Newton developed the laws of mechanics. Brian Newton put those laws into application when he ran a 79 In order to drag a 100-kg log along the ground at constant velocity, you have to pull on it with a force of 400 N at an marathon in about 8.5 h while carrying a bag containing 51 angle of 35 0 from the horizontal. kg of coal. (By doing this, he set a strange but impressive (a) Draw a free body diagram of the situation. world record in 1983.) Suppose Brian Newton wants to (b) What is the resistive force exerted by the ground? remove the bag from the finish line. He drags the bag with a (c) What force must you exert if you want to give the log force of 280 N at If the coefficient of kinetic friction an acceleration of 2 m/s 2? between the bag and the pavement is 0.16, what is the magnitude of the net acceleration of the bag? 76 If you use a force of 30.0 N pulled at 12 0 to the horizontal to slide a 12.0-kg wooden crate across a floor at a constant velocity, what is the coefficient of sliding friction between crate and floor? 80 The largest flowers in the world are the Rafflesia Arnoldii, found in Malaysia. A single flower is almost a meter across and has a mass up to 11.0 kg. Suppose you cut off a single flower and drag it along with a force of 42.0 N and at an angle of If the flower's velocity is constant, what is the coefficient of kinetic friction between the flower and the ground? 77 A 200-kg crate is pushed with a force of 800 N downward at If the coefficient of friction is 0.20, calculate the acceleration of the crate. 81 Use trig to solve the following problems. (a) Find q if tan q = (b) Find q if sin q = (c) Find q if cos q = (d) Find q if tan q = A force of 30 N accelerates a 9.0-kg wagon at 2.0 m/s 2 along the sidewalk when it is applied to the handle at (e) Find q if sin q = (f) Find q if cos q = (a) How large is the frictional force? (b) What is the coefficient of friction? (a) q = (b) q = (c) q = (d) q = (e) q = (f) q =

19 Chapter 6: Vectors Trig Review (a) 82 Use trig to solve the following problems. (a) Find the tan Solve for all sides and all angles for the following right triangles. (b) Find the sin (c) Find the cos (d) Find the tan 58 0 (e) Find the sin 40 0 (f) Find the cos 71 0 (a) 0.53 (b) 1.00 (c) 1.00 (d) 1.6 opp 9.4 adj 7.61 angle 51 0 (c) 0.64 (f) Solve for all sides and all angles for the following right triangles. 83 Solve for all sides and all angles for the following right triangles. hyp 9.65 hypothesis 4.7 opp 2.5 angle 32 0 adj 5.1 angle opp 5.1 angle

20 Chapter 6: Vectors Trig Review (a) 86 Solve for all sides and all angles for the following right triangles. 89 Find the vertical and horizontal components of a force of 50 N that is directed 50 0 above the horizontal N vert 32.2 N. horiz Missing side 9.62 adj 7.0 side angle A 110-N force and a 55-N force both act on an object point P. The 110-N force acts at The 55-N force act at 0 0. What is the magnitude and direction of the resultant force? opp 7.0 side N 87 A right triangle has two sides A and B. (a) If tan q = A/B which side of the triangle is longer if the tangent is greater than one? (b) If tan q = A/B which side of the triangle is longer if the tangent is less than one? (c) If tan q = A/B what does it mean if the tangent equals one? A 40-N and a 70-N force act concurrently. (a) Find the magnitude of the resultant force when the angle between them is (b) Find the magnitude of the resultant force when the angle between them is (c) Find the magnitude of the resultant force when the angle between them is (d) Find the magnitude of the resultant force when the (a) side A; (b) side B; (c) Side A = side B they have the same length. angle between them is (e) Find the magnitude of the resultant force when the angle between them is A heavy box is pulled across a wooden floor with a rope. The rope makes an angle of 60 0 with the floor. A force of 75 N is exerted on the rope. What is the component of the force parallel to the floor? (a) 110 N (b) 107 N (c) 96 N (d) 81 N (e) 30 N

21 Chapter 6: Vectors Analytically Adding Vectors (b) 92 Two 15-N forces act concurrently on point P. (a) Find the magnitude of their resultant when the angle between them is (b) Find the magnitude of their resultant when the angle between them is (c) Find the magnitude of their resultant when the angle between them is (d) Find the magnitude of their resultant when the angle between them is (e) Find the magnitude of their resultant when the angle between them is (a) 30 N (b) 29 N (c) 21 N (d) 15 N (e) 0 N 93 Joanne pulls on a trunk with a 12-N force. Bev pulls at right angles to Joanne. How hard must Bev pull to make the resultant force on the trunk 13 N? 5 N 94 Find the magnitude and direction of the resultant of a 60 N force that acts at an angle of 45 0 clockwise from the +Y axis, a 20 N force that acts at an angle of 90 0 from the +Y axis, and a 40 N force that acts at an angle of clockwise from the +Y axis. 68 N at 24 0 clockwise from the +Y axis