Physics final (conceptual questions)
A woman bounces on a trampoline, going a little higher with each bounce. Explain how she increases the total mechanical energy.
When a woman bounces on a trampoline, she transfers some muscular energy to depress the trampoline further each time to rebound higher. Thus, she acquires more potential energy for the next descent and the total mechanical energy of the woman will be increased.
Water waves are a combination of longitudinal and transverse waves. Defend the following statement: "When water waves hit a vertical wall, the wall is a node of the longitudinal displacement but an antinode of the transverse displacement"
When wave hits the wall, there is no further motion, forming a node (a place of no motion). After hitting the wall, the wave reflects backwards and particles vibrate perpendicular to wave motion (antinote = place of maximum displacement)
A projectile moves in a parabolic path without air resistance. Is there any point at which acceleration is ppd to veloctiy? Parallel?
Acceleration is always pointing down, velocity never does, so the two can't be parallel; but they can be ppd at the peak of the path
You exert a push P on an object and it pushes back on you with a force F. Under which of the following circumstances must P and F equal? a. When P and F are stationary. b. When P and F are moving at a constant velocity. c. When P and F are accelerating.
All three
A student thinks that all real oscillations must be damped. Is the student right?
Yes
Does the kinetic energy of an object depend on the frame of reference in which it is measured?
Yes
Does the vertical speed of an element of a horizontal, taut string, through which a wave is travelling, depend on the wave speed?
Yes
Why is a solid substance able to transport both longitudinal waves and transverse waves, but a homogeneous fluid is able to transport only longitudinal waves?
As a transverse wave travels through a solid medium it relies on the shear strength of that medium to maintain the propagation. Fluid has little shear strength and the wave dissipates almost immediately. Longitudinal waves can propagate through water because they rely on the simple push-pull action of one particle to another.
Can the basic equations of kinematics be used when the acceleration varies in time? Can they be used when the acceleration is zero?
As long as the acceleration is constant, even at zero, it can be used
Are astronauts weightless because they're beyond the pull of gravity?
Astronauts in orbit are still under the gravitational force, however there is no supportive force acting on the astronaut and hence he is in a sustained state of weightlessness.
A sailor drops a wrench from the top of a sailboat's mast as the sailboat moves rapidly in a straight line with a constant speed. Where does the wrench fall?
At the base of the mast because the falling wrench moves at the same speed relative to the boat
A car speeds up as its engine delivers a constant power. Is the acceleration greater at the beginning of this process or at the end? Explain.
At the beginning
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 falls vertically downward into the box? What happens to its energy?
Both speed and energy decrease
When a book slides along a tabletop, the force of friction does negative work on it. Can friction ever do positive work? Explain with reference to a box in the back of an accelerating truck.
Yes, a box in an accelerating truck would be dragged along with it.
Can an object exert a force on itself?
Yes, but it cannot change its center of mass. (Dynamic tension)
Is it possible for the translational kinetic energy of an object to change without changing its rotational kinetic energy?
Yes, but only if the force is applied at the center of mass
If the speed of the particle is greater than zero, can the acceleration of the particle be zero?
Yes; acceleration is the *change* in velocity over a time interval, so a constant velocity means no acceleration.
Can an object be in equilibrium if it is in motion? Explain.
Yes; if all the forces on it are balanced, it will be in equilibrium regardless of whether it is in motion or not.
Can a single force applied to a body change both its translational and rotational motions? Explain.
Yes; in fact, if the force is applied to its center of mass, it will cause both motions
If a metal wire has its length doubled and it diameter tripled, by what factor does its Young's modulus change?
Young's modulus remains constant regardless of length or width.
An elevator is hoisted by its cables at constant speed. Is the total work done on the elevator positive, negative or zero? Explain.
Zero. There is no change in kinetic energy
What should you do to the length of the string of a simple pendulum to a) double its frequency b) double its period c) double its angular frequency
a) 1/4th original length b) 4 times original length c) 1/4th original length
a) determine the correct dimensions of force. b) knowing the dimensions of force, what are its units in the international system in terms of base SI units?
a) [MLT^-2] b) kg*m/s^2
An object thrown straight up in the air feels no air resistance. How can the object have an acceleration when it has stopped moving at its highest point?
Constant downward acceleration due to gravity
A pendulum bob is a globe filled with water. What will happen to the frequency of vibration if the pendulum bob had a small hole that slowly leaked water?
Decreases
What kind of deformation does a cube of Jell-O exhibit when it jiggles?
Deformation of shape
If the average velocity of an object over a certain time interval is zero, what can you say about the displacement of the boat over that time interval?
Displacement would be zero
The fundamental physical quantities are mass (kg), length (l), and time (s). Suppose you chose to use force (N) instead of mass. How would this affect the units of mass of those fundamental quantities?
F = [MLT^-1] m = [FL^-1 T^-2] So, mass = Ns^2/m
People often rub their hands together when they're cold to warm them up. How does doing this procedure heat? Where does the heat come from?
Friction
Does a car's kinetic energy change more when the car speeds up from 10 m/s to 15 m/s or when it speeds up from 15 m/s to 20 m/s? Explain.
From 10-15: 1/2 m(15^2-10^2) = 62.5 m From 15-20: 1/2 m(20^2-15^2) = 87.5 m So the change in kinetic energy is greater from 15-20 m/s
You drive a car up a steep hill at a constant speed. Discuss all of the forces that act on the car. What pushes it up the hill?
Gravity, friction, normal force
A machine gun fires at a steel plate. Is the force on the plate greater if the bullets embed in the plate or it they bounce off it? Explain.
Greater if it bounces
You throw a baseball straight up in the air so that it rises to a maximum height much greater than your height. Is the magnitude of the ball's acceleration greater while it is being thrown or after it leaves your hand? Explain.
Greater while being thrown because of the high velocity. Once it leaves your hand, the acceleration becomes constant
A glider is attached to a fixed ideal spring and oscillates on a horizontal, frictionless air track. A coin rests atop the glider and oscillates with it. At what points in the motion is the frictional force on the coin the greatest and least?
Greatest at the end points, least at the equilibrium point
Consider a skydiver who has stepped off a helicopter and is falling through the air. Before she reaches terminal speed, and long before she opens her parachute: a) does her speed increase, decrease, or stay constant? b) does her acceleration increase, decrease, or stay constant?
Her speed increases at a constant acceleration of 9.8m/s^2
When a string is barely strong enough to lift a weight, it can lift the weight when you apply a steady pull. But if you jerk the string, it will break. Why
If the external force is greater than the tensile strength of the string, it will break
Suppose a car's standard tires are replaced with tires that have a diameter that is 30% larger. By what factor will the car's speedometer be off? In what direction?
If the radius is increased by 30%, then the speed shown would be 30% *less* than the actual speed
The driver of a speeding, empty truck slams on the brakes and slides to a stop in a distance D. If the truck carries a load that is equal to its own weight, what will its stopping distance be in terms of D?
If you double the mass, you also double the normal and frictional forces, so the effects of the added mass cancel out. This means that the stopping distance will still be D.
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?
It deformed the ball
An apple falls from a tree and feels no air resistance. As it is falling, which of the following is true? (a) Its momentum is conserved. (b) Total mechanical energy is conserved. (c) Its kinetic energy is conserved.
Just mechanical energy
A projectile has the same initial kinetic energy no matter what the angle of projection. Why doesn't it rise to the same maximum height in each case?
Kinetic energy = 1/2 mv^2. So, it is independent of the angle
Three archers each fire four arrows at a target. Joe's arrows hit 10 cm above the center of the target, 10 cm below it, 10 cm to its right, and 10 cm to its left. Flo's arrows all hit with in 1 cm of a point 20 cm to its right of center. And finally, Moe's arrows all hit within 1 cm of the target's center. Rate the archers with respect to their precision and accuracy.
Moe is both precise and accurate, Flor is precise, and Joe is neither
In the cabin of a certain ship, a soda can rests in a saucer-shaped indentation in a built-in counter. The can tilts as the ship slowly rolls. Is the can more stable when it is full, half-full or empty?
Most stable when its half-full
A simple pendulum exhibits simple harmonic motion when the amplitude of oscillations are small. Will the motion still be periodic when its amplitude is large?
No
Does the center of gravity of a solid body always lie within the material of the body? If not, give a counterexample.
No, doughnut
Can a force of static friction do work? If not, why not? If so, give an example.
No, frictional force is equal and opposite applied force. So if an object is at rest, no work is done
Is a bouncing ball an example of simple harmonic motion?
No, it doesn't follow a sinusoidal curve
At the highest point of its parabolic trajectory, a shell explodes into two fragments. Is it possible for both of the fragments to fall straight downwards after the explosion? Why or why not?
No, momentum is conserved
If a pendulum clock keeps perfect time at the base of a mountain, will it keep perfect time at the top of the mountain?
No, period relies on gravitational acceleration, which decreases with height. So the pendulum's period would increase (gain time)
For wave motions discussed in this chapter, does the speed of propagation depend on the amplitude? Why or why not?
No, the speed depends on the frequency and wavelength
In uniform circular motion, the acceleration is ppd to the velocity at every moment. Is this true when the motion is not uniform (i.e. when the speed is not constant)
No, this is false
A tennis player hits a tennis ball with his racket. Consider the system made up of the ball and its racket. Is the total momentum of the system the same just before and just after the ball it hit? Is the total momentum the same 2 s later when the ball is in midair at the highest point in its trajectory? Explain any differences between the two.
Not the same two seconds later
The center of gravity of an object can be located outside of the object. Give two examples where this is the case?
A doughnut would have its center of gravity in the center (where the hole is). A horseshoe would have its center of gravity somewhere in the u-bend, but not in the horseshoe itself.
Which of the following particles have accelerations? a. a particle moving along a straight trajectory with constant speed b. a particle moving along a straight trajectory that is slowing down c. A particle moving along a curved trajectory that has constant speed d. A particle moving along a curved trajectory that is speeding up
Only b, c, and d have accelerations. a has constant speed, therefore no acceleration. Even though c has constant speed, its along a curved trajectory so it still has a rotational acceleration
Which of the following conditions must be true of the motion if the basic equations of kinematics are to describe the motion? a. The velocity of the object must remain constant. b. The acceleration of the object must remain constant. c. The velocity of the object must increase with time. d. The position of the object must increase with time. e. The velocity of the object must always be in the same direction as its acceleration.
Only constant acceleration must be true
A non-zero net force acts on an object. Is it possible for any of the following quantities to be constant? (a) Speed (b) Velocity (c) Kinetic Energy
Only possible for speed and kinetic energy
A car has the same kinetic energy when it is traveling south at 30 m/s as it does when it is traveling northwest at 30 m/s. Is the momentum the same in both cases? Explain.
Since moment is a vector quantity, direction is important. So the momentum is different in each case.
For transverse waves on a string, is the wave speed the same as the speed of any part of the string?
Since the speed of a rope particle depends on the location of the wave, we can conclude that the wave speed is not the same as the speed of any part of the string
Why is a tapered water glass with a narrow base easier to tip over than a glass with straight sides? Does it matter whether the glass is full or empty
Stability depends on height of the center of gravity, which will be higher in the narrower-based glass
You are balancing a wrench by suspending it at a single point. Is the equilibrium stable, unstable or neutral if the point is above, at, or below the wrench's center of gravity? In each case, give the reasoning behind your answer.
Stable above the center of mass if the wrench is hanging vertically, stable on the center of mass if the wrench is hanging horizontally.
What parameters affect the density of water?
Temperature, pressure, and salinity
Raindrops hitting the side windows of a car in motion often leave diagonal streaks even if there is no wind. Why? Is this the same explanation for diagonal streaks on the windshield?
The air flow past the window drags the drops horizontally across the glass while at the same time gravity is making the drops run vertically down the glass. The net result is that the drops are moving across the glass in two directions at the time giving you the overall diagonal movement. Not the same for windshield; since it is in the front of the car, there is no horizontal drag of the raindrops. Only wind could affect this.
You throw a baseball upward with a speed v. When the ball returns from where you threw it, how does its speed compare if there is no air resistance vs if there is?
The ball would be faster with no air resistance to slow it down
What is the current standard for the meter for Weights and Measures?
The distance light travels in a vacuum in 1/299,792,458 seconds
A spring has a spring constant k. Now the spring is cut in half. What is the relationship between k and the spring constant k' of each resulting smaller spring? Explain your reasoning.
k'=2k
If a long rope is hung from a ceiling and waves are sent up the rope from its end, why does the speed of the waves change as they ascend? Does the speed increase or decrease?
The speed of the wave changes since there's a change in tension. This speed increases as it ascends.
When you push a box with a 200 N force instead of a 50 N force, you can feel that you are making a greater effort. But when you put a 200 N box onto a table instead of 50 N, is the table really doing anything different?
The table will always exert a force equal and opposite to that applied.
A pail of water can be whirled in a vertical path so that no water is spilled. Why does the water stay in the pail, even when its above your head?
The tendency of the water is to move in a straight line path tangent to the circular path followed by the container. (As a result, at the top of the circular path, the water presses against the bottom of the pail, and the normal force exerted by the pail on the water provides the radial force required to keep the water moving in its circular path)
What is the current standard for the second used by International Committee for Weights and Measures?
The time required for 9,192,631,770 cycles of the radiation corresponding to the transition between the two lowest energy states of the cesium atom.
The pilot of a boat moving north - the same direction that it's pointing - reverses the direction of the boat's propeller. The boat then moves with an acceleration directed south. Assume the acceleration of the boat remains constant. What happens to the boat?
The velocity changes directions
In a transverse wave on a string, the motion of the string is perpendicular to the length of the string. How, then, is it possible for energy to move down the string?
The vibration of the particles is only in direction ppd to the length of the string. The energy is transferred from atom to atom and finally reaches the end point. In this way, even though the wave motion is ppd to the length of the string, the energy must be traveling along the length too
A student stands at the top of a building of height h and throws a ball up into the air with an initial speed vi. When the ball passes him on the way down, he throws another ball downward, leaving his hand at the same speed vi just as the first ball passes. Which ball has the greater speed when it hits the ground? What does this mean about which ball hits the ground first?
They both hit the ground at the same time and speed
At the instant you fire a bullet horizontally from a rifle, you drop a bullet from the height of the gun barrel. If there is no air resistance, which bullet hits the level ground first?
They both hit the ground at the same time! This is because the bullet which is fired is under no horizontal forces (since we are ignoring air resistance), and both bullets are under the same vertical force of gravity
The work done by a force is the product of force and distance. The torque due to a force is the product of force and distance. Does that mean that torque and force are equivalent? Explain.
Torque = force x distance ppd from motion Work = force x distance along motion Torque is in nm, which is dimensionally equivalent to work's joules.
For a simple pendulum, clearly distinguish between the angular speed (w) and the angular frequency (w). Which is constant and which is variable?
*Angular frequency* of a simple pendulum is *constant*. Instantaneous *angular velocity* due to rotational motion *changes with time*
In the equation below, make a list for each set of quantities that must have the same dimensions. Include both symbols and multiplicative terms, e.g. for X + YZ, the quantities would be X, Y, Z and YZ. A/(L+MN)+BC=(C+D/E)/PQ
*L,MN *C, D/E To add these variables together, they must include the same dimensions
A falling skydiver reaches terminal speed with her parachute closed. After the parachute is opened, what parameters change to decrease this terminal speed?
The drag force is proportional to the speed squared and to the effective area of the falling object. At terminal velocity, the drag and gravity forces are in balance. When the parachute opens, its effective area increases greatly, causing the drag force to increase greatly. Because the drag and gravity forces are no longer in balance, the greater drag force causes the speed to decrease, causing the drag force to decrease until it and the force of gravity are in balance again.
People often call their electric bill a "power bill," yet the quantity on which the bill is based is expressed in kilowatt-hours. What are people really being billed for?
The electric bill is prepared on the basis of number of kilo-watt hour consumed. Kilowatt hour is a unit of electrical energy, so they're really paying for electricity.
A ball is thrown from the edge of a cliff. Regardless of how hard it is thrown, due to air resistance, the ball will eventually end up moving vertically downward. Justify this statement.
The force from air resistance will eventually cause the ball to stop moving horizontally, and the ball will then only move in the vertical direction under the force of gravity
Why does the long pole of a tight rope walker help her stay balanced?
The long pole increases her moment of inertia
A sharpshooter fires a rifle while standing with the butt of the gun against her shoulder. If the forward momentum of the bullet is the same as the backward momentum of the rifle, why isn't it as dangerous to be hit by the gun as by the bullet?
The mass and velocity are considerably less compared to the bullet; therefore the kinetic energy is less
What is the current standard for the kilogram used by International Committee for Weights and Measures?
The mass of a particular platinum-iridium alloy sphere
In mechanics, we often assumed that springs were massless. Why? Why is this NOT a good assumption when discussing waves on a string?
The mass of the spring would be very small compared to the mass of the system. But when talking about the propagation of waves, the wave speed depends on the mass of the string
If a pendulum has a period of 2.5s on earth, what would its period in a space station orbiting the earth be? If a mass hung from a vertical spring has a period of 5 s on earth, what would its period be on the space station?
The period of the pendulum would be infinity since there is no gravitational acceleration in space (g=0). The period of the spring doesn't depend on g, so it would be the same at the space station as on earth
In general, the normal force is not equal to the weight. a) Give an example in which these forces are equal in magnitude b) Give at least two examples in which they are not.
a) a block sitting on flat ground at rest will have a normal force equal to its mass x gravity (weight) b1) a block on an incline will have its normal force at an angle to the force of gravity, so cos(theta) needs to be taken into consideration. b2) When an elevator is accelerating upwards, the normal force of an object inside if greater than the object's weight and vise versa if the elevator is moving down.
a) define accuracy and precision so that the difference between them is clear. b) explain why the two concepts are similar, despite their differences.
a) accuracy reflects how close a measurement is to a true value, whereas precision reflects how reproducible a measurement is. b) they both reflect how close a measurement is to a specific value, whether that value is the true value or not.
What forces cause an a) automobile, b) propeller-driven airplane, and c) a rowboat to move?
a) friction b) thrust c) thrust
A taut, light cord B connects block 1 to larger mass block 2. Cord A exerts a force on block 1 to accelerate it forward. a) how does the magnitude of the force exerted by cord A on block 1 compare to the magnitude of the force exerted by cord B on block 2? b) How does the acceleration of block 2 compare to the acceleration of block 1? c) Does cord B exert a force on block 1? If so, forward or backward? Equal to, larger, or smaller than the force exerted by cord B on block 2?
a) larger because tension of cord A = (m1 + m2)a, whereas tension of cord B = m2a b) equal c) yes, backwards and equal
A juggler juggles three balls in a continuous cycle. Any one ball is in contact with one of his hands for one fifth of the time. (a) Describe the motion of the center of mass of the three balls. (b) What average force does the juggler exert on one ball while he is touching it?
a) movement is up when ball goes up, down when all 3 balls fall. b) 5 times the weight of one ball
a) If an equation is dimensionally correct, does that mean the equation must be true? b) If the equation is not dimensionally correct, does that mean that the equation cannot be true?
a) no, it isn't always true. For example, you cannot have 20 apples equaling 5 apples. This dimensionally correct but not true. b) Yes, a dimensionally incorrect equation can never be true. For example, 1 apple does not equal 1 orange.
A person holds a ball in her hand. a) identify all the external forces on the, then b) identify all the external forces after she drops it
a) normal force of your hand and downward force of gravity b) force of gravity and air resistance
A massive tractor is rolling down a country road. In a perfectly inelastic collision, a small sports car runs into the machine from behind. a) Which vehicle experiences a change in momentum of larger magnitude? b) Which vehicle experiences a larger change in kinetic energy?
a) same for both b) car
Three objects of uniform density - a solid sphere, a solid cylinder, and a hollow cylinder - are placed atop an incline. They are all released from rest at the same elevation and roll without slipping. (a) Which object reaches the bottom first? (b) Which object reaches it last?
a) sphere b) hollow cylinder
2. A simple pendulum feels three forces as it swings back and forth, and the three force on it are the gravitational force, tension in the string, and air resistance on the pendulum bob. a) Which of these forces, if any, does no work on the pendulum at any time. b) Which of these forces does negative work on the pendulum at all times.
a) tension in the string b) air resistance
a) give an example in which the net force acting on an object is zero and yet the net torque is non-zero. (b) give an example of a case where the net torque acting on an object is zero and yet the net force is non-zero.
a) torque = force x distance, so torque will always be zero if force is zero. b) in order for torque to be zero and force be non-zero, the distance must be zero.
a) does a rigid object in uniform rotation about a fixed axis satisfy the first and second conditions for equilibrium? Why? b) does it then follow that every particle in this object is in equilibrium? Explain.
a) when a rigid object is in uniform rotation about a fixed axis, then the object cannot have linear motion and have only rotational motion. Thus it satisfies the first condition of equilibrium. Since rotational motion is uniform, no torque acts on it, thus satisfies the second condition. b) yes
Two waves travel on the same string. Is it possible for them to have a) different frequencies b) different wavelengths c) different speeds d) different amplitudes e) the same frequency but different wavelengths
a) yes b) yes c) no (speed depends on the medium's properties) d) yes e) no (wave speed = frequency times wavelength. Since the speed must be the same for both waves, it isn't possible to have two waves with the same frequency but different wavelengths)
