Unit 06 Examples. Stuff you asked about:

Transcription

1 Unit 06 Examples Today s Concepts: 1. Force due to gravity 2. Force due to strings 3. Force due to springs (just a little bit) Mechanics Lecture 5, Slide 1 Stuff you asked about: Can you go over all of the forces acting on stacked objects like in the blocks at rest bridge question? I do not understand the horizontal and vertical components. I'm not sure how or when to use them. That also applies to vectors. Please go over Bridge Q4 (Pulleys and ropes). To go over more force body diagras Still a little confused on how forces act upon objects, would like to see some examples Could you go over more tension examples? some more examples of pulleys review the blocks on top of each other problem and drawing that free body diagram. I need more practice with the pulley problem and understanding tension. I don t feel confident about the forces and exactly when the accelerations are zero. Tension also throws me off. I don t understand when or if the tensions of the strings change. Can you go over why the blocks at rest question doesn't have the forces that the 2 and 6 kg blocks act upon it? more examples with unequal tension please Please review pulleys and ropes bridge question and ski example from pre-lecture. Mechanics Lecture 5, Slide 2 1

2 Force of gravity F grav = mg = weight Units are Newtons or pounds (4.4N = 1lb) 1kg * 9.81m/sec 2 = 9.81N (1slug * 32.2ft/sec 2 = 32.2lb) (1lbm * 32.2ft/sec 2 = 1lbf) A 1kg bowling ball is in free fall. (Ignore air resistance and take down as positive.) Which of the following is the correct application of Newton s second law to this situation? A) F ma B) F ma mg C) F ma mg D) Don t sweat this in 2111 Mechanics Lecture 5, Slide 3 Strings/Force from Tension Unless specifically stated, all strings have negligible mass. (Not a bad approximation.) Force from string is always parallel to string. Magnitude is always the same at both ends 1m 1 0 kg S 1 In the top situation, the string is tied to a wall and the force due to tension in the string is m 1 g. In the bottom situation, two masses are held by the string. What is the force due to tension in the bottom situation? 1m 1 0 kg 1m 1 0 kg A) 2*m 1 g B) m 1 g C) 0 Mechanics Lecture 5, Slide 4 2

3 Checkpoint A box of mass m is hung with a string from the ceiling of an elevator that is accelerating upward. Which of the following best describes the tension T in the string: a A) T < mg B) T = mg C) T > mg Mechanics Lecture 5, Slide 5 Example 6.1 (The elevator) Let s say that m is 5kg and the elevator is accelerating upwards at 2m/sec 2. What is the tension in the string? a Mechanics Lecture 5, Slide 6 3

4 You are traveling on an elevator up the Sears tower. As you near the top floor and are slowing down, your acceleration A) is upward B) is downward C) is zero Mechanics Lecture 5, Slide 7 You are traveling on an elevator up the Sears tower, and you are standing on a bathroom scale. As you near the top floor and are slowing down, the scale reads A) More than your usual weight B) Less than your usual weight C) Your usual weight Mechanics Lecture 5, Slide 8 4

5 In the above plot, what can you say about the slope of the position graph between 0 second and 3 seconds? A.It s positive and getting smaller in magnitude B.It s positive and getting bigger in magnitude C.It s zero D.It s negative and getting bigger in magnitude E.It s negative and getting small in magnitude In the above plot, what can you say about the slope of the position graph between 3 seconds and 6 seconds? A.It s positive and getting smaller in magnitude B.It s positive and getting bigger in magnitude C.It s zero D.It s negative and getting bigger in magnitude E.It s negative and getting small in magnitude 5

6 In the above plot, is there a point where the slope is zero? A.Yes, about 0.4 seconds B.Yes, about 5.6 seconds C.Yes, about 3 seconds D.Both (A) and (B) E.No, it s never zero. Let s say I wanted to know the acceleration from the above position plot. I now know (a) a time where the velocity is zero, (b) how far the object fell after that time and (c) how long it took to fall that distance. How could I solve for the acceleration, a? A.y f = y o + v oy *t + ½ a*t 2 B.v fy = v oy + a*t C.v f2 = v o2 + 2*a*Dy 6

7 A cart with mass m 2 is connected to a mass m 1 using a string that passes over a frictionless pulley, as shown below. The cart is held motionless. m 2 The tension in the string is A) m 1 g B) m 2 g C) 0 g m 1 Mechanics Lecture 5, Slide 13 A cart with mass m 2 is connected to a mass m 1 using a string that passes over a frictionless pulley, as shown below. Initially, the cart is held motionless, but is then released and starts to accelerate. a m 2 After the cart is released, the tension in the string is A) = m 1 g B) > m 1 g C) < m 1 g g m 1 Mechanics Lecture 5, Slide 14 7

8 Example 6.2 (two carts) A cart with mass m 2 = 10kg is connected to a mass m 1 = 5kg using a string that passes over a frictionless pulley, as shown below. Initially, the cart is held motionless, but is then released and starts to accelerate. What is the acceleration of m 1? What is the force due to tension in the string? m 2 m 1 Mechanics Lecture 5, Slide 15 Stuff you asked about: Can you go over all of the forces acting on stacked objects like in the blocks at rest bridge question? I do not understand the horizontal and vertical components. I'm not sure how or when to use them. That also applies to vectors. Please go over Bridge Q4 (Pulleys and ropes). To go over more force body diagras Still a little confused on how forces act upon objects, would like to see some examples Could you go over more tension examples? some more examples of pulleys review the blocks on top of each other problem and drawing that free body diagram. I need more practice with the pulley problem and understanding tension. I don t feel confident about the forces and exactly when the accelerations are zero. Tension also throws me off. I don t understand when or if the tensions of the strings change. Can you go over why the blocks at rest question doesn't have the forces that the 2 and 6 kg blocks act upon it? more examples with unequal tension please Please review pulleys and ropes bridge question and ski example from pre-lecture. Mechanics Lecture 5, Slide 16 8

9 Clicker A block, m 1 with a mass of 3kg is hung from a rope which is then attached through a pulley to another hanging block, m 2 with a mass of 5kg. How does the tension force on m 1 compare to its weight? A) T > W B) T = W C) T < W m 1 m 2 Class Problem 1 A block, m 1 with a mass of 3kg is hung from a rope which is then attached through a pulley to another hanging block, m 2 with a mass of 5kg. What is the magnitude of the acceleration of these two blocks? Take some time to create a free body diagram of each mass. m 1 m 2 9

10 Bridge 4 In the following setups, all masses are at rest, the ropes and pulleys are massless, and the pulleys and surfaces are frictionless. Bridge 4 In the below setups, all masses are at rest, the ropes and pulleys are massless, and the pulleys and surfaces are frictionless. How are the tensions in all the ropes related? A. T A = T B = T D < T C < T E B. T D = T A < T B < T C = T E C. T A = T B = T C = T D = T E D. T A = T B = T D = T E < T C 10

11 Bridge 3 Three blocks on top of each other rest on a surface as shown. Which of the following represents best the free body diagram of the block in the middle (i.e. the green block)? Checkpoint A block sits at rest on a horizontal frictionless surface. Which of the following sketches most closely resembles the correct free body diagram for all forces acting on the block? Each arrow represents a force. A B C D The only forces acting on the box are gravity (acting downward) and normal force (acting upward). Mechanics Lecture 5, Slide 22 11

12 A block slides down a frictionless inclined plane. Which of the following sketches most closely resembles the correct free body diagram for all forces acting on the block? A B C D Mechanics Lecture 5, Slide 23 Example 6.3 (Block on Ramp) 0.4m 1m A 1kg block slides down a frictionless ramp. The ramp has dimensions of 1m horizontally and 40cm vertically. What is the acceleration of the block? Mechanics Lecture 5, Slide 24 12

13 Example 6.4: Prelecture Skier A 60kg skier slides down a 30 o slope, opposed by a 72N frictional force. If it takes her 4second to reach the bottom, how long is the slope? Mechanics Lecture 5, Slide 25 Example 6.5 (Cords Supporting a Mass) Three cords support a m=15 kg mass as shown. Find the tensions in all three cords if θ 1 = 47 and θ 2 = 28 Mechanics Lecture 5, Slide 26 13

14 Three blocks of increasing mass are connected by string and are pulled across a frictionless surface by a 60N. What can we say about the acceleration of m 3, m 2 and m 1? T 2 T m 3 =30kg m 2 =20kg 1 F =60N 10kg A. a 1 > a 2 > a 3 B. a 1 < a 2 < a 3 C. a 1 > a 2 = a 3 D. a 1 = a 2 = a 3 Mechanics Lecture 5, Slide 27 Three blocks of increasing mass are connected by string and are pulled across a frictionless surface by a 60N. What can we say about the magnitude of F, T 2 and T 1? T 2 T m 3 =30kg m 2 =20kg 1 F =60N 10kg A. F > T 1 > T 2 B. F < T 1 < T 2 C. F > T 1 = T 2 D. F = T 1 = T 2 Mechanics Lecture 5, Slide 28 14

15 Example 6.6 (Three Blocks) Three blocks of increasing mass are connected by string and are pulled across a frictionless surface by a 60N. What are F, T 2 and T 1? T 2 T 30kg 20kg 1 10kg F =60N Mechanics Lecture 5, Slide 29 Springs X f DX The harder you pull on them, the more they stretch. Expressed as Hooke s Law: F = -kdx L Mechanics Lecture 5, Slide 30 15

16 A box of mass m is hung by a spring from the ceiling of an elevator. When the elevator is at rest, the length of the spring is L = 1m. L a As the elevator accelerates upward, the length of the spring will be m A. L < 1 m B. L = 1 m C. L > 1 m Mechanics Lecture 5, Slide 31 Example 6.7 (Spring in an elevator) A mass of 5kg is hung vertically from a spring with a spring constant of k=100n/m. The spring has an unstretched length of 0.75m. L m a What is its length if the elevator is stationary? What is its length if the elevator is accelerating upwards at 2m/sec 2? What is the force of the spring on the top of the elevator? Mechanics Lecture 5, Slide 32 16

17 The Physics Donkey Because you re tired of hauling your TI-83 all over campus, you decide to bring your donkey and cart with you to COD. After physics class, you load all your books and stuff into the cart and tell the donkey to head off to Calc III. But the donkey replies (it s a talking physics donkey) There s no point in me trying. According to Newton s 3 rd Law, no matter how hard I pull on the cart, the cart will pull back on me with an equal and opposite force. The two forces add up to zero and the cart won t accelerate. Since the cart isn t moving now, and a=0, it will never move. The donkey lays down and takes a nap. Mechanics Lecture 5, Slide 33 Why is the physics donkey wrong? A. Because the donkey is less massive so the force of the donkey on the cart is always greater than the force of the cart on the donkey. B. Because the force of the donkey on the cart is greater than the force of the cart on the donkey for the brief instant of time when the donkey takes his first step. C. The donkey is correct that the forces are the same, but it doesn t matter in this case. D. Because the cart is more massive so the force of gravity is greater on the cart than on the donkey. E. The donkey is correct and the cart can not accelerate without an additional push. Mechanics Lecture 5, Slide 34 17