2048C FINAL REVIEW

A flywheel of moment of inertia 0.4 kgm2 rotating initially at 300 rpm comes to rest in 20 sec under constant retarding torque. Calculate the constant retarding torque. Answer: ___________________

0.628Nm

(a) Can the equations of kinematics be used in a situation in which the acceleration varies in time? Yes No (b) Can they be used when the acceleration is zero? Yes No

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Answers may vary, but some of the possible answers are, a V-shaped boomerang, a barstool, an empty coffee cup, a satellite dish, and a curving plastic slide at the edge of a swimming pool each have a center of mass that is not within the bulk of the object.

No, just as an object need not be moving to have mass.

Must an object be rotating to have a nonzero moment of inertia? yes no Explain your answer.

No, just as an object need not be moving to have mass.

Which is most elastic among following: Air Water Iron Glass

Iron

Is a bouncing ball an example of simple harmonic motion? (a) yes (b) no (c) insufficient information Is the daily movement of a student from home to school and back simple harmonic motion? (a) yes (b) no (c) insufficient information Why or why not? (Explain your answers to both parts.)

Neither are examples of simple harmonic motion, although they are both periodic motion. In neither case is the acceleration proportional to the position. Neither motion is so smooth as SHM. The ball's acceleration is very large when it is in contact with the floor, and the student's when the dismissal bell rings.

Consider a small raindrop and a large raindrop falling through the atmosphere. A. Compare their terminal speeds. (a) The larger drop has higher terminal speed. (b) Both raindrops have the same terminal speed. (c) The larger drop has lower terminal speed. (b) What are their accelerations when they reach terminal speed?

(a) (b) alarger drop = 0 m/s2 asmaller drop = 0 m/s2

A 0.115 kg ball is thrown straight up into the air with an initial speed of 15.5 m/s. (a) Find the momentum of the ball at its maximum height. (b) Find the momentum of the ball halfway up to its maximum height.

(a) Correct answer: 0 (b) Correct answer: 1.26 kgm/s

An ice skater starts a spin with her arms stretched out to the sides. She balances on the tip of one skate to turn without friction. She then pulls her arms in so that her moment of inertia decreases by a factor of 4. In the process of her doing so, what happens to her kinetic energy? (a) It increases by a factor of 4. (b) It increases by a factor of 2. (c) It remains constant. (d) It decreases by a factor of 4.

(a) It increases by a factor of 4.

A baseball and a basketball, having the same mass, are dropped through air from rest such that their bottoms are initially at the same height above the ground, on the order of 1 m or more. Which one strikes the ground first? (Assume air resistance) (a) both strike the ground at the same time (b) the baseball (c) the basketball

(a) both strike the ground at the same time

What is the direction of angular velocity ( ) as you view a clock hanging on a vertical wall? (a) clockwise (b) counterclockwise (c) into the wall (d) out of the wall

(a) clockwise

If global warming continues over the next one hundred years, it is likely that some polar ice will melt and the water will be distributed closer to the equator. How would that change the time period of the Earth? (a) increase (b) decrease (c) no change

(a) increase

Which of the following pairs of physical quantities have the same dimensions (a) momentum and impulse (b) linear velocity and angular velocity (c) linear momentum and angular momentum (d) force and tension

(a) momentum and impulse

As an object thrown upward moves in its parabolic path, at what point along its path are the velocity and acceleration vectors for the object perpendicular to each other? (a) the highest point (b) nowhere (c) the launch point

(a) the highest point

A ball rolls without slipping down incline A, starting from rest. At the same time, a box starts from rest and slides down incline B, which is identical to incline A except that it is frictionless. Which arrives at the bottom first? (a) The ball arrives first. (b) The box arrives first. (c) Both arrive at the same time. (d) It is impossible to determine.

(b) The box arrives first.

When a bus starts suddenly, the upper part of sitting passenger experiences a jerk in backward direction due to (a) inertia of rest (b) inertia of motion (c) change in momentum (d) centripetal force

(b) inertia of motion

A cyclist rides a bicycle with a wheel radius of 0.500 m across campus. A piece of plastic on the front rim makes a clicking sound every time it passes through the fork. If the cyclist counts 320 clicks between her apartment and the cafeteria, how far has she traveled? (a) 0.50 km (b) 1.5 km (c) 1.0 km (d) 0.80 km (e) 1.8 km

(c) 1.0 km

A bomb, initially at rest, explodes into several pieces. Is kinetic energy of the system conserved? (a) Yes (b) No (c) Insufficient information

(c) Insufficient information

When a torque acting on a body is zero, which of the following is constant? (a) force (b) linear momentum (c) angular momentum (d) impulse

(c) angular momentum

A rubber ball is dropped onto the floor. What force causes the ball to bounce? (a) friction (b) air resistance (c) reaction force of the floor (d) gravity.

(c) reaction force of the floor

A car of mass m traveling at speed v crashes into the rear of a truck of mass 4m that is at rest and in neutral at an intersection. If the collision is perfectly inelastic, what is the speed of the combined car and truck after the collision? (a) v (b) v/4 (c) v/3 (d) 2v (e) None of those answers is correct.

(c) v/3

A ball of clay falls freely to the hard floor. It does not bounce noticeably, and it very quickly comes to rest. What, then, has happened to the energy the ball had while it was falling? (a) It has been used up in producing the downward motion. (b) It has been transformed back into potential energy. (c) It has been transferred into the ball by heat. (d) It is in the ball and floor (and walls) as energy of invisible molecular motion. (e) Most of it went into sound.

(d) It is in the ball and floor (and walls) as energy of invisible molecular motion.

A particle is in motion. For its motion in certain time, displacement covered is (a) always equal to distance covered (b) always less than distance covered (c) greater than distance covered (d) less than or equal to distance covered

(d) less than or equal to distance covered

A hollow sphere is filled with water. It is hung by a long thread. As the water flows out of a hole at its bottom, the period of oscillation will (a) go on decreasing (b) go on increasing (c) will first decrease then increase (d) will first increase and then decrease till the sphere is empty.

(d) will first increase and then decrease till the sphere is empty.

If the net work done by external forces on a particle is zero, which of the following statements about the particle must be true? (a) Its velocity is zero. (b) Its velocity is unchanged. (c) More information is needed. (d) Its velocity is decreased. (e) Its speed is unchanged.

(e) Its speed is unchanged.

A body of mass M rests on a horizontal floor. If it is just made to move by applying the minimum necessary horizontal force and the same force continues to act afterwards. If the coefficient of static and kinetic friction is 0.4 and 0.3 respectively, then the acceleration of the body is (a) 2.94 m/s2 (b) 0.98 m/s2 (c) 3.98 m/s2 (d) zero.

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A person has thrown a stone upto maximum horizontal distance 200m. Calculate the maximum vertical height it has reached (show your calculations).

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A playground merry-go-round of radius R = 2.20 m has a moment of inertia I = 240 kg m2 and is rotating at 9.0 rev/min about a frictionless vertical axle. Facing the axle, a 22.0-kg child hops onto the merry-go-round and manages to sit down on the edge. What is the new angular speed of the merry-go-round?

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In an engine, a piston oscillates with simple harmonic motion so that its position varies according to the expression, x = 4.00 cos (5t + π/4) where x is in centimeters and t is in seconds. At t = 0, find the position of the piston. At t = 0, find velocity of the piston. At t = 0, find acceleration of the piston. Find the period and amplitude of the motion.

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The displacement of a particle vibrating in SHM is given by y = 3 sin ωt + 4 cos ωt. Calculate the amplitude of the vibrating particle.

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(c) an acceleration directed away from the center of its path

A car moving around a circular track with constant speed has (a) zero acceleration (b) an acceleration in the direction of its velocity (c) an acceleration directed away from the center of its path (d) an acceleration directed toward the center of its path (e) an acceleration with a direction that cannot be determined from the given information

Is it possible to add a vector quantity to a scalar quantity? Yes No Explain your answer.

Addition of a vector to a scalar is not defined. Think of adding age(scalar) to the direction south(vector) - It just doesn't make sense.

A 1 kg ball is moving in uniform circular motion around a post that it is tied to with a rope (consider the rope to have no mass).If the ball is travelling at 5m/s at a radial distance of 1.5 m from the post, then how large is the tension in the rope? (a) 10 N (b) 17 N (c) 19 N (d) 21 N (e) 23 N

Answer (c)Use componentsofforce: Tcosα =mg and Tsinα = mv2/r; diving we get, tanα = (v2/rg);This gives α = 59 deg, Therefore T = mg/cos(59) = 19 N

Two forces are acting on an object. Which of the following statements is correct? (a) The object is in equilibrium if the forces are equal in magnitude and opposite in direction. (b) The object is in equilibrium if the net torque on the object is zero. (c) The object is in equilibrium if the forces act at the same point on the object. (d) The object is in equilibrium if the net force and the net torque on the object are both zero. (e) The object cannot be in equilibrium because more than one force acts on it.

Answer (d). For an object to be in equilibrium, it must be in both translational equilibrium and rotational equilibrium. Thus, it must meet two conditions of equilibrium, namely Fnet = 0 and τnet= 0.

A baseball and a basketball, having the same mass, are dropped through air from rest such thattheir bottoms are initially at the same height above the ground, on the order of 2m or more.Which one strikes the ground first? (Assume air resistance) (a)both strike the ground at the same time(b) the baseball(c) the basketball(d) more information is needed

Answer: (b)

A ball thrown up vertically returned to the thrower after 4s. The velocity with which it was thrown up was (a)60 m/s (b) 30 m/s c) 9.8 m/s(d) 20 m/ (e) 40 m/s

Answer: (d)vf= vi+ at, where vf= 0, t = 2s, a = -9.8 m/s2, which gives vi~ 20 m/s

The center of gravity of an object may be located outside the object. Give two examples for which that is the case.

Answers may vary, but some of the possible answers are, a V-shaped boomerang, a barstool, an empty coffee cup, a satellite dish, and a curving plastic slide at the edge of a swimming pool each have a center of mass that is not within the bulk of the object.

A remote controlled car is navigating a 1 m radius circular turn on flat ground. What is the minimum coefficient of static friction between the tires and the ground required for the car to make this turn without slipping at a speed of 3 m/s? (a) μs= 0.47 (b) μs= 0.68 (c) μs= 0.85 (d) μs= 0.92 (e) μs= 1.1

Correct answer: (d): application of force; motion in a circular path Use mv2/r =f =μ(mg)which gives μ = v2/rg =0.92

Can the magnitude of a vector have a negative value? Yes No Explain your answer.

Can the magnitude of a vector have a negative value? Yes No Explain your answer.

If the radius of the earth contracts to 1/ (2 of its present value, what would be the length of √2)the day in hours? (assume mass does not change) (a) 6 h (b) 8 h (c) 12 h (d) 3 h (e) 24 h

Correct (d) 3h Use conservation of angular momentum and assume mass of the earth does not change.

A 7.0-g bullet is fired into a 170-g block of wood at rest on a horizontal surface. After impact, the block slides 8.40 m before coming to rest. If the coefficient of friction between the block and the surface is 0.430, what is the speed of the bullet before impact? (a) 166 m/s (b) 76 m/s (c) 213 m/s (d) 185 m/s (e) 247 m/s

Correct answer (c) Use kinematic equation: v2 = 2as = 2*μk*g*s to calculate v.And use conservation of momentum: mvi = (m1+m2) v, calculate vi

A quantity xis related byx = c(a−b)h, where c= dimensionless constant and a, band hhave dimension of length only, the quantity xis (a)Area (b) Volume (c) Length (d) Velocity

Correct answer: (a)

As a projectile thrown upward moves in its parabolic path, at what point along its path are the velocity and acceleration vectors for the projectile perpendicular to each other? (a)the highest point (b) nowhere (c) the launch point.

Correct answer: (a)

From a waterfall, water is pouring down at the rate of 50 kg/s on the blades of the turbine. If the height of the fall be 200 m, the power delivered to the turbine is (a) 98 KW (b) 105 KW (c) 0 (d) 96 KW

Correct answer: (a)Use P = mgh/t = (m/t) gh = (50) (9.8)(200) = 98,000 W = 98 KW

A car of mass m traveling at speed v crashes into the rear of a truck of mass 4m that is at rest and in neutral at an intersection. If the collision is perfectly inelastic, what is the speed of the combined car and truck after the collision? a) v/5 (b) v/4 (c) 5v (d) 4v (e) v

Correct answer: (a)v/5; use conservation of linear momentum; m1v1 = (m1+m2) v

What is the magnitude of the vector (12i-5j) m/s? Here i and j are unit vectors. (a)12 m/s (b) 13 m/s (c) 5 m/s (d) -5 m/s (e) 14 m/s

Correct answer: (b)

The position vector of a particle of mass 2.20 kg as a function of time is given by = (6.00 î + 5.50 t ĵ), where is in meters and t is in seconds. Determine the magnitude of the angular momentum of the particle about the origin as a function of time. (a) 70 kg.m2/s (b) 72 kg.m2/s (c) 74 kg.m2/s (d) 76 kg.m2/s (e) 78 kg.m2/s

Correct answer: (b) 72.6 kg.m2/sUse L = r × p = r × mv = 6*2.2*5.5 = 72.6 kg.m2/s

An astronaut hits a golf ball on the Moon. Which of the following quantities, if any, remain constant as a ball travels through the vacuum there? (Select all that apply.) (a)speed b) horizontal component of velocity (c) vertical component of velocity (d)velocity (e) acceleration.

Correct answer: (b) and (e)

An ice skater starts a spin with her arms stretched out to the sides. She balances on the tip of one skate to turn without friction. She then pulls her arms in so that her moment of inertia decreases by a factor of 3. In the process of her doing so, what happens to her kinetic energy? (a) It increases by a factor of 9. (b) It increases by a factor of 3. (c) It remains constant. (d) It decreases by a factor of 3.(e) It decreases by a factor of 1/3.Correct

Correct answer: (b)Rotational KE = ½ Iω2 and use conservation of angular momentum: Iω = constant

A rubber ball is dropped onto the floor. What force causes the ball to bounce? (a)friction (b) air resistance (c) reactionforce of the floor (d) gravity.

Correct answer: (c)

A flywheel of moment of inertia 0.5 kgm2 rotating initially at 600 rpm comes to rest in 30 sec under constant retarding torque. The constant retarding torque of the flywheel is (a) 1.60 Nm (b) 1.47 Nm (c) 1.05 Nm (d) 1.83 Nm

Correct answer: (c)Hint: f = 600/60 = 10 rev/s, α = ω/t = 2πf/t = 2π*10/30 = (2/3) π, which gives τ = Iα = 1.05 Nm

An ice cube has been given a push and slides without friction on a level table. Which is correct? A.It is in stable equilibrium. B.It is in unstable equilibrium. C.It is not in equilibrium. D.It is in neutral equilibrium.

Correct answer: (d)

A 2.85 gm leaf is dropped from a height of 3.50 m above the ground. Assume the net downward force exerted on the leaf is F = mg -bv,where the drag factor is b= 0.0320 kg/s.Calculate the terminal speed of the leaf.(a)0.87 m/s (b) 0.67 m/s c) 0.77 m/s (d) 0 (e) 9.8 m/s

Correct answer: 0.873 m/sWhen v =vT, F =0; which gives 0 = mg-bvT; vT= mg/b = 0.00285*9.8/0.0320 = 0.87 m/s

A girl is swinging on a swing in the sitting position. How will the time period be affected if she stands up? Increase Decrease Remains unchanged uncertain

Decrease

An open box slides across a frictionless, icy surface of a frozen lake. What happens to the speed of the box as water from a rain shower vertically downward into the box? (a) Increases (b) Decreases (c) Remains constant

Decreases

Which of the following particles, if any, have an acceleration? (a) a particle moving in a straight line with constant speed (b) a particle moving around a curve with constant speed (c) Neither of the particles has an acceleration. Explain your answer.

The particle moving around a curve has acceleration perpendicular to the circular path and directed toward the center of the path

An object executes circular motion with constant speed whenever a net force of constant magnitude acts perpendicular to the velocity. What happens to the speed if the force is not perpendicular to the velocity?

The speed changes. The tangential force component causes tangential acceleration.

A passenger sitting in the rear of a bus claims that he was injured when the driver slammed on the brakes, causing a suitcase to come flying toward the passenger from the front of the bus. If you were the judge in this case, what disposition would you make? (a) Passenger's statement is true. (b) Passenger's statement is false. Why?

The suitcase would have had the same magnitude and direction of velocity as the traveling bus. When the brakes were applied to the wheels of the bus, causing it to stop, the suitcase would have continued traveling forward. The only way the suitcase could have suddenly started moving backward with respect to the bus is if the bus were initially traveling in reverse before the driver hit the brakes; and in this case it is exremely unlikely that it would be traveling fast enough to cause this to happen.

Both torque and work are products of force and distance. How are they different? Do they have the same units?

There are two major differences between torque and work. The primary difference is that the displacement in the expression for work is directed along the force, whereas the important distance in the torque expression is perpendicular to the force. The second difference involves whether there is motion or not - in the case of work, there is work done only if the force succeeds in causing a displacement of the point of application of the force. However, a force applied at a perpendicular distance from a rotation axes results in a torque whether or not there is motion. As far as units are concerned, the mathematical expressions for both work and torque result in the product of newtons and meters, but this product is called a joule in the case of work and remains as a newton-meter in the case of torque.

A recording disc rotates steadily at 45 rpm on a table. A mass 0.02 kg is dropped gently at 0.04m from its axis and sticks on the disc then the rate of rotation decreases to 36 rpm. The moment of inertia of the disc is (a) 1.2 × 10-3 kgm2 (b) 1.3 × 10-4 kgm2 (c) 1.3 × 10-5 kgm2 (d) 1.3 × 10-6 kgm

Use kinematic equation to calculate the initial velocity: vf2 = vi2 +2asvi2 - 2gs =0vi2 = 9.8 which gives vi = 3.13 m/s; this is the final velocity for the collision equation for two bodies. Now use conservation of linear momentum: m1v1i = (m1 + m2) vf which gives, v1i = (0.409) *3.13/0.009 ~ 142.24 m/s

The bob of a simple pendulum is in the form of a hollow sphere filled with mercury. If a little mercury is drained off, the time period of pendulum Will increase Will decrease Will remain same

Will increase

The bob of a simple pendulum is in the form of a hollow sphere filled with mercury. If a little mercury is drained off, the time period of pendulum Will increase Will decrease Will remain same

Will remain same

A student thinks that any real vibration must be damped. Is the student correct? Yes No If so, give convincing reasoning. If not, give an example of a real vibration that keeps constant amplitude forever if the system is isolated.

Yes

A projectile is launched at some angle to the horizontal with some initial speed vi, and air resistance is negligible. (a) Is the projectile a freely falling body? Yes No (b) What is its acceleration in the vertical direction? (Let up be the positive direction.) (c) What is its acceleration in the horizontal direction?

Yes, -9.8 m/s2, 0

If a car is traveling eastward, can its acceleration be westward? yes no Explain.

Yes, if this occurs the acceleration of the car is opposite the velocity, meaning it is slowing down.

If a body shrinks, then moment of inertia of the body (a) increases (b) decreases (c) remains constant (d) decreases and becomes zero.

decreases

You throw a ball vertically upward so that it leaves the ground with velocity 3.38 m/s. (a) What is its velocity when it reaches its maximum altitude? (b) What is its acceleration at this point? (c) What is the velocity with which it returns to ground level?

magnitude 0 m/s 9.8 m/s2 3.38 m/s

Is a bouncing ball an example of simple harmonic motion? Yes no (c) insufficient information Is the daily movement of a student from home to school and back simple harmonic motion? Yes no (c) insufficient information Why or why not? (Explain your answers to both parts.)

no for both.