A. B. C. CT1

The force acting on an object is proportional to the final speed. Incorrect Explanation: A decrease in the rate of speeding up is due to the force being 'used up.' 

A. B. C. CT2

For objects falling vertically, regardless of mass, the same force applied for the same amount of time produces the same motion. 

For objects on frictionless surfaces, regardless of mass, the same force applied for the same amount of time produces the same motion. The student explains linear acceleration with a reversed or otherwise incorrect relationship between force, mass, and acceleration. 

A. B. C. D. CT3

The student explains curved motion by having an outward force balancing an inward force. The student thinks that an outward force exists with all curved motion. 

A. B. C. CT4

A force perpendicular to the direction of motion will cause the object to speed up. A force perpendicular to the direction of motion will cause the object to slow down. 

A. B. C. D. CT5

A. B. C. D. The student thinks that only forces exactly in the direction of motion (or opposite) can speed up or slow down an object. All other forces just change the direction of motion. The student thinks that all unbalanced forces on an object will either cause the object to speed up or slow down. 

Chapter 7 Energy of a System 7.1 Systems and Environments A. System 1. Single particle 2. Many particles 3. Region of space B. Environment Surroundings of the system C. Isolated System

Concept Question 6: Two forces of the same magnitude act on a block on a frictionless horizontal plane. In case A the force acts at an angle above the horizontal and in case B the force acts horizontally. In both cases the blocks are pulled the same distance d along the plane. Neither block leaves the plane. Which statement is correct? A. The work done on the block by the force F is the greatest in case A. B. The work done on the block by the force F is the greatest in case B. C. The work in the same in both cases. D. There isn’t enough information to tell. F F Case ACase B d d

7.2 Work Done by a Constant Force A. Force along Displacement W = Fr Units: Nm = Joule B. Force at Angle to Displacement W = Frcos rr  F

7.2 Work Done by a Constant Force C. Zero, Negative and Total Work W is zero if  = 90 or 270 W is negative if 90 <  < 270 W TOT = (F TOT cos)d or W TOT = W P7.1 (p.189)

7.3 The Scalar Product of Two Vectors A·B = ABcos i·i = j·j = k·k = 1 i·j = j·i = i·k = k·i = j·k = k·j = 0 W = F·r F·r = F x x + F y y + F z z P7.10 (p.189) B  A    

Concept Question 7: If F = 3i -6j and d = -5i + 11j, the work done by the force F moving a distance d is A. 81 J. B. -51 J. C. -81i N. D. 51j N. E. -81 J.

Fig. 7.7a, p Work Done by a Varying Force F xn x n xnxn F xn

Fig. 7.7, p.189

7.4 Work Done by a Varying Force Work equals the area under the Force vs. Displacement curve. P7.15 (p.190) P7.16 (p.190)

A. B. C. D. E. CT8

7.5 Kinetic Energy and the Work- Kinetic Energy Theorem K = mv 2 /2 W TOT = K P7.35 (p.191) P7.57 (p.193)

CT9

7.6 Potential Energy of a System gravity and spring example  U = W external agent  U = -W C

Work done by person = +mgh

7.6 Potential Energy of a System U g = mgy near the surface of the Earth for a Earth/mass system U s = ½kx 2 for a spring/block system P7.37 (p.191)

7.7 Conservative and Non- Conservative Forces

Conservative Force Definition 1: The work is independent of the path for a conservative force. W 1 = W 2 = W 3

Conservative Force Definition 2: The total work around a closed path is zero for a conservative force. Work done by gravity = -mghWork done by gravity = +mgh Total work around a closed path = -mgh + mgh = 0. The force of gravity is a conservative force.

W 1 = W 2 W tot = W 1 - W 2 = 0 W 1 = W 3 W tot = W 1 – W 3 = 0 W 2 = W 3 W tot = W 2 – W 3 = 0 Conservative Force Definition 2: The total work around a closed path is zero for a conservative force.

7.7 Non-Conservative Force Example Friction

7.7 Conservative Force Example P7.39 (p.192)

7.8 Relationship Between Conservative Forces and Potential Energy W c =  F x dx = -U in one dimension

xixi F = -kx xfxf -kx f -kx i

7.8 Relationship Between Conservative Forces and Potential Energy F x = -dU/dx, etc.

7.9 Energy Diagrams and Equilibrium of a System The slope of the U vs. x graph is the negative of the x component of the force. Equilibrium occurs when F x = 0 or when the slope is zero. At a minimum in U vs. x the equilibrium is stable, at a maximum it is unstable and when U is constant equilibrium is neutral.

Figure 8-10 A Ball Rolling on a Frictionless Track

Figure 8-11 Gravitational Potential Energy Versus Position for the Track Shown in Figure 8-10

A Mass on a Spring U = kx 2 /2

Conceptual Questions: An object starts from point A. 10. The speed at A is the same as at B,C,D,E,F,G? 11. The speed is the greatest at A,B,C,D,E,F,G? 12. At which points is the force equal to zero? A,B,C,D,E,F,G 13. The magnitude of the force is greatest at A,B,C,D,E,F,G?

How many hours per week on average are you putting into PHYS201 outside of class? A.less than 2 B.2 C.3 D.4 E.5 F.6 G.greater than 6