A. B. C. D. E. v x. ΣF x

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2 Q4.3 The graph to the right shows the velocity of an object as a function of time. Which of the graphs below best shows the net force versus time for this object? 0 v x t ΣF x ΣF x ΣF x ΣF x ΣF x 0 t 0 t 0 t 0 t 0 t A. B. C. D. E.

3 A4.3 The graph to the right shows the velocity of an object as a function of time. Which of the graphs below best shows the net force versus time for this object? 0 v x t ΣF x ΣF x ΣF x ΣF x ΣF x 0 t 0 t 0 t 0 t 0 t A. B. C. D. E.

4 Newton s laws & applications, ch. 4-5 Newton s law & equilibrium concepts, & F = ma calculations F = ma F x = ma x, F y = ma y Friction forces: f k = µ k n kinetic is fixed; f s µ n s static is an upper limit. Apparent weight; accelerating vertically, more generally, w = mg + ma apparent w = mg ma apparent y Other forces: pulleys, 2 circular motion (centripetal force: mv ) R

5 30 45 Which tension is larger?

6 A 20.0 cm-long horizontal spring is compressed by a displacement of 5.0 cm from equilibrium, with a 20 kg block attached to it, initially stationary. The surface is frictionless. Just after release the block is found to accelerate at a rate of 2.0 m/s 2. a) What is the spring constant? b) What is acceleration as the block passes the equilibrium point? c) What is velocity as the block passes the point 2.0 cm from equilibrium? d) What power is provided by spring force at release? At equilibrium point? At 2.0 cm from equilibrium?

7 Ch. 6-7: Work, Kinetic, Potential Energy Work converts between energy types. W = F s or Fs cosθ ; varying forces, springs specific case, F = kx W = 1 2 kx2 W F dx or F dl = x Work-Energy theorem: W = K 2 K 1 wit K = 1 2 mv2 Power: P = dw is rate of doing work. dt mechanical version, P = F v Potential energy: (conservative forces), U = W c ; gravity/springs: U = mgh, Alternative Work-Energy theorem, E = W other K + U = F vs. U: du F ; x = U ˆ F i U ˆ j U kˆ = + + U dx x y y U = 1 2 kx 2 0

8 Potential Energy: a) Find an unstable equilibrium position. b) For what region does this potential produce negative F x? c) Find turning points for a particle in this potential U (J) with total E = 1.0 J. 2 0 x(m)

9 Suppose this system is released with initial upward velocity with magnitude v o. Find the velocity once the left box reaches a position h below its starting position. The ramp angle is θ, with no friction. Both masses = M, and the pulley is massless. v o h

10 Suppose this system is released with initial upward velocity with magnitude v o. Find the acceleration, and the tension in the string. Show your work. The ramp angle is θ, with no friction. Both masses = M, and the pulley is massless. v o h

11 Q5.2 A cable attached to a car holds the car at rest on the frictionless ramp (angle α). The ramp exerts a normal force on the car. How does the magnitude n of the normal force compare to the weight w of the car? A. n = w B. n > w C. n < w D. not enough information given to decide

12 A5.2 A cable attached to a car holds the car at rest on the frictionless ramp (angle α). The ramp exerts a normal force on the car. How does the magnitude n of the normal force compare to the weight w of the car? A. n = w B. n > w C. n < w D. not enough information given to decide

13 A suitcase is sent sliding up a ramp with friction, at an angle of θ from horizontal, with initial velocity v o. (a) Draw a proper force diagram. (b) If the suitcase goes a distance d along the ramp before stopping, what is coefficient of friction? (c) Will the acceleration going down the ramp be the same as going up?

14 Suppose the pendulum bob has mass of 15 kg. Find the tension in the string at position Q if at the release point P the string has an angle of 30 with the vertical, and the string has length 20 cm. P R Q

15 Suppose the ball of mass M is attached to a string and a massless horizontal spring pivoted at the center. The ball moves at a constant speed in such a way that the radius R includes an extension of the spring (spring constant k = 1 N/m) so that the spring pulls with a force Mg/2. The angle is such that the string has length 2R. Find the string tension and v. What work is done by the string and spring forces?

16 A conservative force and a non-conservative force act on an object. The work done by the non-conservative force is negative and yet the object s speed increases. (i) T or F: The potential energy increases and the mechanical energy decreases. (ii) T or F: The potential energy decreases and the mechanical energy increases.

17 Two constant forces F1 = i and F1 = 4.0 N are the only ones acting on an object of mass of 2.0 kg. What is the net work done on the object as it moves from a point with coordinates (7.0 m, 8.0 m) to a point with coordinates (9.0 m, 8.0 m)? a. 0 J b. -6 J c. +6 J d. -10 J e. +10 J 3.0 N ˆ f. cannot be determined since we do not know whether the forces are conservative. ˆj

18 A person lifts a heavy load to a vertical height of 2,0 m in 3 seconds. If he/she had done this more slowly in 6 seconds, the work on the load would have been: 1 twice as great 2 four times as great 3 the same 4 half as great

19 U = (3.8J m 2 ) / y 2 Given, (a) What is the direction of F? (b) Find F vector at point (0.1 m, 0.2 m, 0.3 m).

20 Suppose the boxes are static, with masses M A < M B. The ramp angle is θ, and there is no friction from A to ramp, but sufficient static friction between A and B to maintain a static situation. What is the tension? The friction force?

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23 Given 850N and 750N boxes, (a) tension in two ropes if there is no friction and a = 4.9 m/s 2? (b) Same question, if kinetic friction coefficient µ = 0.10?

24 Two massless springs have spring constant K, and masses are both m/2. a) What is compression of each spring at equilibrium? b) Suppose upper mass is held at a vertical position corresponding to the unstretched lengths of the two springs. What is z 2?

25 A weighs 3w, B weighs w. A slides down at constant speed. Friction coefficient is same for A to ramp and for A to B. Find the coefficient of friction.

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