Lecture Notes 5 PDF

Storyline Chapter 5: The Laws of Motion Physics for Scientists and Engineers, 10e Raymond A. Serway 1 John W. Jewett, Jr. The Concept of Force 2 The Concept of Force 3  The Concep...

Storyline Chapter 5: The Laws of Motion Physics for Scientists and Engineers, 10e Raymond A. Serway 1 John W. Jewett, Jr. The Concept of Force 2 The Concept of Force 3  The Concept of Force  F1 = F12 + F2 2 = 2.24 units  1.00 unit  θ = tan  −1   2.00 unit  = tan ( 0.500 ) −1 = 26.6° 4 Newton’s First Law and Inertial Frames 5  Newton’s First Law and Inertial Frames If an object does not interact with other objects, it is possible to identify a reference frame in which the object has zero acceleration. Inertial frame of reference 6 Newton’s First Law and Inertial Frames 7  Newton’s First Law and Inertial Frames In the absence of external forces and when viewed from an inertial reference frame, an object at rest remains at rest and an object in motion continues in motion with a constant velocity (that is, with a constant speed in a straight line). 8  Quick Quiz 5.1 Which of the following statements is correct? (a) It is possible for an object to have motion in the absence of forces on the object. (b) It is possible to have forces on an object in the absence of motion of the object. (c) Neither statement (a) nor statement (b) is correct. (d) Both statements (a) and (b) are correct. 9  Quick Quiz 5.1 Which of the following statements is correct? (a) It is possible for an object to have motion in the absence of forces on the object. (b) It is possible to have forces on an object in the absence of motion of the object. (c) Neither statement (a) nor statement (b) is correct. (d) Both statements (a) and (b) are correct. 10  Mass Mass is a property that specifies how much resistance an object exhibits to changes in its velocity m1 a2 ≡ m2 a1 11 Newton’s Second Law  F m   1 a ∝F a∝ m 12  Newton’s Second Law When viewed from an inertial reference frame, the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass:   a∝ ∑F m 13  Newton’s Second Law   ∑ F = ma ∑ Fx ma = = x ∑ Fy ma = y ∑ Fz maz 14  Quick Quiz 5.2 An object experiences no acceleration. Which of the following cannot be true for the object? (a) A single force acts on the object. (b) No forces act on the object. (c) Forces act on the object, but the forces cancel. 15  Quick Quiz 5.2 An object experiences no acceleration. Which of the following cannot be true for the object? (a) A single force acts on the object. (b) No forces act on the object. (c) Forces act on the object, but the forces cancel. 16  Quick Quiz 5.3 You push an object, initially at rest, across a frictionless floor with a constant force for a time interval ∆t, resulting in a final speed of v for the object. You then repeat the experiment, but with a force that is twice as large. What time interval is now required to reach the same final speed v? (a) 4 ∆t (b) 2 ∆t (c) ∆t (d) ∆t /2 (e) ∆t /4 17  Quick Quiz 5.3 You push an object, initially at rest, across a frictionless floor with a constant force for a time interval ∆t, resulting in a final speed of v for the object. You then repeat the experiment, but with a force that is twice as large. What time interval is now required to reach the same final speed v? (a) 4 ∆t (b) 2 ∆t (c) ∆t (d) ∆t /2 (e) ∆t /4 18  Units of Force SI unit of force: newton (N) 2 1 N ≡ 1 kg ⋅ m/s 1 lb ≡ 1 slug ⋅ ft/s 2 1 1 N ≈ lb 4 19 Newton’s Second Law   ∑ F = ma 20  Example 5.1: An Accelerating Hockey Puck A hockey puck having a mass of 0.30 kg slides on the frictionless, horizontal surface of an ice rink. Two hockey sticks strike the puck simultaneously, exerting the forces on the puck shown in the figure. The force F1 has a magnitude of 5.0 N, and is directed at θ = 20° below the x axis. The force F2 has a magnitude of 8.0 N and its direction is φ = 60° above the x axis. Determine both the magnitude and the direction of the puck’s acceleration. 21  Example 5.1: An Accelerating Hockey Puck ∑F x = F1x + F2 x = F1 cos θ + F2 cos φ  ay  β = tan   −1 ∑F y = F1 y + F2 y = F1 sin θ + F2 sin φ  ax  ax = ∑ = F x F1 cos θ + F2 cos φ −1  17  = tan  =  31° m m  29  = ay = ∑ Fy F1 sin θ + F2 sin φ m m ( 5.0 N ) cos ( −20° ) + (8.0 N ) cos ( 60° ) ax = 29 m/s 2 0.30 kg ( 5.0 N ) sin ( −20° ) + (8.0 N ) sin ( 60° ) a y = 17 m/s 2 0.30 kg a= ( 29 m/s 2 2 ) + (17 m/s ) 2 2 = 34 m/s 2 22  Example 5.1: An Accelerating Hockey Puck Suppose three hockey sticks strike the puck simultaneously, with two of them exerting the forces shown in the figure. The result of the three forces is that the hockey puck shows no acceleration. What must be the components of the third force? F3 x = − ( 0.30 kg ) ( 29 m/s 2 ) = −∑ Fx = −8.7 N F3 y = − ( 0.30 kg ) (17 m/s 2 ) = −∑ Fx = −5.2 N 23 The Gravitational Force and Weight   ∑ F = ma     with a g= = and ∑ F Fg   Fg = mg Fg = mg 24 The Gravitational Force and Weight g varies with geographic location Fg = mg 25 The Gravitational Force and Weight Fg = mg Moon 2 g Moon ≈ 1.6 m/s inertial mass vs. gravitational mass 26  Quick Quiz 5.4 Suppose you are talking by interplanetary telephone to a friend who lives on the Moon. He tells you that he has just won a newton of gold in a contest. Excitedly, you tell him that you entered the Earth version of the same contest and also won a newton of gold! Who is richer? (a) You are. (b) Your friend is. (c) You are equally rich. 27  Quick Quiz 5.4 Suppose you are talking by interplanetary telephone to a friend who lives on the Moon. He tells you that he has just won a newton of gold in a contest. Excitedly, you tell him that you entered the Earth version of the same contest and also won a newton of gold! Who is richer? (a) You are. (b) Your friend is. (c) You are equally rich. 28  Conceptual Example 5.2: How Much Do You Weigh in an Elevator You have most likely been in an elevator that accelerates upward as it moves toward a higher floor. In this case, you feel heavier. In fact, if you are standing on a bathroom scale at the time, the scale measures a force having a magnitude that is greater than your weight. Therefore, you have tactile and measured evidence that leads you to believe you are heavier in this situation. Are you heavier? No; your weight is unchanged. 29  Newton’s Third Law  If two objects interact, the force F12 exerted by object 1 on object 2 is equal in magnitude  and opposite in direction to the force F21 exerted by object 2 on object 1:   F12 = −F21 30 Newton’s Third Law   Fg = FEp   FpE = −FEp 31 Newton’s Third Law    ∑ F =n + mg =0 ⇒ n ˆj − mg ˆj = 0 n = mg 32 Free-Body Diagram 33  Quick Quiz 5.5 Part I If a fly collides with the windshield of a fast-moving bus, which experiences an impact force with a larger magnitude? (a) the fly (b) the bus (c) The same force is experienced by both. 34  Quick Quiz 5.5 Part I If a fly collides with the windshield of a fast-moving bus, which experiences an impact force with a larger magnitude? (a) the fly (b) the bus (c) The same force is experienced by both. 35  Quick Quiz 5.5 Part II If a fly collides with the windshield of a fast-moving bus, which experiences the greater acceleration? (a) the fly (b) the bus (c) The same acceleration is experienced by both. 36  Quick Quiz 5.5 Part II If a fly collides with the windshield of a fast-moving bus, which experiences the greater acceleration? (a) the fly (b) the bus (c) The same acceleration is experienced by both. 37  Conceptual Example 5.3: You Push Me and I’ll Push You A large man and a small boy stand facing each other on frictionless ice. They put their hands together and push against each other so that they move apart. Who moves away with the higher speed? The boy 38  Conceptual Example 5.3: You Push Me and I’ll Push You Who moves farther while their hands are in contact? The boy 39  Analysis Models Using Newton’s Second Law 40  Analysis Model: The Particle in Equilibrium  ∑F = 0 ∑F y =T − Fg =0 or T = Fg 41  Analysis Model: The Particle Under a Net Force   ∑ F = ma 42  Analysis Model: The Particle Under a Net Force T ∑ Fx= T= max or ax= m ∑F y =n − Fg =0 or n =Fg 43  Analysis Model: The Particle Under a Net Force ∑Fy = 0 ⇒ n − Fg − F = 0 n = Fg + F = mg + F 44  Analysis Model: Particle in Equilibrium  ∑F = 0 45  Analysis Model: Particle Under a Net Force   ∑ F = ma 46  Example 5.4: A Traffic Light at Rest A traffic light weighing 122 N hangs from a cable tied to two other cables fastened to a support as the figure. The upper cables make angles of θ1 = 37.0° and θ2 = 53.0° with the horizontal. These upper cables are not as strong as the vertical cable and will break if the tension in them exceeds 100 N. Does the traffic light remain hanging in this situation, or will one of the cables break? 47  Example 5.4: A Traffic Light at Rest ∑F y =0 ⇒ T3 − Fg =0 ⇒ T3 =Fg Force x Component y Component  T1 − T1 cos θ1 T1 sin θ1  T2 T2 cos θ 2 T2 sin θ 2  T3 0 − Fg (1) ∑ Fx =−T1 cos θ1 + T2 cos θ 2 = 0 ( 2) ∑ = Fy T1 sin θ1 + T2 sin θ 2 + ( = − Fg ) 0 48  Example 5.4: A Traffic Light at Rest  cos θ1  −T1 cos θ1 + T2 cos θ 2 =0 ⇒ T2 =T1    cos θ 2   cos θ1  T1 sin θ1 + T2 sin θ 2 + ( − Fg ) = 0 ⇒ T1 sin θ1 + T1   ( sin θ 2 ) − Fg = 0  cos θ 2  Fg T1 = sin θ1 + cos θ1 tan θ 2 122 N T1 = 73.4 N sin 37.0° + cos 37.0° tan 53.0°  cos 37.0°  =T2 (= 73.4 N )   97.4 N  cos 53.0°  49  Example 5.4: A Traffic Light at Rest Suppose the two angles in the figure are equal. What would be the relationship between T1 and T2?  cos θ1  T2 T= 1  T1  cos θ 2  50  Conceptual Example 5.5: Forces Between Cars in a Train Train cars are connected by couplers, which are under tension as the locomotive pulls the train. Imagine you are on a train speeding up with a constant acceleration. As you move through the train from the locomotive to the last car, measuring the tension in each set of couplers, does the tension increase, decrease, or stay the same? The tension decreases. 51  Conceptual Example 5.5: Forces Between Cars in a Train When the engineer applies the brakes, the couplers are under compression. How does this compression force vary from the locomotive to the last car? (Assume only the brakes on the wheels of the engine are applied.) The force decreases. 52  Example 5.6: The Runaway Car A car of mass m is on an icy driveway inclined at an angle θ as in the figure. (A) Find the acceleration of the car, assuming the driveway is frictionless. 53  Example 5.6: The Runaway Car ∑ Fx mg = = sin θ max ∑F y n − mg cos θ = = ma y ax = g sin θ 54  Example 5.6: The Runaway Car (B) Suppose the car is released from rest at the top of the incline and the distance from the car’s front bumper to the bottom of the incline is d. How long does it take the front bumper to reach the bottom of the hill, and what is the car’s speed as it arrives there? 55  Example 5.6: The Runaway Car 1 2 1 2 x f = xi + vxi t + ax t → d = ax t 2 2 2d 2d =t = ax g sin θ vxf 2 = 2ax d vxf = 2a x d = 2 gd sin θ 56  Example 5.6: The Runaway Car What previously solved problem does this situation become if θ = 90°? In free fall: = sin θ g sin ax g= = 90° g 57  Example 5.7: One Block Pushes Another Two blocks of masses m1 and m2 , with m1 > m2 , are placed in contact with each other on a frictionless, horizontal surface as in the figure. A constant horizontal force F is applied to m1 as shown. 58  Example 5.7: One Block Pushes Another (A) Find the magnitude of the acceleration of the system. ∑ F= x F= ( m1 + m2 ) ax F ax = m1 + m2 59  Example 5.7: One Block Pushes Another (B) Determine the magnitude of the contact force between the two blocks. ∑ F= x P= 12 m2 ax F  m2  ax = → P12 = m2 ax =  F m1 + m2  m1 + m2  60  Example 5.7: One Block Pushes Another ∑F x =F − P21 =F − P12 =m1ax P12= F − m1ax  F  = F − m1    m1 + m2   m2  = F  m1 + m2  61 62  Example 5.7: One Block Pushes Another  Imagine that the force F is is applied toward the left on the right-hand  block of mass m2. Is the magnitude of the force P12 the same as it was when the force was applied toward the right on m1? When the force 𝐅𝐅⃗ is applied from the right, we have:  m1 P12 = F m1 + m2 This is greater than before because m1 > m2. 63  Example 5.8: Weighing a Fish in an Elevator A person weighs a fish of mass m on a spring scale attached to the ceiling of an elevator as illustrated in the figure. (A) Show that if the elevator accelerates either upward or downward, the spring scale gives a reading that is different from the weight of the fish. 64  Example 5.8: Weighing a Fish in an Elevator ∑F y=T − Fg = 0 ⇒ T = Fg = mg ( elevator at rest or moving with constant v ) ∑F y =T − mg =ma y T ma y + mg =  ay   ay  = mg  += 1 Fg  + 1  g   g  65  Example 5.8: Weighing a Fish in an Elevator (B) Evaluate the scale readings for a 40.0-N fish if the elevator moves with an acceleration ay = ±2.00 m/s2.  2.00 m/s 2  T ( 40.0 N )=  2 + 1 48.2 N  9.80 m/s   −2.00 m/s 2  T ( 40.0 N )=  2 + 1 31.8 N  9.80 m/s  66  Example 5.8: Weighing a Fish in an Elevator Suppose the woman in the figure tires of watching the scale and exits the elevator. Then the elevator cable breaks and the elevator and its remaining contents are in free fall. What happens to the reading on the scale?  ay   −g  T Fg  + 1 →= = T Fg  1 0 +=  g   g  67  Example 5.9: The Atwood Machine When two objects of unequal mass are hung vertically over a frictionless pulley of negligible mass as in the figure, the arrangement is called an Atwood machine. The device is sometimes used in the laboratory to determine the value of g by measuring the acceleration of the objects. Determine the magnitude of the acceleration of the two objects and the tension in the lightweight string. 68  Example 5.9: The Atwood Machine ∑F y T m1 g = =− m1a y ∑ F=y m2 g − T= m2 a y −m1 g + m2 g = m1a y + m2 a y  m2 − m1  ay =  g  m1 + m2   2m1m2  T = m1 ( g + a y )=  g  m1 + m2  69  Example 5.9: The Atwood Machine Describe the motion of the system if the objects have equal masses, that is, m1 = m2. No acceleration for m =1 m= 2 m: m−m  0  ay  =  g ⇒= ay  = g 0 m+m  2m  70  Example 5.9: The Atwood Machine What if one of the masses is much larger than the other: m1 >> m2? m1 falls as if m2 were not there  m2 − m1   −m1  if m1 >> m2 → a y =  g ≈  g = −g  m1 + m2   m1  71 Example 5.10: Acceleration of Two Objects Connected by a Cord A ball of mass m1 and a block of mass m2 are attached by a lightweight cord that passes over a frictionless pulley of negligible mass as in the top figure. The block lies on a frictionless incline of angle θ. Find the magnitude of the acceleration of the two objects and the tension in the cord. 72 Example 5.10: Acceleration of Two Objects Connected by a Cord ∑F y =T − m1 g − m1a y =m1a ∑ F= m g sin θ −= x′ 2 T m a= m a 2 x′ 2 ∑F = n − m g cos θ = y′ 20 =T m1 ( g + a ) m2 g sin θ − m1 ( g + a ) = m2 a  m2 sin θ − m1  a= g  m1 + m2   m1m2 ( sin θ + 1)  T = g  m1 + m2  73 Example 5.10: Acceleration of Two Objects Connected by a Cord What happens in this situation if θ = 90°? It becomes an Atwood machine!  m2 sin θ − m1   m2 − m1  a  = g → a  g  m1 + m2   m1 + m2   m1m2 ( sin θ + 1)   2m1m2  T  = g →T  g  m1 + m2   m1 + m2  74 Example 5.10: Acceleration of Two Objects Connected by a Cord What if m1 = 0? Describes a mass sliding down a frictionless inclined plane, similar to the sliding car problem  m2 sin θ − m1   m2 sin θ − 0   m2 sin θ  a  = g → a  = g  g  m1 + m2   0 + m2   m2  75 Forces of Friction 76 Forces of Friction 77  Coefficients of Friction f s ≤ µs n =f s f= s ,max µs n f k = µk n 78  Quick Quiz 5.6 You press your physics textbook flat against a vertical wall with your hand. What is the direction of the friction force exerted by the wall on the book? (a) downward (b) upward (c) out from the wall (d) into the wall 79  Quick Quiz 5.6 You press your physics textbook flat against a vertical wall with your hand. What is the direction of the friction force exerted by the wall on the book? (a) downward (b) upward (c) out from the wall (d) into the wall 80  Quick Quiz 5.7 Charlie is playing with his daughter Torrey in the snow. She sits on a sled and asks him to slide her across a flat, horizontal field. Charlie has a choice of (a) pushing her from behind by applying a force downward on her shoulders at 30° below the horizontal or (b) attaching a rope to the front of the sled and pulling with a force at 30° above the horizontal. Which would be easier for him and why? 81 82  Quick Quiz 5.7 Charlie is playing with his daughter Torrey in the snow. She sits on a sled and asks him to slide her across a flat, horizontal field. Charlie has a choice of (a) pushing her from behind by applying a force downward on her shoulders at 30° below the horizontal or (b) attaching a rope to the front of the sled and pulling with a force at 30° above the horizontal. Pulling up on the rope decreases the normal force, which, in turn, decreases the force of kinetic friction. 83  Example 5.11: Experimental Determination of µs and µk The following is a simple method of measuring coefficients of friction. Suppose a block is placed on a rough surface inclined relative to the horizontal as shown in the figure. The incline angle is increased until the block starts to move. Show that you can obtain µs by measuring the critical angle θc at which this slipping just occurs. 84  Example 5.11: Experimental Determination of µs and µk ∑= F mg sin θ − x = f 0s ∑F = n − mg cos θ = y 0  n  fs mg = sin θ  =  sin θ n tan θ  cos θ  µ s n = n tan θ c µ s = tan θ c 85 86  Example 5.12: The Sliding Hockey Puck A hockey puck on a frozen pond is given an initial speed of 20.0 m/s. If the puck always remains on the ice and slides 115 m before coming to rest, determine the coefficient of kinetic friction between the puck and ice. 87  Example 5.12: The Sliding Hockey Puck ∑F x =− fk =max ∑F y =n − mg =0 − µk n = − µ k mg = max ax = − µ k g 2 vxi + 2ax ( x f − xi ) vxf = 2 vxi 2 − 2 µ k gx f vxi 2 + 2ax x f = 0= ( 20.0 m/s ) 2 2 vxi µk = µk = 0.177 2 gx f 2 ( 9.80 m/s ) (115 m ) 2 88  Example 5.13: Acceleration of Two Connected Objects When Friction Is Present A block of mass m2 on a rough, horizontal surface is connected to a ball of mass m1 by a lightweight cord over a lightweight, frictionless pulley as shown in the figure. A force of magnitude F at an angle θ with the horizontal is applied to the block as shown, and the block slides to the right. The coefficient of kinetic friction between the block and surface is µk. Determine the magnitude of the acceleration of the two objects. 89  Example 5.13: Acceleration of Two Connected Objects When Friction Is Present ∑ F= F cos θ − f − T= m a= x k 2 x m2 a ∑F = n + F sin θ − m g = y 0 2 ∑F y T m1 g = =− m1a y =m1a =n m2 g − F sin θ =f k µ k ( m2 g − F sin θ ) F cos θ − µ k ( m2 g − F sin θ ) − m1 ( a + g ) = m2 a F ( cos θ + µ k sin θ ) − ( m1 + µ k m2 ) g a= m1 + m2 90  Assessing to Learn A baseball is struck by a bat. While the ball is in the air, what objects exert forces on the ball? 1. Earth 2. Bat 3. Air 4. Bat, Air 5. Earth, Bat 6. Earth, Air 7. Earth, Bat, Air 8. There are no forces on the ball. 9. The answer depends on whether the ball is going up, going down, or at its highest point. 91  Assessing to Learn Three blocks are stacked as shown below. How many forces are acting on the bottom block (m3)? 1. One force 2. Two forces 3. Three forces 4. Four forces 5. Five forces 6. Six forces 7. More than six forces 8. No forces act on the block 9. Cannot be determined 92  Assessing to Learn A block of mass m is on a rough surface, with a spring attached and extended. As the block moves up the incline a small distance, how many forces are exerted on the mass? 1. One force 2. Two forces 3. Three forces 4. Four forces 5. Five forces 6. Six forces 7. Seven forces 8. More than 7 forces 9. None of the above 9. Impossible to determine 93  Assessing to Learn A monkey hangs on a rope. What forces act on the monkey? (Ignore forces due to the air.) 1. Friction, Gravitation 2. Tension, Gravitation 3. Friction, Tension, Gravitation 4. Normal, Friction, Gravitation 5. More than one answer is true 6. None of the above 7. Cannot be determined 94  Assessing to Learn A thin wire is stretched horizontally between two walls. If a weight W is hung on the wire, what is true about the tension T in the wire? 1. TW 4. The relationship between T and W cannot be determined. 95  Assessing to Learn Consider the following three items. A. 100 g of steam on the Moon B. 10 g of water on the Earth C. 20 g of ice floating in water on the Earth Put these items in order of increasing weight: 1. A < B < C 2. A < C < B 3. B < A < C 4. B < C < A 5. C < A < B 6. C < B < A 7. None of the above 8. Impossible to determine 96  Assessing to Learn Consider the following three items. A. 100 g of steam on the Moon B. 10 g of water on the Earth C. 20 g of ice floating in water on the Earth Put these items in order of increasing mass: 1. A < B < C 2. A < C < B 3. B < A < C 4. B < C < A 5. C < A < B 6. C < B < A 7. None of the above 8. Impossible to determine 97  Assessing to Learn Consider the following three items. A. 100 g of steam on the Moon B. 10 g of water on the Earth C. 20 g of ice floating in water on the Earth Put these items in order of increasing density: 1. A < B < C 2. A < C < B 3. B < A < C 4. B < C < A 5. C < A < B 6. C < B < A 7. None of the above 8. Impossible to determine 98  Assessing to Learn An astronaut floats inside an orbiting space station. Which of the following are true? A. No forces act on the astronaut. B. The astronaut has no mass. C. The astronaut has no weight. 1. A only 2. B only 3. C only 3. A and B 5. A and C 6. B and C 7. all are true 8. none are true 99  Assessing to Learn Consider the three situations shown below. In each case two small carts are connected by a spring. A constant force F is applied to the leftmost cart in each case. In each situation the springs are compressed so that the distance between the two carts never changes. Which of the following statements must be true regarding the compression of the spring in each case? Assume the springs are identical. 1. Compression A = Compression B = Compression C 2. B = C < A 3. A < B = C 4. A < B < C 5. B < A < C 6. C < A < B 7. A < C < B 8. None of the above 100 9. Cannot be determined  Assessing to Learn Consider the three situations below, labeled A, B, and C. Ignore friction. After each system is released from rest, how do the tensions in the strings compare? 1. A = B = C 2. B = C < A 3. A = C < B 4. A < B < C 5. A < C < B 6. B < A < C 7. B < C < A 8. C < A < B 9. C < B < A 10. Impossible to determine 101  Assessing to Learn Two blocks are arranged as shown and kept at rest by holding the 1 kg block in place. The tension in the string is closest to: 1. 9 N 2. 10 N 3. 11 N 4. 12 N 5. 13 N 6. 10 N at the left end; 12 N at the right 7. 10 N in the left segment; 11 N in the middle segment; 12 N in the right segment 8. Smoothly varying from 10 N by the left block to 12 N by the right block 9. None of the above 10. Impossible to determine 102  Assessing to Learn Two blocks are arranged as shown and released from rest. The tension in the string is closest to: 1. 9 N 2. 10 N 3. 11 N 4. 12 N 5. 13 N 6. 10 N at the left end; 12 N at the right 7. 10 N in the left segment; 11 N in the middle segment; 12 N in the right segment 8. Smoothly varying from 10 N by the left block to 12 N by the right block 9. None of the above 10. Impossible to determine 103  Assessing to Learn A car accelerates down a straight highway. Which of the free-body diagrams shown below best represents the forces on the car? 1. 2. 3. 4. 5. None of these 6. Cannot be determined 104  Assessing to Learn A mass of 5 kg sits at rest on an incline making an angle of 30° to the horizontal. If μs = 0.7, what is the friction force on the block? 1. 43.3 N, down the incline 2. 25 N, up the incline 3. 10 N, down the incline 4. 30.3 N, up the incline 5. None of the above 105  Assessing to Learn Two blocks, having the same mass but different sizes, slide with the same constant speed on a smooth surface, then move onto a surface having friction coefficient μk. Which stops in the shorter time? 1. M1 2. M2 3. Both stop in the same time 4. Cannot be determined 106  Assessing to Learn Two blocks, M1 > M2, having the same speed, move from a frictionless surface onto a surface having friction coefficient μk. Which stops in the shorter time? 1. M1 2. M2 3. Both stop in the same time 4. Cannot be determined 107