Physics Exam 3 Review
Gravitational Potential Energy Formula
(Ug)f = (Ug)i + W
Work done in pulling a suitcase
A strap inclined upward at 45 degrees pulls a suitcase through the airport. The tension in the strap is 20 N. How much work does the tension do if the suitcase is pulled a total of 100 m at a constant speed? Known T = 20 N theta = 45 degrees distance of displacement = 100 meters find W W = Td cos (theta) = (20N)(100m)cos(45) W = 1400 J
In the impulse approximation, A. A large force acts for a very short time. B. The true impulse is approximated by a rectangular pulse. C. No external forces act during the time the impulsive force acts. D. The forces between colliding objects can be neglected.
A. A large force acts for a very short time.
Nuclear Energy, Enuclear
An enormous amount of energy is stored in the NUCLEUS, the tiny core of an atom. Certain nuclei can be made to break apart, releasing some of this NUCLEAR ENERGY, which is transformed into the kinetic energy of the fragments and then into thermal energy. The ghostly blue glow of a nuclear reactor results from high-energy fragments as they travel through water.
Starting from rest, a wheel with constant angular acceleration spins up to 25 rpm in a time t. What will its angular velocity be after time 2t? A. 25 rpm B. 50 rpm C. 75 rpm D. 100 rpm E. 200 rpm
B. 50 rpm
Gravitational Potential Energy Ug
Gravitational Potential Energy is stored energy associated with an object's HEIGHT ABOVE THE GROUND. As a roller coaster ascends, energy is stored as gravitational potential energy. As it descends, this stored energy is converted into kinetic energy.
Thermal Energy, Eth
Hot objects have more thermal energy than cold objects because the molecules in a hot object jiggle around more than those in a cold object. Thermal energy is the sum of the microscopic kinetic and potential energies of all the molecules in an object. In boiling water, some molecules have enough energy to escape the water as steam
Torque
Mechanics a twisting force that tends to cause rotation.
If an object is rotating clockwise, this corresponds to a ______ angular velocity.
NEGATIVE
Robert pushes the box to the left at constant speed. In doing so, Robert does ______ work on the box.
Positive
You awake in the night to find that your living room is on fire. Your one chance to save yourself is to throw something that will hit the back of your bedroom door and close it, giving you a few seconds to escape out the window. You happen to have both a sticky ball of clay and a super-bouncy Superball next to your bed, both the same size and same mass. You've only time to throw one. Which will it be? Your life depends on making the right choice! A. Throw the Superball. B. Throw the ball of clay. C. It doesn't matter. Throw either.
Superball!
Each of the boxes shown is pulled for 10 m across a level, frictionless floor by the force given. Which box experiences the greatest change in its kinetic energy?
The heaviest box
Chapter 9 Preview Looking Ahead: Conservation of Momentum
The momentum of these pool balls before and after they collide is the same—it is conserved. • You'll learn a powerful new before-and-after problem-solving strategy using this law of conservation of momentum.
Moment of inertia is
The rotational equivalent of mass.
total energy
The total energy is the sum of the different kinds of energies present in the system
A child slides down a playground slide at a constant speed. The energy transformation is
Ug -> Eth
Kinetic Energy Formula
W = DK = Kf - Ki
The Law of Conservation of Energy
Work done on a system represents energy that is transferred into or out of the system. This transferred energy changes the system's energy by exactly the amount of work W that was done. Writing the change in the system's energy as DELTA E, we can represent this idea mathematically as DE = W
A tow rope pulls a skier up the slope at constant speed. What energy transfer (or transfers) is taking place?
W→Ug W→Eth
Thermograph
shows heat energy that is made picture in the book shows the thermal energy made from friction as a book is dragged across the floor
work is simply energy being transferred
the joule is the unit of all forms of energy
conversions for radians and stuff
theta full circle = s/r = ((2 pi r) / r) = 2 pi rad 1 revolution = 2 pi rad = 360 degrees 1 radian = 1 rad((360/(2 pi rad)) = 57.3 degrees
I swing a ball around my head at constant speed in a circle with circumference 3 m. What is the work done on the ball by the 10 N tension force in the string during one revolution of the ball?
10J
Ball A has half the mass and eight times the kinetic energy of ball B. What is the speed ratio vA/vB?
4
Creating thermal energy by rubbing
A 0.30 kg block of wood is rubbed back and forth against a wood table 30 times in each direction. The block is moved 8.0 cm during each stroke and pressed against the table with a force of 22 N. How much thermal energy is created in this process? n = w + F = mg + F = (0.30 kg)(9.8 m/s2) + 22N + 24.9N The friction force is then fk = ukn = (0.20)(24.9 N) = 4.98 N The total displacement of the block is 2 x 30 x 8 = 4.8 m Thus the thermal energy is D Eth = fk x Dx = (4.98)(4.8m) = 24 J
Example 7.12 The torque on a flagpole
A 3.2 kg flagpole extends from a wall at an angle of 25° from the horizontal. Its center of gravity is 1.6 m from the point where the pole is attached to the wall. What is the gravitational torque on the flagpole about the point of attachment? PREPARE FIGURE 7.26 shows the situation. For the purpose of calculating torque, we can consider the entire weight of the pole as acting at the center of gravity. Because the moment arm r⊥ is simple to visualize here, we'll use Equation 7.11 for the torque. SOLVE From Figure 7.26, we see that the moment arm is r⊥ = (1.6 m) cos 25° = 1.45 m. Thus the gravitational torque on the flagpole, about the point where it attaches to the wall, is We inserted the minus sign because the torque tries to rotate the pole in a clockwise direction. -1.45 x 3.2 kg x 9.8 m/s^2 = -45 N x m
A ball rolls around a circular track with an angular velocity of 4π rad/s. What is the period of the motion?
A = 1/2 s T = 2pi / w
Conceptual Example Speed of a Bobsled after Pushing
A two-man bobsled has a mass of 390 kg. Starting from rest, the two racers push the sled for 50 m with a net force of 270 N. Neglecting friction, what is the sled'd speed at the end of the 50 m? m = 390 kg d = 50 m F 270 N vi = 0 m/s DK = Kf - Ki = W The sled's final kinetic energy is thus Kf = Ki + W Using our expressions for kinetic energy and work, we get 1/2 m(vfinal)^2 = 1/2 m(v initial)^2 + (F)(d) Because V initial = 0 the work-energy equation reduces to 1/2 m(v final)^2 = (F)(d) We can solve vf = (2Fd/m)^1/2 = 8.3 m/s SO, in conclusion 8.3 m/s, about 18 mps, seems a reasonable speed for two fast pushers to attain.
Pulling back on a bow
An archer pulls back the string on her bow to a distance of 70 cm from its equilibrium position. To hold the string at this position takes a force of 140 N. How much elastic potential is stored in the bow Fs = -kx k = F/x = 140N / 0.70m = 200 N/m Us = 1/2kx^2 = 1/2(200N/m)(0.70m)^2 = 49 J Assess When the arrow is released, this elastic potential energy will be transformed into the kinetic energy of the arrow. According to Table 10.1, the kinetic energy of a 100 mph fastball is about 150J, so 49 J of kinetic energy for a fast-moving arrow is plausible.
Using the Law of Conservation of Energy example hitting the bell
At the county fair, Katie tries her hand at the ring-the-bell attraction, as shown in Figure 10.21. She swings the mallet hard enough to give the ball an initial upward speed of 8.0 m/s. Will the ball ring the bell, 3.0 m from the bottom? 1/2 m(vf)^2 + mg(yf) = 1/2m(vi)^2 + mg(yi) let's ignore the bell for a moment and figure out how far the ball would rise if there were nothing in its way. We know that the ball starts at yi = 0m and that its speed vf at the highest point is 0 m/s. Thus the energy equation simplifies to mgyf = 1/2 mvi^2 This is easily solved for the height yf yf = (vi^2)/(2g) = (8.0 m/s)^2 / 2(9.8 m/s)^2 = 3.3m This is higher than the point where the bell sits so the ball would actually hit it on the way up So yes, it seems reasonable that Katie could swing the mallet hard enough to make the ball rise about 3m.
A light plastic cart and a heavy steel cart are both pushed with the same force for 1.0 s, starting from rest. After the force is removed, the momentum of the light plastic cart is ________ that of the heavy steel cart. A. Greater than B. Equal to C. Less than D. Can't say. It depends on how big the force is.
B. Equal to
The total momentum of a system is conserved A. Always. B. If no external forces act on the system. C. If no internal forces act on the system. D. Never; it's just an approximation.
B. If no external forces act on the system.
An object's angular momentum is proportional to its A. Mass. B. Moment of inertia. C. Kinetic energy. D. Linear momentum.
B. Moment of inertia.
In an inelastic collision, A. Impulse is conserved. B. Momentum is conserved. C. Force is conserved. D. Energy is conserved. E. Elasticity is conserved.
B. Momentum is conserved
Which factor does the torque on an object not depend on? A. The magnitude of the applied force B. The object's angular velocity C. The angle at which the force is applied D. The distance from the axis to the point at which the force is applied
B. The object's angular velocity
Kinetic Energy of a Bicycle
Bike 1 has a 10kg frame and 1 kg wheels Bike 2 has a 9 kg frame and 1.50 kg wheels Both bikes thus have the same 12.0 kg total mass. What is the kinetic energy of each bike when they are ridden at 12.0 m/s? Model each wheel as a hoop of radius 35.0 cm. Total Kinetic Energy of the Bike is K = Kframe + 2Kwheel = 1/2mv^2 + 2Mv^2 K1 = 1/2(10kg)(12 m/s)^2 + 2(1kg)(12 m/s)^2 K1 = 1010 J K2 = 1/2(9kg)(12m/s)^2 + (1.5kg)(12 m/s)^2 K2 = 1080J The kinetic energy of the second bike is higher than the first bike. Radius of the wheel was not necessary for the calculation of this problem. Cyclists must convert their internal chemical energy into the kinetic energy of the bikes. Racing cyclists want to preserve as little energy as possible. Having lighter tires makes them easier to move. Shaving weight of the wheels is more useful than taking weight off the frame
A mosquito and a truck have a head-on collision. Splat! Which has a larger change of momentum? A. The mosquito B. The truck C. They have the same change of momentum. D. Can't say without knowing their initial velocities.
C!
A net torque applied to an object causes A. A linear acceleration of the object. B. The object to rotate at a constant rate. C. The angular velocity of the object to change. D. The moment of inertia of the object to change.
C. The angular velocity of the object to change.
Impulse is A. A force that is applied at a random time. B. A force that is applied very suddenly. C. The area under the force curve in a force-versus-time graph. D. The time interval that a force lasts.
C. The area under the force curve in a force-versus-time graph.
The fan blade is slowing down. What are the signs of ω and α? A. ω is positive and α is positive. B. ω is positive and α is negative. C. ω is negative and α is positive. D. ω is negative and α is negative. E. ω is positive and α is zero.
C. ω is negative and α is positive.
Chapter 7 Bllsht. Goal
Chapter Goal: To understand the physics of rotating objects. • To start something moving, apply a force. To start something rotating, apply a torque, as the sailor is doing to the wheel. • You'll see that torque depends on how hard you push and also on where you push. A push far from the axle gives a large torque. • In this chapter, you'll learn to use angular velocity, angular acceleration, and other quantities that describe rotational motion.
The fan blade is speeding up. What are the signs of ω and α? A. ω is positive and α is positive. B. ω is positive and α is negative. C. ω is negative and α is positive. D. ω is negative and α is negative.
D. ω is negative and α is negative.
Work for thermal energy
DELTA Eth = W W = FDx = fkDx
Elastic/Spring Potential Energy, Us
Elastic potential energy is energy stored when a spring or other elastic object, such as this archer's bow, is stretched. This energy can later be transformed into the kinetic energy of the arrow.
Chemical Energy, Echem
Electric forces cause atoms to bind together to make molecules. Energy can be stored in these bonds, energy that can later be released as the bonds are rearranged during chemical reactions. When we burn fuel to run our car or eat food to power our bodies, we are using chemical energy.
A light plastic cart and a heavy steel cart are both pushed with the same force for a distance of 1.0 m, starting from rest. After the force is removed, the kinetic energy of the light plastic cart is ________ that of the heavy steel cart.
Equal to
When a spring is stretched by 5cm, its elastic potential is 1 J. What will its elastic potential energy be if it is compressed by 10 cm?
I'm PRETTY sure it's -2 J ****
Try It Yourself: Water Balloon Catch
If you've ever tried to catch a water balloon, you may have learned the hard way not to catch it with your arms rigidly extended. The brief collision time implies a large, balloon bursting force. A better way to catch a water balloon is to pull your arms in toward your body as you catch it, lengthening the collision time and hence reducing the force on the balloon.
Racing up a skyscraper
In the Empire State Building Run - Up, competitors race up the 1576 steps of the Empire State Building, climbing a total vertical distance 320 meters. How much gravitational potential energy does a 70 kg racer gain during this race? Preparation we choose y = 0m and hence Ug = 0J at the gound floor of the building. Solve At the top, the racer's gravitational potential energy is Ug = mgy = (70kg)(9.8 m/s2)(320 meters) = 2.2x10^5 J
Example 7.16 Angular acceleration of a falling pole
In the caber toss, a contest of strength and skill that is part of Scottish games, contestants toss a heavy uniform pole, landing it on its end. A 5.9-m-tall pole with a mass of 79 kg has just landed on its end. It is tipped by 25° from the vertical and is starting to rotate about the end that touches the ground. Estimate the angular acceleration. PREPARE The situation is shown in FIGURE 7.37, where we define our symbols and list the known information. Two forces are acting on the pole: the pole's weight which acts at the center of gravity, and the force of the ground on the pole (not shown). This second force exerts no torque because it acts at the axis of rotation. The torque on the pole is thus due only to gravity. From the figure we see that this torque tends to rotate the pole in a counterclockwise direction, so the torque is positive.
Conservative Forces
Interactions forces that can store useful energy are called CONSERVATIVE FORCES. The name comes from the important fact that, as we'll see, the mechanical energy of a system is conserved when only conservative forces act. Gravity and elastic forces are conservative forces, and later we'll find that the electric force is a conservative force as well.
Rank in order, from largest to smallest, the gravitational potential energies of the balls.
Just know the higher an object is, the higher the gravitational potential is The direction, whether upwards or downwards, is irrelevant.
Kinetic Energy, K
Kinetic energy is the energy of motion. All moving objects have kinetic energy. The heavier an object and the faster it moves, the more kinetic energy it has. The wrecking ball in this picture is effective in part because of its LARGE kinetic energy.
kinetic rotational energy
Krot = 1/2(m1)(r1)^2(w)^2 + 1/2(m2)(r2)^2(w)^2 + ...
Friction is a ______________ force.
NONCONSERVATIVE When two objects interact via friction force, energy is not stored. It is usually transformed into thermal energy.
The angular displacement of a rotating object is measured in
RADIANS
Rotational Dynamics
Rotational Dynamics. We have defined the angular displacement, angular speed and angular velocity, angular acceleration, and kinetic energy of an object rotating about an axis. ... A spinning or revolving object has angular velocity ω.
Rotational motion
Rotational motion is the motion of objects that spin about an axis.
Work done in pushing a crate
Sarah pushes a heavy crate 3.0 m along the floor at a constant speed. She pushed with a constant horizontal force of magnitude 70N. How much work does Sarah do on the crate? F = 70N d = 3.0m velocity is constant Find W W = Fd W = (70N)(3.0m) W = 210 J
Tangential Acceleration • Tangential acceleration is the component of acceleration directed tangentially to the circle. • The tangential acceleration measures the rate at which the particle's speed around the circle increases.
Tangential Acceleration • Tangential acceleration is the component of acceleration directed tangentially to the circle. • The tangential acceleration measures the rate at which the particle's speed around the circle increases. • Tangential acceleration is the component of acceleration directed tangentially to the circle. • The tangential acceleration measures the rate at which the particle's speed around the circle increases.
Example 7.18 Starting an airplane engine
The engine in a small air-plane is specified to have a torque of 500 N ⋅ m. This engine drives a 2.0-m-long, 40 kg single-blade propeller. On start-up, how long does it take the propeller to reach 2000 rpm? The propeller can be modeled as a rod that rotates about its center. The engine exerts a torque on the propeller. FIGURE 7.38 shows the propeller and the rotation axis.
the work-energy equation
The total energy of a system changed by the amount of work done on it: DE = DK + DUg + DUs + DEth + DEchem + ... = W
Law of Conservation of Energy
The total energy of an isolated system remains constant: DE = DK + DUg + DUs + DEth + DEchem + ... = 0 The law of conservation of energy is similar to the law of conservation of momentum. A system's momentum changes when an external force acts on it, but the total momentum of an isolated system does not change. Similarly, a system's energy changes when external forces do work on it, but the total energy of an isolated system does not change.
Lifting a book increases the system's gravitational potential energy.
The work done is W = Fd, where d = Dy = yf -yi is the vertical distance that the book is lifted. From the free body diagram, we see that F = mg. f this problem
Gravitational Potential Energy
To find an expression for gravitational potential energy, let's consider the system of the book and earth. The book is lifted at a constant speed from its initial position at yi to a final heigh yf. The lifting force of the hand is external to the system and so does work W on the system, increasing its energy.
Rotational Kinematics
Total linear acceleration vector is defined by vector sum. Magnitude of total linear acceleration. Angle between linear acceleration and linear velocity vectors. Relation between angular acceleration and angular velocity. Kinematic equation for rotation.
A skier is gliding down a gentle slope at a constant speed. What energy transformation is taking place?
Ug→Eth
A child is on a playground swing, motionless at the highest point of his arc. What energy transformation takes place as he swings back down to the lowest point of his motion?
Ug→K
Rotational Kinetic Energy
We've found an expression for the kinetic energy of an object moving along a line or some other path. This energy is called translational kinetic energy Consider now an object rotating about a fixed axis, such as a windmill blade. Although the blade has no overall translational motion, each particle in the blade is moving and hence has kinetic energy. Adding up the kinetic energy for all the particles that make up the blade, we find that the blade has rotational kinetic energy, the kinetic energy due to rotation.
Energy Transformations
We've seen that all systems contain energy in many different forms. But if the amounts of each form of energy never changed, the world would be a very dull plave. What makes the world interesting is that ENERGY OF ONE KIND CAN BE TRANSFORMED INTO ENERGY OF ANOTHER KIND. The gravitational potential energy of the roller coaster at the top of the track is rapidly converted into kinetic energy as the coaster descends; the chemical energy of gasoline is transformed into the kinetic energy of your moving car.
A crane lowers a girder into place at constant speed. Consider the work WgWg done by gravity and the work WTWT done by the tension in the cable. Which is true?
Wg>0Wg>0 and WT<0
Potential Energy
When two or more objects in a system interact, it is sometimes possible to STORE energy in the system in a way that the energy can be easily recovered. For instance, the earth and a ball interact by the gravitational force between them. If the ball is lifted up into the air, energy is stored in the ball + earth system, energy that can later be recovered as kinetic energy when the ball is released and falls. Similarly, a spring is a system made up of countless atoms that interact via their atomic "springs". If we push a box against a spring, energy is stored that can be recovered when the spring later pushes the box across the table. This sort of stored energy is called potential energy since it has the POTENTIAL to be converted into other forms of energy, such as kinetic or thermal.
Speed at the bottom of a water slide
White at the county fair, Katie tries the water slide. The starting point is 9.0m above the ground. She pushes off with initial speed of 2.0 m/s. If the slide is frictionless, how fast will Katie be traveling at the bottom? y initial = 9 v initial = 2 m/s find velocity final yf = 0m Conservation of mechanical energy gives Kf + (Ug)f = Ki + (Ug)i or 1/2 m(vf)^2 + mg(yf) = 1/2m(vi)^2 + mg(yi) considering yf = 0m, we can reduce the formula to 1/2 m(vf)^2 = 1/2m(vi)^2 + mg(yi) we are solving for vf vf = (vi^2 + 2gyi)^1/2 vf = ((2.0 m/s)^2 + 2(9.8 m/s)^2(9.0m))^1/2 = 13 m/s
Energy
is the sum of all the different energies present in the system E = K + Ug + Us +Eth + Echem + ...
Isolated System
one that is separated from its surrounding environment in such a way that no energy is transferred into or out of the system. This means that NO WORK IS DONE ON THE SYSTEM. The energy within the system may be transformed from one form into another, but it is a deep and remarkable fact of nature that, during these transformations, the total energy of an isolated system - the sum of all the individual kinda of energy - remains CONSTANT. We say that THE TOTAL ENERGY OF AN ISOLATED SYSTEM IS CONSERVED.
displacement/work trends
w = (F)(d) The larger the displacement, the greater the work done. The stronger the force, the greater the work done
Note the work, unlike momentum...
work is scalar quantity, meaning it has a MAGNITUDE but NOT a direction.
Impulse
• A collision is a short-duration interaction between two objects. • During a collision, it takes time to compress the object, and it takes time for the object to re-expand. • The duration of a collision depends on the materials. • When kicking a soccer ball, the amount by which the ball is compressed is a measure of the magnitude of the force the foot exerts on the ball. • The force is applied only while the ball is in contact with the foot. • The impulse force is a large force exerted during a short interval of time.
Section 7.5 Rotational Dynamics and Moment of Inertia
• A torque causes an angular acceleration. • The tangential and angular accelerations are
Gravitational Torque and the Center of Gravity
• An object that is free to rotate about a pivot will come to rest with the center of gravity below the pivot point. • If you hold a ruler by one end and allow it to rotate, it will stop rotating when the center of gravity is directly above or below the pivot point. There is no torque acting at these positions.
Gravitational Torque and the Center of Gravity
• Gravity pulls downward on every particle that makes up an object (like the gymnast). • Each particle experiences a torque due to the force of gravity. • The gravitational torque can be calculated by assuming that the net force of gravity (the object's weight) acts as a single point. • That single point is called the center of gravity.
Constraints Due to Ropes and Pulleys
• If the pulley turns without the rope slipping on it then the rope's speed must exactly match the speed of the rim of the pulley. • The attached object must have the same speed and acceleration as the rope.
Total Momentum
• If there is a system of particles moving, then the system as a whole has an overall momentum. • The total momentum of a system of particles is the vector sum of the momenta of the individual particles:
Impulse cont'd
• It is useful to think of the collision in terms of an average force Favg. • Favg is defined as the constant force that has the same duration Δt and the same area under the force curve as the real force. • Impulse has units of N ⋅ s, but N ⋅ s are equivalent to kg ⋅ m/s. • The latter are the preferred units for impulse. • The impulse is a vector quantity, pointing in the direction of the average force vector:
Rolling Motion
• Rolling is a combination motion in which an object rotates about an axis that is moving along a straight-line trajectory. • The figure above shows exactly one revolution for a wheel or sphere that rolls forward without slipping. • The overall position is measured at the object's center. • Since 2π/T is the angular velocity, we find v = wr • This is the rolling constraint, the basic link between translation and rotation for objects that roll without slipping.
Momentum and the Impulse-Momentum Theorem
• The average force needed to stop an object is inversely proportional to the duration of the collision. • If the duration of the collision can be increased, the force of the impact will be decreased. • The spines of a hedgehog obviously help protect it from predators. But they serve another function as well. If a hedgehog falls from a tree a not uncommon occurrence—it simply rolls itself into a ball before it lands. Its thick spines then cushion the blow by increasing the time it takes for the animal to come to rest. Indeed, hedgehogs have been observed to fall out of trees on purpose to get to the ground!
Impulse Force
• The effect of an impulsive force is proportional to the area under the force-versus-time curve. • The area is called the impulse J of the force.
Conservation of Momentum
• The forces acting on two balls during a collision form an action/reaction pair. They have equal magnitude but opposite directions (Newton's third law). • If the momentum of ball 1 increases, the momentum of ball 2 will decrease by the same amount.
The Impulse Approximation
• The impulse approximation states that we can ignore the small forces that act during the brief time of the impulsive force. • We consider only the momenta and velocities immediately before and immediately after the collisions.
Looking Ahead: Momentum and Impulse
• The impulse delivered by the player's head changes the ball's momentum. • You'll learn how to calculate this momentum change using the impulse-momentum theorem.
Calculating the Position of the Center of Gravity
• The torque due to gravity when the pivot is at the center of gravity is zero. • We can use this to find an expression for the position of the center of gravity.
Law of Conservation of Momentum
• There is no change in the total momentum of the system no matter how complicated the forces are between the particles. • The total momentum of the system is conserved • Internal forces act only between particles within a system. • The total momentum of a system subjected to only internal forces is conserved.
Chapter 9 Preview Looking Ahead: Impulse
• This golf club delivers an impulse to the ball as the club strikes it. • You'll learn that a longer-lasting, stronger force delivers a greater impulse to an object.
Starting from rest, a marble first rolls down a steeper hill, then down a less steep hill of the same height. For which is it going faster at the bottom?
Same speed at the bottom of both hills