Physics Bachelors Have Successful Careers!

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1 Did You Know? Physics Bachelors Have Successful Careers! 82% In times of economic instability, job security is important. Other important job aspects such as salary and benefits rank highly among physics bachelor graduates working in the private sector. Many physics bachelors go on to enjoy financially rewarding and intellectually stimulating careers Learn more: aip.org/statistics Credit: based on Physics Insight slide from the APS

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3 Class 18 October 11, 2017 Force Problems Scalar Products Work Exam 2: Thursday October 12 (Problem Session) Friday October 13 (175 Willey West Bank)

4 A kg box with dimensions of 0.50 m by 0.50 m by 0.50 m sits on a flatbed truck. The force of static friction is equal to 0.40 times the box s weight. The force of kinetic friction is equal to 0.20 of the box s weight. What is the maximum acceleration of the truck that will not cause the box to move relative to the truck? (a) 1.7 m/s 2 (b) 2.1 m/s 2 (c) 2.6 m/s 2 (d) 3.2 m/s 2 (e) 3.9 m/s 2 4

5 A kg box with dimensions of 0.50 m by 0.50 m by 0.50 m sits on a flatbed truck. The force of static friction is equal to 0.40 times the box s weight. The force of kinetic friction is equal to 0.20 of the box s weight. What is the maximum acceleration of the truck that will not cause the box to move relative to the truck? (e) 3.9 m/s 2 a max = F max = µ smg = µ sg m m a max =(0.40)(9.81) = 3.9 m/s 2 5

6 Forces and Multiparticle Systems Motion in a multiparticle system can be divided into two kinds of motion: Motion of the center of mass Motion of individual masses with respect to the center of mass If the force under study is external to the system, it will result in motion of the center of mass If the force is internal to the system, it will result in motion with respect to the center of mass A special case is motion of a rigid body in which case only motion of the center of mass can result 6

7 A 10.0 kg red cart is connected to a 20.0 kg green cart by a relaxed spring with a spring constant of 60 N/m. The green cart is in contact with a 10.0 kg blue cart. All of the carts are on a low friction track. You push on the red cart in the direction of the green cart with a force of 10.0 N. (a) What is the acceleration of the center of mass of the three cart system? (a) 0.10 m/s 2 (b) 0.25 m/s 2 (c) 0.50 m/s 2 (d) 0.75 m/s 2 (e) 1.0 m/s 2 7

8 A 10.0 kg red cart is connected to a 20.0 kg green cart by a relaxed spring with a spring constant of 60 N/m. The green cart is in contact with a 10.0 kg blue cart. All of the carts are on a low friction track. You push on the red cart in the direction of the green cart with a force of 10.0 N. (a) What is the acceleration of the center of mass of the three cart system? (b) 0.25 m/s 2 Force is 10.0 N and mass is 40.0 kg. 8

9 A 10.0 kg red cart is connected to a 20.0 kg green cart by a relaxed spring with a spring constant of 60 N/m. The green cart is in contact with a 10.0 kg blue cart. All of the carts are on a low friction track. You push on the red cart in the direction of the green cart with a force of 10.0 N. (b) What is the acceleration of each cart at the instant you begin to push? (a) 1.0, 0, 0 m/s 2 (b) 0.25, 0.25, 0.25 m/s 2 (c) 1.0, 0.25, 0.25 m/s 2 (d) 1.0, 1.0,1.0 m/s 2 (e) 0, 0.25, 0.25 m/s 2 9

10 A 10.0 kg red cart is connected to a 20.0 kg green cart by a relaxed spring with a spring constant of 60 N/m. The green cart is in contact with a 10.0 kg blue cart. All of the carts are on a low friction track. You push on the red cart in the direction of the green cart with a force of 10.0 N. (a) What is the acceleration of each cart at the instant you begin to push? (a) 1.0, 0, 0 m/s 2 The spring is initially neither stretched nor compressed, so it exerts no force on either the red or green carts. 10

11 A 10.0 kg red cart is connected to a 20.0 kg green cart by a relaxed spring with a spring constant of 60 N/m. The green cart is in contact with a 10.0 kg blue cart. All of the carts are on a low friction track. You push on the red cart in the direction of the green cart with a force of 10.0 N. (b) What are the forces on each cart when the spring is compressed by 100. mm? 11

12 A 10.0 kg red cart is connected to a 20.0 kg green cart by a relaxed spring with a spring constant of 60 N/m. The green cart is in contact with a 10.0 kg blue cart. All of the carts are on a low friction track. You push on the red cart in the direction of the green cart with a force of 10.0 N. (b) What are the forces on each cart when the spring is compressed by 100. mm? F push on red = 10 N F spring on red = kx =6N F spring on green =6N a green blue = 6 =0.2 m/s2 30 F green on blue = m blue a =2N 12

13 Key points from this problem The acceleration of the center of mass is (External Force)/(Total Mass) regardless of what happens internally The spring obeys Hooke s Law. It can only apply force if it is stretched or compressed. The spring exerts the total Hooke s Law force at both ends, regardless of whether an end is fixed or free to move. 13

14 Scalar Product Two vectors can be multiplied in two different ways Scalar or dot product Vector or cross product The scalar product is a scalar or number. It is equal to the magnitude of vector A times the magnitude of vector B times the cosine of the angle between the two vectors. The scalar product of two perpendicular vectors is zero. The scalar product can be used to calculate the angle between two vectors. A B = A B cos cos = A B A B 14

15 What is the scalar product of the vectors (1,2,3) and (3,2,1)? (a) 2 (b) 4 (c) 7 (d) 10 (e) 12 15

16 What is the scalar product of the vectors (1,2,3) and (3,2,1)? (d) 10 (1, 2, 3) (3, 2, 1) = (1)(3) + (2)(2) + (3)(1) = 10 16

17 Scalar Product What is the angle between the vectors (1,2,3) and (3,2,1)? (a) 23.1 (b) 32.7 (c) 39.3 (d) 44.4 (e)

18 Scalar Product What is the angle between the vectors (1,2,3) and (3,2,1)? (d) 44.4 cos = a b a b a = b = p = p 14 = 3.74 cos = =0.714 =