4.1.1 Extra Practice 4.1 Analyze the effects of a uniform force (magnitude and direction.)

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(b) If the drawers and clothing, with mass 17 kg mass, are removed before the bureau is pushed, what is the new minimum magnitude? 2.

1 4.1.1 Extra Practice 4.1 Analyze the effects of a uniform force (magnitude and direction.) Frictional Forces LEVEL 2 1. (HRW 6-3) A bedroom bureau with a mass of 45 kg, including drawers and clothing, rests on a floor. The coefficient of static friction between the bureau and the floor is (a) What is the magnitude of the minimum horizontal force that a person must apply to start the bureau moving? (b) If the drawers and clothing, with mass 17 kg mass, are removed before the bureau is pushed, what is the new minimum magnitude? 2. (HRW 6-6) A baseball player with mass m = 79 kg, sliding into second base, is retarded by a frictional force of magnitude 470 N. What is the coefficient of kinetic friction µ k between the player and the ground? 3. (HRW 5-Q5) The figure shows overhead views of four situations in which forces act on a block that lies on a frictionless floor. If the force magnitudes are chosen properly, in which situations is it possible that the block is (a) stationary and (b) moving with constant velocity? 4. (HRW 5-14) A block with a weight of 3.0 N is at rest on a horizontal surface. A 1.0 N upward force is applied to the block by means of an attached vertical string. What are the magnitude and direction of the force of the block on the horizontal surface? LEVEL 3 5. (HRW 6-Q3) In the figure, horizontal force F! of magnitude 10 N is applied to a box on a floor, but the box does not slide. Then, as the magnitude of vertical force F! is increased from zero, do the following quantities increase, decrease, or stay the same: (a) The magnitude of the frictional force f! on the box, (b) the magnitude of the normal force N on the box from the floor, (c) the maximum value f!,!"# of the magnitude of the static frictional force on the box. (d) Does the box eventually slide? 6. (HRW 6-Q4) In three experiments, three different horizontal forces are applied to the same block lying on the same countertop. The force magnitudes are F 1 =12N, F 2 = 8N, and F 3 = 4N. In each experiment, the block remains stationary in spite of the applied force. (a) Rank the forces according to the magnitude f s of the static frictional force on the block from the countertop, greatest first. (b) Rank the forces according to the maximum value f s,max of that force, greatest first. 7. (HRW 6-Q5) If you press an apple crate against a wall so hard that the crate cannot slide down the wall, what is the direction of (a) the static frictional force f! on the crate from the wall and (b) the normal force N on the crate from the wall? If you increase your push, what happens to (c) f!, (d) N, and (e) f s,max? 8. (HRW 6-12) In about 1915, Henry Sincosky of Philadelphia suspended himself from a rafter by gripping the rafter with the thumb of each hand on one side and the fingers on the oppositeside (Fig. 6-21). Sincosky s mass was 79 kg. If the coefficient of static friction between hand and rafter was 0.70, what was the least magnitude of the normal force on the rafter from each thumb or opposite fingers? (After suspending himself, Sincosky chinned himself on the rafter and then moved hand-over-hand along the rafter. If you do not think Sincosky s grip was remarkable, try to repeat his stunt.)

9. (HRW 6-13) A worker pushes horizontally on a 35 kg crate with a force of magnitude 110 N. The coefficient of static friction between the crate and the floor is 0.37.

(d) Suppose, next, that a second worker pulls directly upward on the crate to help out. What is the least vertical pull that will allow the first worker s 110 N push to move the crate?

2 9. (HRW 6-13) A worker pushes horizontally on a 35 kg crate with a force of magnitude 110 N. The coefficient of static friction between the crate and the floor is (a) What is the value of f s,max under the circumstances? (b) Does the crate move? (c) What is the frictional force on the crate from the floor? (d) Suppose, next, that a second worker pulls directly upward on the crate to help out. What is the least vertical pull that will allow the first worker s 110 N push to move the crate? (e) If, instead, the second worker pulls horizontally to help out, what is the least pull that will get the crate moving? 10. (HRW 6-25) Block B in Fig weighs 711 N. The coefficient of static friction between block and table is 0.25; angle θ is 30 ; assume that the cord between B and the knot is horizontal. Find the maximum weight of block A for which the system will be stationary. 11. (HRW 6-5) A 2.5 kg block is initially at rest on a horizontal surface. A horizontal force F of magnitude 6.0 N and a vertical force P are then applied to the block. The coefficients of friction for the block and surface are µ s = 0.40 and µ k = Determine the magnitude of the frictional force acting on the block (a) if the magnitude of P is 8.0 N. (b) if the magnitude of P is 10 N. (c) if the magnitude of P is 12 N. LEVEL (HRW 6-63) A 49 kg rock climber is climbing a chimney. The coefficient of static friction between her shoes and the rock is 1.2; between her back and the rock is She has reduced her push against the rock until her back and her shoes are on the verge of slipping. (a) Draw a free-body diagram of her. (b) What is the magnitude of her push against the rock? (c) What fraction of her weight is supported by the frictional force on her shoes? Hanging Objects LEVEL (HRW 5-15) (a) An 11.0 kg salami is supported by a cord that runs to a spring scale, which is supported by a cord hung from the ceiling (figure a). What is the reading on the scale, which is marked in weight units? (b) In figure b, the salami is supported by a cord that runs around a pulley and to a scale. The opposite end of the scale is attached by a cord to a wall. What is the reading on the scale? (c) In figure c, the wall has been replaced with a second 11.0 kg salami, and the assembly is stationary. What is the reading on the scale?

14. (HRW 5-93) Figure a shows a mobile hanging from a ceiling; it consists of two metal pieces (m 1 = 3.5 kg and m 2 = 4.5 kg) that are strung together by cords of negligible mass.

The tension in the top cord is 199 N. What is the tension in (c) the lowest cord and (d) the middle cord? 15. Jack is a cliffhanger. In the picture, Jack is moving along a rope between two cliffs.

The angle of the strings at the nails is 100. The maximum tension of this type of string is 62 N.

3 14. (HRW 5-93) Figure a shows a mobile hanging from a ceiling; it consists of two metal pieces (m 1 = 3.5 kg and m 2 = 4.5 kg) that are strung together by cords of negligible mass. What is the tension in (a) the bottom cord and (b) the top cord? Figure b shows a mobile consisting of three metal pieces. Two of the masses are m 3 = 4.8 kg and m 5 = 5.5 kg. The tension in the top cord is 199 N. What is the tension in (c) the lowest cord and (d) the middle cord? 15. Jack is a cliffhanger. In the picture, Jack is moving along a rope between two cliffs. Jack has mass of 75 kg. The rope is positioned so that each side forms the same angle. Determine the tension in the rope knowing that the angle above Jack is The angle of the strings at the nails is 100. The maximum tension of this type of string is 62 N. Assuming that the picture hangs symmetrically, what is the largest mass that a picture can have to be safely hung? LEVEL In a two-dimensional tug-of- war, Alex, Betty, and Charles pull horizontally on an automobile tire at the angles shown in the overhead view of the figure. The tire remains stationary in spite of the three pulls. Alex pulls with force F! of magnitude 220 N, and Charles pulls with force F! of magnitude 170 N. Note that the direction of F! is not given. What is the magnitude of Betty s force F!? 18. John finds himself in an unfortunate situation (above), hanging from the center of a rope stretched between two buildings. The buildings are 19.0 m apart (horizontally). The rope is 21 m long and does not stretch. If John s mass is 82 kg, what is the tension in the rope? 19. Determine the tension in each of the three ropes shown to the right. Assume the ropes are knotted at point P, rope 2 is horizontal, and rope 3 is vertical. The mass of the hanging block is 5.0 kg. rope P rope 2 rope 3 LEVEL Two weights are hung from the ropes shown. Assume that T 2 is horizontal. Find the tension of T 1, T 2, and T 3, and the unknown weight T 1 T 2 T 3 20 N??

21. Find the unknown tensions, T1 and T2, and the value of m, for the system shown to the right to be in equilibrium. 60 50 T 1 T 2 80 N 22.

(HRW 5-17) In the figure shown, let the mass of the block be 8.5 kg and the angle be 30. Find (a) the tension in the cord and (b) the normal force acting on the block. 24.

(c) How do these forces each change if the skier s mass is double? 25.

(a) What is the frictional force? (b) What is the normal force? LEVEL 3 26. (HRW 6-Q6) A block of mass m is held stationary on a ramp by the frictional force on it from the ramp.

4 21. Find the unknown tensions, T1 and T2, and the value of m, for the system shown to the right to be in equilibrium T 1 T 2 80 N 22. A 130-N bird feeder is supported by three cables as shown. Find the tension in each cable. m Objects on Inclines LEVEL (HRW 5-17) In the figure shown, let the mass of the block be 8.5 kg and the angle be 30. Find (a) the tension in the cord and (b) the normal force acting on the block. 24. A towrope exerts a force on a 50-kg skier, pulling her up a frictionless 20 slope at a constant speed. (a) What force does the towrope exert? (b) What is the normal force on the skier? (c) How do these forces each change if the skier s mass is double? 25. You ve slammed on your car brakes while going down a hill, angled at 15 to the horizontal, causing you to move with constant speed. The mass of your loaded car is 1750 kg. (a) What is the frictional force? (b) What is the normal force? LEVEL (HRW 6-Q6) A block of mass m is held stationary on a ramp by the frictional force on it from the ramp. A force F, directed up the ramp, is then applied to the block and gradually increased in magnitude from zero. During the increase, what happens to the direction and magnitude of the frictional force on the block? 27. (HRW 6-Q7) Reconsider the previous question but with the force F now directed down the ramp. As the magnitude of F is increased from zero, what happens to the direction and magnitude of the frictional force on the block?

28. (HRW 5-Q12) This figure shows four choices for the direction of a force of magnitude F to be applied to a block on an inclined plane. The directions are either horizontal or vertical.

(HRW 6-15) The coefficient of static friction between Teflon and scrambled eggs is about 0.04.

(HW 5-34) A crate of mass m = 100 kg is pushed at constant speed up a frictionless ramp (θ = 30.0 ) by a horizontal force F.

(HRW 6-16) A loaded penguin sled weighing 80 N rests on a plane inclined at angle θ = 20 to the horizontal. Between the sled and the plane, the coefficient of static friction is 0.

5 28. (HRW 5-Q12) This figure shows four choices for the direction of a force of magnitude F to be applied to a block on an inclined plane. The directions are either horizontal or vertical. (For choice b, the force is not enough to lift the block off the plane.) Rank the choices according to the magnitude of the normal force acting on the block from the plane, greatest first. 29. (HRW 6-15) The coefficient of static friction between Teflon and scrambled eggs is about What is the smallest angle from the horizontal that will cause the eggs to slide across the bottom of a Teflon-coated skillet? 30. (HW 5-34) A crate of mass m = 100 kg is pushed at constant speed up a frictionless ramp (θ = 30.0 ) by a horizontal force F. What are (a) the magnitude of F and (b) the magnitude of the force on the crate from the ramp? 31. (HRW 6-16) A loaded penguin sled weighing 80 N rests on a plane inclined at angle θ = 20 to the horizontal. Between the sled and the plane, the coefficient of static friction is 0.25, and the coefficient of kinetic friction is (a) What is the least magnitude of the force F, parallel to the plane, which will prevent the sled from slipping down the plane? (b) What is the minimum magnitude F that will start the sled moving up the plane? (c) What value of F is required to move the sled up the plane at constant velocity? LEVEL A crate slides down an inclined right-angled trough with constant speed. What is the coefficient of kinetic friction between the crate and the trough in terms of θ and g? 33. The block shown has a mass of 5.0 kg and the incline makes an angle of 25 with the horizontal. For the block-incline interface, µ k = 0.30 and µ s = (a) The block is initially at rest. Does it remain stationary, or does it slide? Explain your answer and support with calculations. (b) Based on your answer to (a), state the magnitude of the frictional force. 25

6 Force Applied at an Angle LEVEL (HRW 6-Q1) If the box shown here is stationary and the angle θ between the horizontal and force F is increased somewhat, do the following quantities increase, decrease, or remain the same? (a) F x (b) f s (c) N (i.e. F N ) (d) f s,max (e) If, instead, the box is sliding and θ is increased, does the magnitude of the frictional force on the box increase, decrease, or remain the same? 35. (HRW 6-Q2) Reconsider the previous problem, now for force F angled upward instead of downward as drawn. (a) F x (b) f s (c) N (i.e. F N ) (d) f s,max (e) If, instead, the box is sliding and θ is increased, does the magnitude of the frictional force on the box increase, decrease, or remain the same? 36. (HRW 6-21) An initially stationary box of sand is to be pulled across a floor by means of a cable in which the tension should not exceed 1100 N. The coefficient of static friction between the box and the floor is (a) What should be the angle between the cable and the horizontal in order to pull the greatest possible amount of sand? (b) What is the weight of the sand and box in that situation? N of force are used to pull this 4.0-kg box across the floor, causing it to move at a constant speed of 1.8 m/s. (a) Determine the coefficient of kinetic friction. (b) The box is moved to a different surface. The angle of the string must be adjusted to 25 above the horizontal in order for the box to move at constant speed with the same 18 N of applied force. Determine the coefficient of kinetic friction. (c) Once more the box is moved to a different surface and now the string must be held at an angle of 15 below the horizontal in order for 18 N of force to produce constant speed. Determine the coefficient of kinetic friction. 38. (HRW 6-62) A 5.00 kg stone is rubbed across the horizontal ceiling of a cave passageway. If the coefficient of kinetic friction is 0.65 and the force applied to the stone is angled at θ = 70.0, what must the magnitude of the force be for the stone to move at constant velocity?

You may use g = 10 m/s 2, sin 60 = 0.87, and cos 60 = 0.50.

You may use g = 10 m/s 2, sin 60 = 0.87, and cos 60 = 0.50. 1. A child pulls a 15kg sled containing a 5kg dog along a straight path on a horizontal surface. He exerts a force of a 55N on the sled at an angle of 20º above the horizontal. The coefficient of friction