60 1. What is the mass M in the system as given in the Figure if m=8.0 kg ?   M m 2. If M = 1.1 kg, what is the tension in string 1? From (1) T2 50 40 T1 3. At an instant when a 4.2 kg object has an acceleration equal to (5i + 3j) m/s2, one of the two forces acting on the object is known to be (12i + 22j) N. Determine the magnitude of the other force acting on the object. Newton’s second law)

4. A 5.0-kg mass is suspended by a string from the ceiling of an elevator that is moving upward with a speed which is decreasing at a constant rate of 2.0 m/s in each second. What is the tension in the string supporting the mass? T mg 5.The apparent weight of a fish in an elevator is greatest when the elevator a. moves downward at constant velocity. b. moves upward at constant velocity. c. accelerates downward. d. accelerates upward. e. is not moving. Like the picture Above in 4. (d) 6. If P = 6.0 N, what is the magnitude of the force exerted on block 1 by block 2? T1 T1 T2 p 2kg 3kg 5kg T2

7. Two identical springs with spring constant 50 N/m support a 5 7. Two identical springs with spring constant 50 N/m support a 5.0 N weight as in the picture below. What is the change in length of each spring when the weight is hung on the springs.? All three bodies have the same mass m and . Find the acceleration. m m m 9. As a particle moves along the x axis it is acted upon by a single conservative force given by Fx = (20 – 4.0 x) N where x is in m. The potential energy associated with this force has the value +30 J at the origin (x = 0). What is the value of the potential energy at x = 4.0 m?

10. A 2. 0-kg particle has an initial velocity of (5i – 4j) m/s 10. A 2.0-kg particle has an initial velocity of (5i – 4j) m/s. Some time later, its velocity is (7i + 3j) m/s. How much work was done by the resultant force during this time interval, assuming no energy is lost in the process? 11. The force an ideal spring exerts on an object is given by Fx = –kx, where x measures the displacement of the object from its equilibrium (x = 0) position. If k = 60 N/m, how much work is done by this force as the object moves from 12. The horizontal surface on which the block slides is frictionless. The speed of the block before it touches the spring is 6.0 m/s. How fast is the block moving at the instant the spring has been compressed 15 cm? ( k = 2.000 N/m, M=2.0 kg)) 13. A 0.60-kg object is suspended from the ceiling at the end of a 2.0-m string. When pulled to the side and released, it has a speed of 4.0 m/s at the lowest point of its path. What maximum angle does the string make with the vertical as the object swings up? 

14. A 20-kg mass is fastened to a light spring (k = 380 N/m) that passes over a pulley as shown. The pulley is frictionless, and the mass is released from rest when the spring is unstretched. After the mass has dropped 0.40 m, what is its speed? 15. A 1.2-kg mass is projected up a rough circular track (radius = 0.80 m) as shown. The speed of the mass at point A is 8.4 m/s, and at point B, it is 5.6 m/s. How much work is done on the mass between A and B by the force of friction? 16. The gravitational potential energy U of an object of mass m=10.2 kg near the Earth’s surface is shown in the Figure, where y=0 corresponds to the ground. Assume that the mechanical energy is 200 J and neglect friction. What is the force acting on the object at the location where the kinetic energy is equal to the potential energy

17. A blimp is filled with 200 m3 of helium 17. A blimp is filled with 200 m3 of helium. How much mass can the balloon lift? The density of helium is 1/7 that of air, and the density of air is 1.25 kg/m3. 18. A waiter in a restaurant fills a pitcher full of water and ice so that water would spill out if any more were added. As the ice starts to melt a. the water level in the pitcher falls. b. the water level in the pitcher remains the same. c. water starts to flow out the spout of the pitcher. d. the pressure on the bottom of the pitcher decreases Answer: b) : level remains the same, since the ice displays its volume after melting and the water level is retained.,

19. A container filled with water to a depth H=2. 5 m 19. A container filled with water to a depth H=2.5 m. The container is tightly sailed and above the water the pressure is P1=1.34x105 N/m2. A small hole is punched at a height h=1.0 above the bottom of the container. What is the velocity of the water through the hole? P1 H Water h 20. Water (density 1000 kg/m3) flowing in a horizontal pipe discharges at The rate of 4x10-3 m3/s. At a point in the pipe where the cross-section area is 1.0 x10-3 m2 the pressure is 1.60x105 N/m2 . What is the cross-section area of a concentration in the pipe if the pressure there is reduced to 1.6x105 N/m2 ?. Give your answer in cm2.