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Name: _______________________ Mr. Kepple Chapter 5: Questions Force – HW#1 Date: ___________ Period: _____ 1. In the figure, forces ⃗ and ⃗ are applied to a lunchbox as it slides at constant velocity over a frictionless floor. We are to decrease angle without changing the magnitude of ⃗ . For constant velocity, indicate below whether we should increase, decrease, or maintain the magnitude of ⃗ . ___ X increase ___ decrease ___ maintain Justify your answer: As the angle decreases, the horizontal component of 𝐹 increases. At constant velocity the net force must be zero. Therefore the magnitude of 𝐹 must increase in order to balance out the increase in the horizontal component of 𝐹 . 2. The figure below 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… (a) that the block is stationary? Justify your answer. (b) that the block is moving with a constant velocity. Justify your answer. 2 and 4. Stationary means zero net force. 1 and 3 have unbalanced upward forces, so they will accelerate. Only 2 and 4 can be balanced. 2 and 4. For the block to be moving with constant velocity, the net force acting on the object must be zero. The answer is the same as part (a). 3. The figure shows four choices for the direction of a force of magnitude to be applied to a block on an inclined plane. The directions are either horizontal or vertical. (For choices and , the force is not enough to lift the block off the plane.) Rank the choices according to the magnitude of the normal force on the block from the plane, greatest first. Justify your ranking. d, c, a, b. The magnitude of the normal force can be found by the magnitude of the component of the force that is perpendicular to the incline. 𝑑 and 𝑏 have the greatest perpendicular component and 𝑎 and 𝑐 have the smallest perpendicular component. However 𝑎 and 𝑏 point away from the surface so they will decrease the normal force while 𝑑 and 𝑐 point into the surface which will increase the normal force. 4. The figure gives the free-body diagram for four situations in which an object is pulled by several forces across a frictionless floor, as seen from overhead. For each situation, indicate whether the object’s acceleration ⃗ has an component, a component, or both. Finally give the direction of ⃗ by naming either a quadrant or a direction along an axis. (This should be done with mental calculations.) ___ 𝑥 component? ___ X 𝑥 component? ___ X 𝑥 component? ___ X 𝑥 component? ___ X 𝑦 component? ___ 𝑦 component? ___ X 𝑦 component? ___ X 𝑦 component? What is the direction of the acceleration? What is the direction of the acceleration? What is the direction of the acceleration? What is the direction of the acceleration? +𝑦 +𝑥 Quadrant IV Quadrant III 5. The figure to the right gives three graphs of the velocity component and three graphs of the velocity component . The graphs are not to scale. Which graph best corresponds to the following situations? Justify each answer. (a) Situation 1 in question 4. 𝑎 and 𝑒. Situation 1 has zero horizontal acceleration and positive vertical acceleration. (b) Situation 2 in question 4. 𝑏 and 𝑑. Situation 2 has zero vertical acceleration and positive horizontal acceleration. (c) Situation 3 in question 4. 𝑏 and 𝑓. Situation 3 has positive horizontal acceleration and negative vertical acceleration. (d) Situation 4 in question 4. 𝑐 and 𝑓. Situation 3 has negative horizontal acceleration and negative vertical acceleration. Name: _______________________ Mr. Kepple Newton’s Laws Problem Set Force – HW#2 Date: ___________ Period: _____ 1. Superman must stop a 120-km/h train in 150 m to keep it from hitting a stalled car on the tracks. If the train’s mass is kg, how much force must he exert? How much force does the train exert on Superman? 2 km h m = m/s h s km 𝑣 2 = 𝑣0 2 + 2𝑎𝑥 𝐹 = 𝑚𝑎 𝑣 2 − 𝑣0 2 𝑎= 2𝑥 𝑎= − 𝑣0 2 2𝑥 𝐹𝑇𝑆 𝑣0 2 =𝑚 − 2𝑥 𝐹𝑇𝑆 𝑚𝑣0 2 =− 2𝑥 2 𝐹𝑇𝑆 = − 2 5 𝐹𝑇𝑆 ≈ − 6 N 𝐹𝑆𝑇 ≈ + 6 N 2. A 0.140-kg baseball traveling 35.0 m/s strikes the catcher’s mitt, which, in bringing the ball to rest, recoils backward 11.0 cm. What was the average force applied by the ball on the glove? 𝐹𝐺𝐵 𝑚𝑣0 2 =− 2𝑥 𝐹𝐺𝐵 = − 4 5 2 2 𝐹𝐺𝐵 = −779 55 𝑁 𝐹𝐺𝐵 ≈ −78 N 3. What average force is required to stop a 950-kg car in 8.0 s if the car is traveling at 95 km/h? 𝑣 = 𝑣0 + 𝑎𝑡 𝑎= 𝑣 − 𝑣0 𝑡 95 km h 𝐹 = 𝑚𝑎 𝐹=𝑚 h s 𝑣 − 𝑣0 𝑡 𝐹 = 95 −2 8 9 = 8N 𝐹≈− N m =2 km 9 m/s 4. A fisherman yanks a fish vertically out of the water with an acceleration of 2.5 m/s2 using very light fishing line that has a breaking strength of 18 N (about 4 lb). The fisherman unfortunately loses the fish as the line snaps. What can you say about the mass of the fish? 𝐹 = 𝑚𝑎 𝑇 𝑎 𝑚𝑔 𝑚= 𝑇 − 𝑚𝑔 = 𝑚𝑎 𝑚𝑎 + 𝑚𝑔 = 𝑇 𝑇 𝑚= 𝑎+𝑔 8 25+98 𝑚= 4 kg 𝑚≈ 5 kg In order to break the fishing line the fish must have had a mass greater than 1.5 kg. 5. A 75-kg petty thief wants to escape from a third-story jail window. Unfortunately, a makeshift rope made of sheets tied together can support a mass of only 58 kg. What acceleration must the thief descend with in order for the sheets to not break? 𝐹 = 𝑚𝑎 𝑇 𝑎 𝑚𝑔 𝑎= 𝑚𝑔 − 𝑇 = 𝑚𝑎 75 9 8 − 58 9 8 75 𝑎 = 2 22 m/s² 𝑚𝑔 − 𝑇 𝑎= 𝑚 𝑎 ≈ 2 2 m/s² The rope can support his weight as long as he maintains a downward acceleration of at least 2.2 m/s². 6. An elevator (mass 4850 kg) is to be designed so that the maximum acceleration is 0.0680 . What are the maximum and minimum forces the motor should exert on the supporting cables? 𝑎max when elevator accelerates upward 𝐹 = 𝑚𝑎 𝑇 𝑎 𝑚𝑔 𝑇=𝑚 𝑔+ 8 𝑔 𝑇 = 485 8 4 N 𝐹 = 𝑚𝑎 𝑇 𝑇 − 𝑚𝑔 = 𝑚𝑎 𝑇 =𝑚 𝑔+𝑎 𝑇=5 8 𝑎min when elevator accelerates downward 𝑚𝑔 − 𝑇 = 𝑚𝑎 𝑎 𝑚𝑔 𝑇 =𝑚 𝑔−𝑎 𝑇=𝑚 𝑔− 98 8 𝑔 𝑇 = 485 9 2 𝑇 = 44 4 N 98 Name: _______________________ Mr. Kepple Free Body Diagrams Force – HW #3 Date: ___________ Period: _____ 1. Draw the free-body diagram for a basketball player (a) just before leaving the ground on a jump (b) while in the air 𝑁 𝑚𝑔 𝑚𝑔 2. Sketch the free-body diagram of a baseball (a) at the moment it is hit by the bat (b) after it has left the bat and is flying toward the outfield. 𝑁 (if air resistance is ignored) 𝑚𝑔 𝑚𝑔 3. A box weighing 77.0 N rests on a table. A rope tied to the box runs vertically upward over a pulley and a weight is hung from the other end (see picture). Determine the force that the table exerts on the box if the weight hanging on the other side of the pulley weighs (a) 30.0 N, (b) 60.0 N, and (c) 90.0 N. 𝐹 = 𝑚𝑎 (a) 30 N hanging weight 𝑁 + 𝑇 − 𝑚1 𝑔 = 0 𝑁 = 𝑚1 𝑔 − 𝑚2 𝑔 𝑁 + 𝑚2 𝑔 = 𝑚1 𝑔 𝑁 = 77.0 − 30.0 𝑁 = 𝑚1 𝑔 − 𝑚2 𝑔 𝑁 = 47.0 N (b) 60 N hanging weight 𝑁 = 𝑚1 𝑔 − 𝑚2 𝑔 𝑁 = 77.0 − 60.0 𝑁 = 17.0 N (a) 90 N hanging weight 𝑁 𝑇 𝑁=0 The box is lifted up off the table! 𝑚1 𝑔 𝑇 𝑚2 𝑔 4. At the instant a race began, a 65-kg sprinter exerted a force of 720 N on the starting block at a 22° angle with respect to the ground. (a) What was the horizontal acceleration of the sprinter? (b) If the force was exerted for 0.32 s, with what speed did the sprinter leave the starting block? (a) horizontal acceleration (b) final speed 𝐹𝑥 = 𝑚𝑎𝑥 𝐹 cos 𝜃 = 𝑚𝑎 𝑎= 𝑎= 𝐹 cos 𝜃 𝑚 +𝑦 𝑣 = 𝑣0 + 𝑎𝑡 𝐹 𝑁 𝑣 = 0 + 10. 7 03 𝜃 𝑣 = 3. 86 m/s 𝑚𝑔 𝑣 ≈ 3.3 m/s 7 0 cos 65 +𝑥 𝑎 = 10. 7 m/s² ≈ 10 m/s² 5. The block shown in the picture has a mass of = 7.0 kg and lies on a smooth frictionless plane tilted at an angle = .0 to the horizontal. (a) Determine the acceleration of the block as it slides down the plane. (b) If the block starts from rest 12.0 m up the plane from its base, what will be the block’s speed when it reaches the bottom of the incline? (a) acceleration (b) speed at bottom 2 2 𝑣= 2 +𝑦 𝑣 = 𝑣0 + 𝑎𝑥 𝐹𝑥 = 𝑚𝑎𝑥 𝑚𝑔 sin 𝜃 = 𝑚𝑎 𝑎 = 𝑔 sin 𝜃 𝑎 = 9.80 sin 𝜃 𝑣= .0 𝑁 𝑣0 + 𝑎𝑥 0+ 3.67 1 𝜃 𝑚𝑔 𝑣 = 9.39 m/s +𝑥 𝑎 = 3.67 m/s² 6. Suppose a block were given an initial speed of 4.5 m/s up the inclined plane from the previous problem. Starting from the bottom, how far up the plane would the block go? Ignore friction. Since the forces acting on the block remain the same the acceleration will remain 𝑎 = 3.67 m/s² 𝑣 2 = 𝑣0 2 + 𝑎𝑥 𝑣 2 − 𝑣0 2 𝑥= 𝑎 𝑥= 0 2 − 4.5 3.67 𝑥 = − .758 m 2 𝑥 ≈ .8 m up the ramp Mr. Kepple Name: _______________________ Dynamics FRQ Force – HW#4 Date: ___________ Period: _____ 𝑚 𝑚 A block of mass rests on a horizontal frictionless table, as shown above. It is connected to one end of a string that passes over a massless pulley and has another block of mass hanging from its other end. The whole apparatus is released from rest. You may assume that the pulley is frictionless and the mass of the string is negligible (a) On the figure below, draw and label all the forces that act on each block. (b) Construct a free-body diagram for this situation. 𝑁 𝑚 +𝑦 𝑇 𝑚 𝑇 𝑚 𝑔 𝑎 𝑁 𝑚 𝑇 𝑚 𝑔 𝑇 𝑚 +𝑥 𝑚 𝑔 𝑚 𝑔 (c) Calculate the acceleration of the system for 𝐹𝑥 𝑇 𝑚 𝑎𝑥 𝑚 𝑎 𝐹𝑥 and 𝑚 𝑎𝑥 𝑚 𝑔−𝑇 𝑚 𝑔− 𝑚 𝑎 𝑚 𝑎 𝑚 𝑎 𝑚 𝑎+𝑚 𝑎 𝑚 𝑔 𝑎 𝑚 +𝑚 𝑚 𝑔 𝑎 . 𝑚 𝑔 𝑚 +𝑚 𝑎 + 𝑎 𝑎 33𝑔 3 67 m/s² 𝑎 ≈ 3 3 m/s² 𝑔 (d) Calculate the tension in the string for 𝑎 and 𝑚 𝑔 𝑚 +𝑚 𝑇 𝑇 𝑚 𝑎 𝑚 𝑚 𝑔 𝑚 +𝑚 . 𝑇 + 𝑇 98 13 67 𝑁 𝑇 ≈ 13 N 𝑚 (e) Suppose instead of mass being on a horizontal table, it is placed on the inclined plane shown above. Indicate below whether the acceleration of the system would be greater than, less than, or equal to the answer in part (c). ___ Greater than ___ X Less than ___ Equal to Justify your answer. When placed on an inclined plane, a component of the weight of block 1 will point down the ramp, opposing the tension in the string. This results in a decrease in the net force acting on block 1, which in response leads to a decrease in the acceleration of the system.