1. A copper container (mass 100g) holds 200 g of water. The temperature of the container and water is 20oC. A 150-g piece of copper heated to 80oC is placed in the water. The water is stirred thoroughly. After sufficient time elapses, to what temperature does the water change? From 1-5 below choose the best answer. Assume that no heat is transferred to or from the environment. The specific heat of water is 4.2 J/g.K, and the specific heat of copper is 0.40 J/g.K.
1. 23oC 3. 25oC 5. 27oC
2. 24oC 4. 26oC
(Answer: 5)
2. A half sphere of radius r is fixed to a horizontal floor. The inner surface of the sphere is smooth. A small ball of mass m is at the bottom point P of the sphere and is given an initial velocity v as in Figure. The initial velocity v is sufficiently large so that the small ball reaches a point Q at height r. Find the magnitude of the normal force exerted by the sphere on the small ball when the ball passes through the point Q. The acceleration due to gravity is denoted as g.
3. As shown in the figure below, potential difference V exists between two parallel plates (a, b) that have a small hole. Uniform electric field E and magnetic flux density B exist in the region above the plates, and are perpendicular to each other. The direction of E is parallel to this page and plate b. The direction of B is perpendicular to this page, from back to front. A positively charged particle of charge q and mass m, initially at rest in the hole of plate a, is accelerated by potential difference V so that it enters the region above the plate perpendicularly to E and B and travels straight through the region
4. A mass M slides without friction on the roller coaster track shown in figure. The curved sections of the track have radius of curvature R. The mass begins its descent from the height h. At some value of h, the mass will begin to lose contact with the track. Indicate on the diagram where the mass loses contact with the track and calculate the minimum value of h for which this happens!
Answer : hmin = 3R/4
5. A bowling ball of uniform density is thrown along a horizontal alley with initial velocity V0 in such a way that it initially slides without rolling. The ball has mass m, coefficient of static friction μs and coefficient of sliding friction μd with the floor. Ignore the effect of air friction. Compute the velocity of the ball when it begins roll without sliding.
Answer: v = 5/7 V0
6. Assume all surfaces to be frictionless and the inertia of pulley and cord negligible (see figure). Find the horizontal force necessary to prevent any relative motion of m1, m2 and M.
7. A projectile of mass m is shot (at velocity v) at a target of mass M, with a hole containing a spring of constant k. The target is initially at rest and can slide without friction on a horizontal surface. Find the distance ∆x that the spring compresses at maximum.
8. A pendulum of mass m and length l is released from rest in a horizontal position. A nail a distance d below the pivot causes the mass to move along the path indicated by the dotted line. Find the minimum distance d in terms of l such that the mass will swing completely round in the circle shown in the figure.
answer: d = 3l/5
9. A stone is thrown from ground level over horizontal ground. It just clears three walls, the succesive distances between them being r and 2r. The inner wall is 15/7 times as high as the outer walls which are equal in height. The total horizontal range is nr, where n is an integer. Find n.
answer: n = 4
11. A body slides down a rough plane inclined to the horizontal at 30o. If 70% of the initial potential energy is dissipated during the descent, find the coefficient of sliding friction.
answer:μ = 0.404
12..A thin uniform stick of mass m with its bottom end resting on a frictionless table is released from rest an angle θo to the vertical. Find the force exerted by the table upon the stick at an infinitesimally small time after its release.
13. A particle makes SHM along a straight line and its velocity when passing through points 3 and 4 cm from the center of its path is 16 and 12 cm/s, respectively. Find:
(a).the amplitude
(b).the time period of motion
Answer:(a). A =5 cm
(b). T =1.57 s
14. A shell flying with velocity v = 500m/s bursts into three identical fragments so that the kinetic energy of the system increases = 1.5 times. What maximum velocity can one of the fragments obtain?
14. A shell flying with velocity v = 500m/s bursts into three identical fragments so that the kinetic energy of the system increases = 1.5 times. What maximum velocity can one of the fragments obtain?
Answer: Vmax = 1km/s
15. A small bob of mass 50 g oscillates as a simple pendulum, with amplitude 5 cm and period 2 s. Find the velocity of the bob and the tension in the supporting thread when velociy of the bob is maximum.
15. A small bob of mass 50 g oscillates as a simple pendulum, with amplitude 5 cm and period 2 s. Find the velocity of the bob and the tension in the supporting thread when velociy of the bob is maximum.
Answer: Vmax = 5πcm/s ; T =13.11 N
16. The rod of mass 1 kg have axes rotate without friction on the center of mass, as in the picture. A hunk of clay has a speed of 10 m/s collides with a stick and stay stuck on sticks. Loss of energy at this event is...
16. The rod of mass 1 kg have axes rotate without friction on the center of mass, as in the picture. A hunk of clay has a speed of 10 m/s collides with a stick and stay stuck on sticks. Loss of energy at this event is...
Answer: 3,84 joule
17. A 4 kg mass objects are given an initial velocity of 10 m/s from the lower end of the inclined plane as shown. Objects experienced friction from a field of 16 N and sin α = 0.85. The objects stopped after a distance. ...
17. A 4 kg mass objects are given an initial velocity of 10 m/s from the lower end of the inclined plane as shown. Objects experienced friction from a field of 16 N and sin α = 0.85. The objects stopped after a distance. ...
A.3 m C.5 m E.8 m
B.4 m D.6 m
Answer: B
18.Three balls each radius 30 cm, 30 cm and 20 cm is structured like the picture on the side with a small ball is above the two large balls. A small ball of mass m, the mass of each large ball M, acceleration of gravity g. Magnitude of force that are carried out by one of the big ball on a small ball is. ...
Answer: 5mg/8
19. A block of 144 grams of mass above the floor slick flat-linked with the three spring with make up as depicted in the picture above. The spring have constants respectively is k1= 20 N/m; k2= 60 N/m; and k3= 30 N/m. If block has been warped from the share point with small deviations, then the resulting harmonic vibration period is approaching. ...
Answer: 0,12π detik
20.An object of mass m = 1.5 kg depending on the other end of the rope (length L = 225 cm) above a vehicle open backs (such as pictures). At first the vehicle moving with velocity v (figure a). If after hit the wall of the vehicle stopped with mass m swingof θ = 37o (figure b), then the speed v is. ...
Answer: 3,0 m/s
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