Physics 107 Midterm Exam 2

What is the equation for angular acceleration, α, when θ is the angle, ω is the angular velocity, and t is the time?
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What is the equation for angular acceleration, α, when θ is the angle, ω is the angular velocity, and t is the time?
Angular acceleration is defined as the rate of change of angular velocity, that is, α=Δω/Δt.
When is angular acceleration negative?
Angular acceleration is the rate of change of angular velocity and is negative when angular velocity (ω) decreases.
How can an object rotating clockwise have a positive angular acceleration?
The clockwise rotation of an object produces negative angular velocity. Therefore, when the object is slowing down and rotating clockwise, the angular acceleration is positive.

In a circular motion, the clockwise rotation of the object produces negative angular velocity. Therefore, for an object which is slowing down and rotating, clockwise would have a positive angular acceleration.
Does the speed of an object in uniform circular motion change? Why?
No, because speed is constant in the uniform circular motion.

The speed of the object is constant for uniform circular motion. Thus, the speed of the object does not change with time.
What is the equation for centripetal acceleration in terms of angular velocity and the radius?
ac=rω^2.
Is there a net force acting on an object in uniform circular motion?
Yes, the object is accelerating, so a net force must be acting on it.

For an object in uniform circular motion, the net force acts toward the center of the circular path to give it centripetal acceleration.
Two different size boxes made of the same material are located on a flat surface. If Box A has been filled so that it only has ⅓ the mass of Box B, but it has twice the bottom surface area what is the relationship between the forces that must be used to overcome the friction generated by each box to move them parallel along the floor?
Box B requires 3 times as much force to overcome friction. Static friction only depends on the coefficient of static friction and the normal force which is calculated as N = mg in this situation.

Static friction is calculated as fsmax = μsN, meaning that it only depends upon the two materials in contact (the coefficient of static friction) and the weight of the box on the flat surface (the normal force). Surface area does not impact friction.
Open the simulation and select 50 kg for the mass on the sphere on the left, and 200 kg for the mass of the sphere on the right. Separate the forces by 4 m. Which mass, if either, pulls with the greater magnitude of force?
The objects pull with the exact same magnitude of force.

Newton's second law must be true. Gravity acts on both objects with a force of equal magnitude. The objects pull on each other with a force of Gm^1m^2/r^2. The only difference in the two forces is the direction.
A wooden block rests on a ramp inclined at 30degrees with the horizontal. How does the magnitude of the normal force on the block change if you lower the ramp to an incline of 15degrees?
it increases

The magnitude of the normal force on the block equals the component of the gravitational force perpendicular to the ramp. This component increases as the ramp becomes less inclined. Therefore, the normal force on the block will increase as the ramp is lowered to 15 degrees.
The frictional force...
...supplies the centripetal force and is numerically equal to it. Centripetal force is perpendicular to velocity and causes uniform circular motion. The larger the Fc, the smaller the radius of curvature size r and the sharper the curve. The second curve has the same v, but a larger Fc produces a smaller r'.

Fc=(mv^2)/r
What is the angular velocity of an object moving along a radius of 300m, having a centripetal acceleration of 50m/s^2?50=300ω^2 ω = +/- 0.41 rad/s The angular velocity can be obtained by using the relation ac=rω^2.What is the angle formed between the vectors of centripetal acceleration and centripetal force?0 degrees The angle between the centripetal acceleration and the centripetal force is 0 degrees. Both physical quantities are directed toward the center of the circulating body.What does it mean when motion is described as relative?It means that motion depends on the frame of reference selected. An object that is in motion by one reference frame may appear to be at rest by some other reference frame.Describe the difference between inertial frames of reference and non-inertial frames of reference.Non-inertial frames of reference are accelerating, relative to inertial frames. The key feature of inertial frames of reference is that Newton's laws apply with only forces arising from the basic physical interactions being present. Inertial frames can only move with constant velocity relative to one another. If a frame of reference is accelerating relative to an inertial frame, it is non-inertial, since an object at rest in the non-inertial frame would not have the net force on it equal to zero (a violation of Newton's 1st law), but equal to its mass times the frame's acceleration.How can you tell that an object is in motion?When there is a change in the background and position of the moving object with respect to the frame of reference. The background and the object are relative to each other. Hence, motion can occur only when both are changing with respect to each other.What is angular velocity?The angular velocity ω is the rate of change of the angle subtended by the circular path.Two forces are acting on an object. A third force is applied to the object and brings the object into translational equilibrium. Which of the following must be true about the third force? I. It is smaller than the other two forces. II. It has the same magnitude as the vector sum of the other two forces. III. It acts in the same direction as the other two forces.II only Translational equilibrium means that the vector sum of the forces on an object is zero. In order for this to occur, the third force must cancel out the other two forces. It will be the same size as the sum of the other two. This means it will be larger than either of the other two forces. It must also act in the opposite direction as the sum of the other two forces.Considering Newton's third law, why don't two equal and opposite forces cancel out each other?Because the two forces acts on different systems. The force pairs in Newton's third law do not cancel because they act on different systems.Newton's universal law of gravitationStates that every particle in the universe attracts every other particle with a force along a line joining them. The force is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.How would your weight be affected on the Moon versus when you are on the Earth?You would weigh less on the Moon than on Earth because gravity on the Moon is weaker than gravity on Earth. On the Moon, you would have the same mass as on Earth but less weight.State the law of universal gravitation in words only.Gravitational force between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.Newton's law of universal gravitation explains the paths of what?a planet moving around the Sun Gravitational force keeps planets in their respective orbits.The Cavendish experiment marked a milestone in the study of gravity. What important value did the experiment determine? Explain why this was so difficult in terms of the masses used in the apparatus and the strength of the gravitational force.The experiment measured the gravitational constant G. Gravity is a very weak force. It is only noticeable when one or both of the attractive objects are very massive, such as the Earth. Cavendish was able to measure the attraction of much less massive objects (on the order of a few kilograms).Explain why the string, pins, and pencil method works for drawing an ellipse.The string, pins, and pencil method works because the perimeter of the triangle remains constant as you are drawing the ellipse. f1m+mf2 is constant and so is f1f2. This means the perimeter of the triangle f1mf2 is constant, because the string cannot change length, it always represents the perimeter of this triangle.True or False: According to Kepler's Third Law, the ratio of the squares of the periods of any two planets about the Sun would change if the radius of one of the planets changed.False Kepler's Third Law states that the ratio of the squares of the periods of any two planets about the Sun is equal to the ratio of the cubes of their average distances from the Sun. The distance between a planet and the Sun is very different from the radius of the planet (1.5×10^8km vs. 6.37×10^3km for the Earth).In a fictitious universe involving planets orbiting a sun elliptically just like our own, Planet A has a period that is twice as long as Planet B. How much further is the average distance from Planet B to the sun compared to Planet A to the sun?1.6 The average distance from Planet B to the sun is 1.6 compared to Planet A to the sun.If you and a friend are standing side-by-side watching a soccer game, would you both view the motion from the same reference frame?No, we would both view the motion from different reference points because motion is viewed from two different points; the reference frames are similar but not the same. The motions observed are different since the reference frames are located at two different points.Identify all the non-inertial reference frames from the list below: 1. Feeling pushed forward when a car brakes 2. Standing in line and throwing a ball to your friend riding a carousel 3. Watching a cell phone be pushed off the dashboard to the right while your car turns left 4. Playing on the merry-go-round at the playground, and holding on tightly because you feel like you're about to be flung off 5. Pushing off from the ice to begin a speed skating race#1, #3, and #4 In #1 you feel as though you are being pushed forward when the car brakes, but the car is undergoing negative acceleration while you continue at the same velocity forward. In #3 and #4 the force through the turn is pushing you inward, but the velocity of the object (you or the phone) is tangential. Since no force is acting on the phone (friction not sufficient to keep it in place), it slides off the dash. Children that do not hold on tightly on the merry-go-round will also be flung off. In #2 your frame of reference is inertial, although your friend's frame of reference would be non-inertial. In #5, you are accelerating, but your immediate environment (the ice on the ground) is not so this is an inertial frame of reference.How can you express rotation angle in terms of initial angular velocity, angular acceleration, and time?The angular displacement in terms of the initial angular velocity and the angular acceleration is θ=ω0t+12αt^2.What is work?The work done on a system by a constant force is the product of the component of the force in the direction of motion times the distance through which the force acts. For one-way motion in one dimension, this is expressed in equation form as W= Fdcosθ, where W is work, F is the magnitude of the force on the system, d is the magnitude of the displacement of the system, and θ is the angle between the force vector F and the displacement vector d.Three pendulums all have the same length and start from the same height. The first pendulum is very light and has a mass of 67 g. The second pendulum has a mass of 1.5 kg. The final pendulum has a mass of 3.3 kg. Assume that the effects of air drag are negligible. Which pendulum attains the highest velocity?They will all attain the same maximum velocity.Define work for one-dimensional motion.Work is defined as the product of the force and the distance. The product of force and the distance over which the force was acting will get the work done.A friend slides a box along a flat floor to you, which you slow by applying a force at a 30° angle. Is the work you do to slow the box positive or negative? If you instead placed a book directly on top of the box as it passed you, what can you say about the work done by the book?negative work; no work done You do negative work, while the book does no work. Even though you are applying force at a 30° angle, some of the force is still done in the plane parallel to the box's motion. By slowing down the box you are applying a force in the direction opposite to the direction in which the box is traveling (its displacement), which means that you are doing negative work. When you place the book directly on top of the box, the book applies a downward force at 90° (F = mg) to the box's motion along the floor. Since the direction of the force applied by the book is perpendicular to the direction of the box, no work is done.If force and displacement are in opposite directions, will work be positive or negative?negative The work done is positive if the force and displacement have the same direction (cos⁡θ=1), and negative if they have opposite directions (cos⁡θ=−1). (Generally, if the angle between the force and the displacement is between 0∘ & 90∘, the work is positive; between 90∘ and 180∘, it's negative.)True or False: The energy increase of an object acted on only by a gravitational force is equal to the product of the object's weight and the distance the object falls.True The change in energy is the work done by gravity. The force is always the force of gravity, which is the weight of the object and is equal to mg.Farmer Joe drives a tractor for 4 hours. His tractor is pulling a heavy plow across a rocky field. Over the course of 4 hours, is the plow gaining or losing energy?More information is needed. More information is needed to compare the energy gained and lost by the plow. When work is done on a system, energy goes into it. When work is done by a system, energy is removed from it. In this example, we have several unknown quantities: how much work the tractor is doing on the plow, how much work the plow is doing on the field, how much work the field is doing on the plow (due to friction), and how much work the Earth is doing on the plow (due to gravity).Imagine a roller coaster, with an initial speed of 5m/s downhill, descends 20m in height. Now suppose the roller coaster, with an initial speed of 5m/s uphill, coasts uphill, stops, and then rolls back down to a final point 20m below the starting point. Would the final speed be the same in these two cases? Assume friction is negligible.yes When friction is negligible, the change in the kinetic energy of the roller coaster will equal the negative of the change in its potential energy, independent of the path taken. In these two cases, the initial kinetic energy and the change in height (or potential energy) are the same. Therefore the final kinetic energy, and speed, must be the same.Is it possible for the sum of kinetic energy and potential energy of an object to change without work having been done on the object? Explain.No, because the work-energy theorem states that work done on an object is equal to the change in kinetic energy, and change in KE requires a change in velocity. It is assumed that mass is constant.When a coconut falls from a tree, work W is done on it as it falls to the beach. This work is described by the equation: W=Fd=1/2mv2^2−1/2mv1^2. Identify the quantities F, d, m, v1, and v2 in this event.F is the force of gravity, which is equal to the weight of the coconut, d is the distance the nut falls, m is the mass of the coconut, v1 is 0 (the initial velocity), and v2 is the velocity with which it hits the beach.Identify three examples of an object in circular motion.an artificial satellite orbiting the Earth, a race car moving in the circular race track, and a ball tied to a string being swung in a circle around a person's head In circular motion, the body moves in a circular path generally around a second stationary body.NASA recently conducted an experiment where Scott Kelly spent a year in the International Space Station while his identical twin Mark Kelly remained on Earth. Why is this study essential to space exploration?The study allows researchers to determine how spending a year in free-fall impacts a variety of biological processes. Although Scott lived aboard the International Space Station for a year, he still experienced gravity due to the Earth's mass. However, the ISS and the astronauts inside it are constantly in free-fall from the acceleration due to gravity. Being in this state may change everything from bone density to bacteria living in the gut, so NASA wants to understand these changes before sending people on long space missions to explore or colonize other planets.Three pendulums all have the same length and start from the same height. The first pendulum is very light and has a mass of 67 g. The second pendulum has a mass of 1.5 kg. The final pendulum has a mass of 3.3 kg. Assume that the effects of air drag are negligible.They will all attain the same maximum velocity. In this problem, gravitational potential energy is converted entirely into kinetic energy at the bottom of the pendulum's swing. Since mass is on both sides of the equals sign in the formula, mass cancels and therefore does not affect the theoretical outcome.Is it possible to do work on an object without changing the kinetic energy of the object? Explain your reasoning.Yes, it is possible by raising the object to a greater height without acceleration. Work can change the kinetic energy of an object, as described by the work-energy theorem, but it can also change the potential energy of an object by raising it to a greater height at a constant speed (that is, without acceleration).After traveling along a path, a toy car's final velocity is 10m/s. If the car had traveled along the alternate path, as shown in the diagram, would its final velocity have been greater than, less than, or equal to 10m/s? Neglect friction on both paths.equal to The car has the same final velocity because the starting and ending points of both paths are the same.When a car is coasting downhill, how are its potential and kinetic energies changing?potential energy decreasing, kinetic energy increasing Kinetic energy increases as speed increases; however potential energy decreases as the height decreases. (A small amount of energy could also be dissipated in friction & air resistance.)True or False: A car runs out of gas and coasts down one hill and up another until it comes to a stop. The point at which the car stops is lower than the point at which it started coasting because part of the original potential energy has been converted to a quantity of heat, which makes the tires feel warm.true The point at which the car stops is lower than the point at which it started coasting because of the law of conservation of energy. Some of the mechanical energy was converted to thermal energy due to friction, which is why the tires felt warm.A basketball is dropped and each time it bounces, the maximum height it reaches becomes smaller and smaller. Is this an example of a system in which nonconservative forces are acting?yes The basketball is stopped by nonconservative forces each time it bounces and is slowed by air resistance. Its mechanical energy is being dissipated as thermal energy, sound, and surface distortion. The basketball is losing mechanical energy. NextWhat two quantities are crucial to quantifying the translational kinetic energy of an object?mass, speed Translational kinetic energy is equal to 1/2mv^2, where m is mass and v is velocity or speed.Why was the mirror setup essential to the Cavendish experiment?Deflecting the light beam to the scale was essential to amplify small changes in the position of the spheres due to gravity. Gravity between two small masses is very weak, so the displacement of the suspended spheres due to the attractive gravity of the larger spheres is incredibly small and difficult to measure. Cavendish's experimental apparatus relied on shining a light onto a mirror suspended along a wire that also had two spheres attached. When the suspended spheres moved in response to the gravitational force exerted by bringing the larger spheres into close proximity, they slightly twisted the wire to create a new angle between the light source and the mirror. Cavendish could measure the new position of the deflected light more easily than a change in the displacement of the suspended spheres.True or False: To calculate the speed of the pebble dropped from the cliff as it hits the ground requires you to only know the height of the cliff and acceleration due to gravity, assuming air resistance or drag is negligible.True Conservation of mechanical energy of the system gives 1/2mv2=mgh. The mass m cancels, so v=(2gh)1/2, and g and h are known.