physics paper

Physics

1) A uniform circular disc of radius R with a concentric circular hole of radius 2/R rolls down an inclined plane. The fraction of its total energy associated with its rotational motion is

2) A ring starts from rest and acquires an angular speed of 10 rad/s in 2 s. The mass of the ring is 500 g and its radius is 20 cm. The torque on the ring is

(a) 0.02 Nm (b) 0.20 Nm (c) 0.10 Nm (d) 0.01 Nm.

3) A loop and a disc have the same mass and roll without slipping with the same linear velocity v. If the total kinetic energy of the loop is 8 J, the kinetic energy of the disc must be

(a) 6 J (b) 8 J (c) 10 J (d) 12 J.

4) A wheel and an axle, having a total moment of inertia 0.002 kgm2, is made to rotate about a horizontal axis by means of an 800 g mass attached to a cord (assumed massless) that is wound around its axle. The radius of the axle is 2 cm. Starting from rest, how far does the mass fall in order to give the wheel a speed of 3 rev/s?

(a) 2.25 cm (b) 3.25 cm (c) 4.5 cm (d) 5. 25 cm

5) A small meteorite of mass m travelling towards the centre of earth strikes the earth at the equator. The earth is a uniform sphere of mass M and radius R. The length of the day was T before the meteorite struck. After the meteorite strikes the earth, the length of day increases (in sec) by

6) A smooth sphere A is moving on a frictionless horizontal plane with angular speed ω and centre of mass velocity v. It collides elastically and head-on with an identical sphere B which is at rest. All surfaces are frictionless. After the collision, their angular speeds are ωA and , respectively. Then, ωB

(a) ω = 0 (b) ωB = ωA (c) ωA <ωB (d) ωB = ω

Harshana Perera(B.Sc(Phy),BIT,SCJP) 2014T KIT Turn Over

Physics

7) A one-piece cylinder is shaped as shown in Figure 10.15, with a core section protruding from the larger drum. The cylinder is free to rotate around the central axis shown in the drawing. A rope wrapped around the drum, which has radius R1 , exerts a force F1 to the right on the cylinder. A rope wrapped around the core, which has radius R2 , exerts a force F2 downward on the cylinder. (a) What is the net torque acting on the cylinder about the rotation axis (which is the z axis in Figure 10.15)?

8) A uniform rod of length L and mass M is attached at one end to a frictionless pivot and is free to rotate about the pivot in the vertical plane, as shown in Figure 10.18. The rod is released from rest in the horizontal position. What is the initial angular acceleration of the rod and the initial linear acceleration of its right end?

9) A wheel of radius R, mass M, and moment of inertia I is mounted on a frictionless, horizontal axle, as shown in Figure 10.20. A light cord wrapped around the wheel supports an object of mass m. Calculate the angular acceleration of the wheel, the linear acceleration of the object, and the tension in the cord.

10) Two blocks having masses m1 and m2 are connected to each other by a light cord that passes over two identical, frictionless pulleys, each having a moment of inertia I and radius R, as shown in Figure 10.21a. Find the acceleration of each block and the tensions T1 , T2 , and T3 in the cord. (Assume no slipping between cord and pulleys.)

11) A uniform rod of length L and mass M is free to rotate on a frictionless pin passing through one end (Fig 10.23). The rod is released from rest in the horizontal position. (a) What is its angular speed when it reaches its lowest position?

12) Consider two cylinders having masses m1 and m2 , where m1 = m2 , connected by a string passing over a pulley, as shown in Figure 10.24. The pulley has


Physics

a radius R and moment of inertia I about its axis of rotation. The string does not slip on the pulley, and the system is released from rest. Find the linear speeds of the cylinders after cylinder 2 descends through a distance h, and the angular speed of the pulley at this time

13) Find the net torque on the wheel in Figure P10.33 about the axle through O if a = 10.0 cm and b = 25.0 cm

14) A bicycle is turned upside down while its owner repairs a flat tire. A friend spins the other wheel, of radius 0.381 m, and observes that drops of water fly off tangentially. She measures the height reached by drops moving vertically (Fig. P10.60). A drop that breaks loose from the tire on one turn rises h = 54.0 cm above the tangent point. A drop that breaks loose on the next turn rises 51.0 cm above the tangent point. The height to which the drops rise decreases because the angular speed of the wheel decreases. From this information, determine the magnitude of the average angular accelerationof the wheel.

15) The top shown in Figure P10.62 has a moment of inertia of 4.00 *10 -4 kg_m2 and is initially at rest. It is free to rotate about the stationary axis AA. A string, wrapped around a peg along the axis of the top, is pulled in such a manner that a constant tension of 5.57 N is maintained. If the string does not slip while it is unwound from the peg, what is the angular speed of the top after 80.0 cm of string has been pulled off the peg?

16) An electric motor can accelerate a Ferris wheel of moment of inertia I = 20 000 kg_m2 from rest to 10.0 rev/min in 12.0 s. When the motor is turned off, friction causes the wheel to slow down from 10.0 to 8.00 rev/min in 10.0 s. Determine (a) the torque generated by the motor to bring the wheel to 10.0 rev/min and (b) the power that would be needed to maintain this rotational speed.


Physics

17) Two blocks, as shown in Figure P10.71, are connected by a string of negligible mass passing over a pulley of radius 0.250 m and moment of inertia I. The block on the frictionless incline is moving upward with a constant acceleration of 2.00 m/s2. (a) Determine T1 and T2 , the tensions in the two parts of the string. (b) Find the moment of inertia of the pulley.

19) A cylinder of mass 10.0 kg rolls without slipping on a horizontal surface. At the instant its center of mass has a speed of 10.0 m/s, determine (a) the translational kinetic energy of its center of mass, (b) the rotational energy about its center of mass, and (c) its total energy.

20) A bowling ball has a mass of 4.00 kg, a moment of inertia of 1.60 *10 -2 kg_m2, and a radius of 0.100 m. If it rolls down the lane without slipping at a linear speed of 4.00 m/s, what is its total energy?

21) A bowling ball has a mass M, a radius R, and a moment of inertia 2/5MR 2. If it starts from rest, how much work must be done on it to set it rolling without slipping at a linear speed v? Express the work in terms of M and v.

22) Determine the acceleration of the center of mass of a uniform solid disk rolling down an incline making an angle ϴ with the horizontal. Compare this acceleration with that of a uniform hoop. (b) What is the minimum coefficient of friction required to maintain pure rolling motion for the disk?

23) A particle of mass m is shot with an initial velocity vi and makes an angle ϴ with the horizontal, as shown in Figure P11.25. The particle moves in the gravitational field of the Earth. Find the angular momentum of the particle about the origin when the particle is (a) at the origin, (b) at the highest point of its trajectory, and (c) just about to hit the ground. (d) What torque causes its angular momentum to change?

2 4) A 60.0-kg woman stands at the rim of a horizontal turntable having a moment of inertia of 500 kg_m2 and a radius of 2.00 m. The turntable is initially at rest and is free to rotate about a frictionless, vertical axle through its center. The woman then starts walking around the rim clockwise (as viewed from above the system) at a constant speed of 1.50 m/s relative to the Earth. (a) In what direction and with what angular speed does the turntable rotate? (b) How much work does the woman do to set herself and the turntable into motion?

25) A wooden block of mass M resting on a frictionless horizontal surface is attached to a rigid rod of length l and of negligible mass (Fig. P11.39). The rod is pivoted at the other end. A bullet of mass m traveling parallel to the horizontal surface and normal to the rod with speed v hits the block and becomes embedded in it. (a) What is the angular momentum of the bullet–block system? (b) What fraction of the original kinetic energy is lost in the collision?


Physics

26) A light rope passes over a light, frictionless pulley. A bunch of bananas of mass M is fastened at one end, and a monkey of mass M clings to the other (Fig. P11.50). The monkey climbs the rope in an attempt to reach the bananas. (a) Treating the system as consisting of the monkey, bananas, rope, and pulley, evaluate the net torque about the pulley axis. (b) Using the results to part (a), determine the total angular momentum about the pulley axis and describe the motion of the system. Will the monkey reach the bananas?

27) A mass m is attached to a cord passing through a small hole in a frictionless, horizontal surface

(Fig. P11.55). The mass is initially orbiting with speed vi in a circle of radius ri . The cord is then slowly pulled from below, and the radius of the circle decreases to r. (a) What is the speed of the mass when the radius is r ? (b) Find the tension in the cord as a function of r. (c) How much work W is done in moving m from ri to r ? (Note: The tension depends on r.) (d) Obtain numerical values for v,

T, and W when r = 0.100 m, m = 50.0 g, ri= 0.300 m, and vi = 1.50 m/s.

28) A plank with a mass M _ 6.00 kg rides on top of two identical solid cylindrical rollers that have R =5.00 cm and m = 2.00 kg (Fig. P11.67). The plank is pulled by a constant horizontal force of magnitude F = 6.00 N applied to the end of the plank and perpendicular to the axes of the cylinders (which are parallel). The cylinders roll without slipping on a flat surface. Also, no slipping occurs between the cylinders and the plank. (a) Find the acceleration of the plank and that of the rollers. (b) What frictional forces are acting?

29) A uniform rod of mass M and length a lies on a smooth horizontal plane. A particle of mass m moving at a speed v perpendicular to the length of the rod strikes it at a distance a /4 from the centre and stopsafter the collision. Find (a) the velocity of the centre of the rod and (b) the angular velocity of the rod after the collision.

30)


Physics

Part of the track of an amusement park roller coaster is shaped as shown above. A safety bar is oriented lengthwise along the top of each car. In one roller coaster car, a small 0.10-kilogram ball is suspended from this bar by a short length of light, inextensible string.

1Initially, the car is at rest at point A.

i. On the diagram below, draw and label all the forces acting on the 0.10-kilogram ball.

ii. Calculate the tension in the string. The car is then accelerated horizontally, goes up a 30° incline, goes down a 30° incline, and then goes around a vertical circular loop of radius 25 meters. For each of the four situations described in parts (b) to (e), do all three of the following. In each situation, assume that the ball has stopped swinging back and forth.

1) Determine the horizontal component Th

2)Determine the vertical component T of the tension in the string in newtons and record your answer in the space provided. V

3)Show on the adjacent diagram the approximate direction of the string with respect to the vertical. The dashed line shows the vertical in each situation. of the tension in the string in newtons and record your answer in the space provided.

b. The car is at point B moving horizontally 2 to the right with an acceleration of 5.0 m/s .

‘


Physics

A box of mass M, held in place by friction, rides on the flatbed of a truck which is traveling with constantspeed v. The truck is on an unbanked circular roadway having radius of curvature R.a. On the diagram provided above, indicate and clearly label all the force vectors acting on the box.b. Find what condition must be satisfied by the coefficient of static friction μ between the box and the truck bed.Express your answer in terms of v, R, and g.


Physics

31)

A box of mass M, held in place by friction, rides on the flatbed of a truck which is traveling with constant speed v. The truck is on an unbanked circular roadway having radius of curvature R.a. On the diagram provided above, indicate and clearly label all the force vectors acting on the box.b. Find what condition must be satisfied by the coefficient of static friction μ between the box and the truck bed. Express your answer in terms of v, R, and g.

If the roadway is properly banked, the box will still remain in place on the truck for the same speed v even when the truck bed is frictionless.c. On the diagram above indicate and clearly label the two forces acting on the box under these conditionsd. Which, if either, of the two forces acting on the box is greater in magnitude?

32)A rope of length L is attached to a support at point C. A person of mass m1 sits on a ledge at position A holding the other end of the rope so that it is horizontal and taut, as shown. The person then drops off the ledge and swings down on the rope toward position B on a lower ledge where an object of mass m2 is at rest. At position B the person grabs hold of the object and simultaneously lets go of the rope. The person and object then land together in the lake at point D, which is a vertical distance L below position B. Air resistance and the mass of the rope are negligible. Derive expressions for each of the following in terms of m1, m2, L, and g.

(a) The speed of the person just before the collision with the object(b) The tension in the rope just before the collision with the object(c) After the person hits and grabs the rock, the speed of the combined masses is determined to be v’. In terms of v’ and the given quantities, determine the total horizontal displacement x of the person from position A until the person and object land in the water at point D.


Physics


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