Physics 2

What are the indicators that work has changed?

1. Change in velocity 2. Change in height 3. Change in position of mass/planets/etc. 4. Change in position of a charge 5. Compression of a spring 6. Friction 7. Air Resistance

What are the 4 equations relate to Power? (Priority matters!)

1. P= delta of Energy/ time 2. P= W/t 3. P= Fdcos(theta)/t 4. Pi (instantaneous power)=Fvcos(theta)

What is the potential energy equation for the followings: Kinetic energy, gravitational, elastic, electric, capacitor.

1/2mv2 -Gmm/r or mgh 1/2kx2 Kqq/r or qEd or qV 1/2QV or 1/2CV2 or 1/2Q2/C

What is the tension in a rope being pulled from opposite ends with identical forces of 50N?

50N

Car collision problems are frequently used to test your understanding of impulse. Consider the following situation: Air bag increase the time during which the driver comes to rest during a collision. How or why would this prevent injury?

According to Impulse = F(avg) x t, if time increases force must decrease. Less force experienced by the driver would result in less injury. Impulse must remain the same because this is simply the difference between the initial and final momentum—which will not be impacted by the presence or absence of the air bag.

Talk about the equation in inelastic collisions.

Always use conservation of momentum. YOU MUST USE SIGNS. Any velocity vector to the left or down must be given a negative sign. m1+v1=m2+v2 The term "perfectly inelastic" indicates that two objects collided and then stuck together. If they moved off in one direction or the other after the collision, they did so as a single unit with mass equal to the sun of their individual masses. For perfectly inelastic collisions, the equation becomes: m1v1+m2v2= (m1+m2)/v3

For the MCAT, what assumption can you make when you see the term angular frequency?

Angular frequency means the same thing as angular velocity in the MCAT although angular frequency is technically the magnitude of angular velocity.

Define system that is not in equilibrium.

Any problems where the object in question has a non-zero acceleration, or net force, is a non equilibrium problem. (a.k.a "translational acceleration problems")

When you stand on the edge of a jumping board above a pool, you know that the higher the jumping board is the more pain you will experience when you dive into that awesome pool. How might you explain this in physics sense? (hint: potential energy!) How about when the situation involves two objects very far away and not on earth? (Like you're being dropped from space toward someone that is being shoot up in space? Can you come up with the universal potential energy equation?

Anything with mass can have gravitational potential energy and gravitational energy would be the only force you experience (assume no air resistance) when you dive into the pool. From experience, you know that the higher you are the more pain there is waiting for you so from this, we can intuitively conclude that the potential energy (will be convert to kinetic energy when you jump) must be proportional to the height. Gravitational force also involves mass and g, put it all together the equation PE=mgh is easily created. The situation involves two objects can be easily solved using the universal law of gravitation (since it's always true everywhere) the equation is PE=-Gm1m2/r (The negative sign is necessary because without it the formula would predict that as r increases PE decreases. If you have an even basic concept of PE you will see that cannot be. A rock gets more PE as it gets farther from the center of the earth, not less. The negative makes it so that as r increases we get a smaller negative number, which is actually a larger value.)

As the angle of incline of a plane increases, what happens to the value of a? What happens to the value of sin theta and cos theta? What happens to the normal force and to the force down the plane? What are the minimum and maximum values for acceleration down an inclined plane?

Because the acceleration down a plane is directly related to the sine of the angle, the greater the angle the closer the sine of the angle will be to one. Therefore, the larger the angle the closer the acceleration will be to 9.8m/s2. The normal force is related to the cosine of the angle, so as the angle increase this value gets closer to zero. Therefore, as the angle increases the normal force decreases. The force down an inclined plane is also related to the sine of the angle, so it too will increase as the angle of incline increases. The theoretical maximum incline is 90 degrees where acceleration would be 9.8 m/s2 and the minimum would be a plane with no angle of incline, where acceleration down the plane would be zero.

As the angles of incline of a plane increases, what happens to the value of a? What happens to the value of sin theta and cos theta ? What happens to the normal force and to the force down the plane? What are the minimum and maximum values for acceleration down an inclined plane?

Because the acceleration down a plane is directly related to the sine of the angle, the greater the angle the closer the sine of the angle will be to one. Therefore, the larger the angle the closer the acceleration will be to 9.8m/s2. The normal force is related to the cosine of the angle,so as the angle increase this value gets closer to zero. Therefore, as the angle increases the normal force decreases. The force down an inclined plane is also related to the sine of the angle,so it too will increase as the angle of incline increases. The theoretical maximum incline is 90 degrees where acceleration would be 9.8 m/s2 and the minimum would be a plane with no angle of incline, where acceleration down the plane would be zero.

What is the other force component that together with centripetal force supports Newton's 3rd law of physics?

Centrifugal force is the other component along with centripetal force that together forms an action-reaction pair. It is equal in magnitude and has opposite direction as centripetal force.

What should you think when you see centripetal force?

Centripetal forces are always caused by some other responsible force (i.e, friction, tension, gravitational force, etc.) "Centripetal force" is really just a categorical name for all forces that act to pull things into circular motion.

What is the equation for thermal expansion? Is there any exception to this rule?

Change in length (delta L)= a x L(initital) x delta T (where a= expansion coefficient) Water is the exception for this rule. While in the liquid phase, it behaves as the rule would predict (i.e volume increases when temperature raises and decreases as temperature falls). However, when water is approaching a few degrees within its freezing point, ice crystals begin to form and thus the volume is expanding.

Describes the energy transformation that take place as a rocket ignites and combusts its rocket fuel, launches into the air, rise to a max height, then falls back to earth and strikes the ground.

Chemical energy stored in the bonds of the rocket fuel is transferred into kinetic and gravitational potential energy as the rocket rises. If air resistance is taken into account some energy will also be dissipated as heat due to drag. Gravitational PE reaches a max at the max height and is then transferred back into kinetic energy (and heat if considering air resistance) as the rocket falls back to earth. When the rocket strikes the ground its kinetic energy is transferred into heat energy.

Name the type of energy possessed or created by each of the following: an explosion, a chemical reaction, a collision, any moving object, any object with height, a spring, a battery, two positive charges, water in a tank.

Chemical energy turns into heat energy and the kinetic energy of any flying debris; In a chemical reaction chemical energy is transferred between reactants and products—in an exothermic reaction heat is released; in a collision the KE of the objects before the collision is transferred into heat energy used to create damage/deformity/etc.; any moving object has kinetic energy; any object with height has gravitational potential energy; a spring stores elastic potential energy; a battery stores chemical energy; two separated charges contain electrical potential energy; water in a tank has gravitational potential energy and kinetic energy of the molecules.

What should you think of energy as?

Energy is the capacity to do work.

What are the two equations for hydraulic lifts knowing that the two heights of the plunger in the system are inversely proportional and same for area.

F=mg(h1/h2) F=mg (A1/A2) (h1= distance traveled by plunger, h2= distance traveled by small plunger) (A1= cross sectional area of small plunger A2= cross sectional area of large plunger)

True or False? 1) A ball moving with twice the kinetic energy can compress a spring twice as far 2) A ball moving with three times the velocity can compress a spring three times as far.

False. Whatever KE the ball has will be transferred completely into elastic PE so we can write KE = 1/2kx2. We see that KE is related to the square of x, so it will require four times the kinetic energy to compress the spring twice as far. 2) True. We can also write 1/2mv2 = 1/2kx2. This shows that velocity and the distance of compression, x, both have a square and are therefore directly and linearly related.

For a pulley, it should be intuitive that the more ropes you have (Ropes that actually lift the mass!) the less force you will need to lift the object. Using this information, gived the equation for force of pulley machine.

Fm=mg / # of vertical ropes (a rope is counted only when it lift the object!)

What is the relationship between the two lever arms in a lever machine? Come up with the overall equation

Fm=mg(L1/L2) L1=long/effort arm and L2= short/load arm

Knowing intuitively that you need more force to push an object higher on a ramp and that the length of the rampe is inversely proportional with the force. What is the force equation for a ramp machine?

Fm=mg(h/d) It should be note that when a problem states a 5 meter long ramp or a ramp that is 5 meter, they are referring to the hypotenuse.

Which way does the friction force vector point for a car driving east down a straight road? For a skidding car with locked brakes? For a gecko climbing a wall? For a car driving around a corner?

For a car driving east the friction vector between the road and the tires also points east. The tendency of the tires is to slide past the road toward the back of the car and friction opposes that sliding. When a car locks its wheels, however, friction points opposite the direction of the car's tendency to slide forward. Friction would point up the wall for a gecko because the geckos hands would tend to slide down the wall. For a car going around a bend momentum makes it want to continue tangent to the circle but friction points toward the center of that circle keeping it in circular motion (an example of a centripetal force).

What is the concept of conservation of relative speed? Why must the collision be elastic?

For completely elastic collisions ONLY, the relative speed before will equal the relative speed after. For the relative speed to be conserved, there must be no loss of energy. The kinetic energy associated with the two masses traveling at their initial velocities before the collision must be available after the collision. This is in addition to the conservation of momentum. Combined these two conservations results in the curious result that the relative speed is conserved. (The relative velocities differ in sign.) In an inelastic collision energy is not conserved. Some energy goes to creating breakage, deformity, etc. and therefore maintaining the relative speed is no longer possible.

How would you relate the concept of "field" and "gravity" together?

Gravity can be thought as a field that exists between any two objects with mass. Field can be thought as an invisible influence that is capable of exerting force on a charge or mass.

When will objects exchange velocities through collision?

If the objects are of equal mass and the collision is perfectly elastic, the two objects will exchange velocities before and after. For equal masses there are two cases -- one ball moving and collides with a ball at rest, and both balls moving and collide. The first case where the balls exchange velocities clearly conserves both momentum and kinetic energy. The initial KE and momentum of the moving ball are simply transferred to the second ball. There is no doubt then that both momentum and KE are conserved. The second case can be understood from the first case. Imagine a reference frame that is moving along with the second (moving) ball. In that reference frame we are back to the first case again where the second ball is at rest. As we've seen, the first case conserves both momentum and energy, so it does also in the second case.

How do we define impulse? Using this information, can you come up with its equations?

Impulse is defined as the change in momentum. Using this we can say that Impluse(J)=delta of p. Looking at the momentum equation, we can see that the only variables that can change is the velocity so we can come up with another equation that is J=m x delta v Substitute v with a x t (acceleration and time) we can come up with the last equation which is J=F(average) x t

In what kind of collision where both kinetic energy and momentum is conserved? What collision where only one of these is conserved? Is it possible for two objects two exchange velocities through a collision?

In an elastic collision, both kinetic and momentum is conserved. Only momentum is conserved in an inelastic collision due to the mass change. Two object can exchange velocities if they are of equal mass and involved in a perfectly elastic collision.

Describe electric potential charge,then think about the relationship between potential energy and distance (higher or lower with increasing distance?), the two charges and potential energy, come up with the overall equation?

In the electrical case, a charge will exert a force on any other charge and potential energy arises from any collection of charges. Intuitively, it should be clear that the effects of energy diminish over long distance so they should have an inversely proportional relationship. Between the two charges, it is reasonably to think that when you increase the charge of one/or both that the repulsion force would increase thus increase the kinetic energy. The two charge should have a directly proportional relationship with potential energy. Overall equation is U=kq1q2/r (k= Coulomb's constant 9 x10^9 N.m^2/C^2

Talk about solving system on an inclined plane that is NOT in equilibrium.

In this special case it is best to use altered coordinate system. Place the "T" on your scratch paper. Call all forces acting down the plane "down forces" and all forces acting up the plan "up forces". The force down the plane due to gravity is always F= mg sin theta. The force of friction is always parallel to the plane opposite the direction of motion. There will never be acceleration perpendicular to the plane so you can ignore those forces.

How would you solve equilibrium on an inclined plane?

In this special case, it is best to use an altered coordinate system. Place the T on your scratch paper. Call all forces acting down the plane "down forces" and all forces acting up the plane "up forces" The force down the plane due to gravity is always F=mgsin theta. The force of friction is always parallel to the plane opposite the direction of motion. There will never be acceleration perpendicular to the plane so you can ignored these forces.

If an object is deformed during a collision it must have undergone which type of collisions?

Inelastic.

What is the requirement for an object that is in rotational equilibrium?

It must not be rotating or it must rotate at a constant angular velocity.

What is the 1st law of thermodynamic?

It states that the change in energy is equal to the sum of work and heat or delta E= W + Q (work= energy via force, heat=energy transfer, flow from hot to cold)

What is kinetic energy? What is the kinetic energy relationship with velocity? What is the overall equation?

Kinetic energy is energy of motion. The kinetic energy of an object is the energy it possesses because of its motion. Kinetic energy is an expression of the fact that a moving object can do work on anything it hits; it quantifies the amount of work the object could do as a result of its motion. Kinetic energy is directly proportional to the square of velocity. The overall equation is K= 1/2 m x v^2

With the simplest equation of torque T=F.l (lever arm), can you come up with the two other variations?

Lever arm can be calculate with the following equation l=rsin(theta) where r=the distance between the force and point of rotation. Another variation of the torque equation is easily created if you assume weight is the only force that cause a net torque. In that case, T=mg.l

A quick note about heat transfer.

MCAT expects you to know that non-conservative forces such as friction dissipates some energy as heat , leaving less energy available to do work (e.g, the velocity of a ball at the bottom of an inclined plane is less with friction than without. This is because the energy dissipated to heat was not available to increase the KE of the ball) However, this use of the word heat refers to an increase in the internal energy of the molecules, not the "heat transfers" Q that is included in the 2st law of thermodynamics delta E = W + Q

What is machine used for and what it is NOT used for, in other words, what is the thing that it can't do?

Machine reduce the amount of force necessary to perform a given amount of work. It cannot and will never reduce or change the amount of work!

In what situation where mechanical energy is conserved? How would you explain this using the equation for mechanical energy?

Mechanical energy is conserved when there is an absence of non-conservative force such as friction, drag, air resistance, etc. We know that the equation of mechanical energy is ME=KE+PE so if there is a presence of non-conservative forces, it will affect the kinetic and potential energy and thus change the mechanical energy( i.e not conserved anymore)

What is momentum? What critical fact you must know about momentum in an isolated system? What system is not consider to be isolated?

Momentum is inertia increased by velocity. Momentum is ALWAYS conserved in an isolated system. System is not considered to be isolated when there are external forces acting upon it (forces can be from any sources such as friction, human, wind, air, etc.)

How would you solve centripetal motion problems?

Most of these problems can be solved by setting the general centripetal force equation given above equal to the equation for whatever force is actually causing the force in that situation. For example, to calculate the velocity of a satellite, we would set mv^2/r equal to the equation for the force due to gravity m1v^2/r=Gm1m2/r^2

What are static and dynamic equilibrium?

Objects at rest are in static equilibrium; objects moving at a constant velocity are in dynamic equilibrium. In both cases the net force experienced by the object must be zero.

What is the equation for angular velocity knowing that it is relate to the tangential velocity and the radius? Using the knowledge you have about circular motion, can you come up with the other equation for angular velocity? What is the unit of angular velocity?

Omega or angular velocity= v/r (v=tangential velocity, r is the radius of the circle) We know that angular velocity is a component of circular motion. It is defined as the rate of angle change over time. Using this, the equation omega=2pi.f should come to mind (f=frequency) The unit of angular velocity is rad/s

What causes friction on a microscopic level? On the molecular level?

On the microscopic level even the very smoothest surface is actually extremely rough. The peaks, valleys, protrusions , etc. of the two surfaces literally collide with one another. On the molecular level, the electron clouds of atoms do occupy real space. When we try to get them to occupy the same space or bring them very close together they will repel one another. This is why what we will just call "contact forces" for the MCAT are often classified as an example of electromagnetic forces. This interaction is actually due to repulsion between electrons.

What portion of the movement of a pendulum represents one cycle? What value must be low for a pendulum to exhibit Simple Harmonic Motion? Why does displace for the pendulum gradually decrease over time?

One cycle for a pendulum would be movement of the bob from one side to the other and then back to the first side. Many students make an error in thinking that one swing to the other side would be one cycle. The clue is that the action must cycle or repeat. When the bob is swinging back it is doing something it has not done before. Once it gets back to the starting point it is then repeating the same motion, and the time to do this is one period. The angle of displacement must be small for SHM. The reason the pendulum will not continue oscillating and reaching the same height is because of nonconservative forces such as air resistance. Energy lost to these sources is not available to the bob so it cannot travel to its original height.

Remember back to the good old days in physics 1 lab, in your final lab exam you have to set up a oscillatory motion experiment, from observation and intuition you know that a heavier weight would stretch the spring more and that the spring constant/its stiffness also plays a role in how long it will stretch. Using these information, can you come up with the the equation for the period of a mass on a spring? Now using that equation you just come up with, how about the period of a pendulum? (Hint: they're quite similiar)

Period is the time it takes for the object to complete one cycle of motion. Using the provided information, it should be easy to come up with the equation T=2pi sqrt(m/k) with mass directly proportional to the period and spring constant inversely proportional to the period. For a pendulum, the two variables involved are the length of the pendulum and acceleration of gravitation/g. Therefore, the equation is T=2pi sqrt(L/g)

What is reverse collision? Name a few exmaples

Reversible collision is the situation where two objects initially are together become separated after the collision. Examples: components of fireworks, radioactive decay, etc.

What is the equation for acceleration down an incline plane?

Since the force parallel to the incline plane has the equation of F=mgsin theta we can see that the acceleration has the equation of gsin theta!

How would one solve non equilibrium problem?

Solve these problems in the same way you would an equilibrium problem, but add "ma" to the losing side. This is because we are pretending that the net forces acting from either side are equal. In reality, because the object is accelerating we know there is a net force and they are not equal. That net force is what causes the object to accelerate. By adding ma to the weaker side we are making them equal again. We use ma instead of using a variable like Fnet simply because we usually know the mass of the object and the acceleration of the system, but don't necessarily know the net force.

What are the differences between static friction and kinetic friction? Is there any similarities? Using these information, can you come up with the equation for the forces of these frictions?

Static friction is caused from the interlocking of the irregularities of two surfaces and it is opposing sliding motion. In other words, it can be thought as the limit threshold for sliding to occur (must exceed static friction) so you only have static friction when no sliding is occured. Kinetic friction is caused from the interactions between two surfaces happens along with sliding motion. This can be though as intermolecular attractions during the sliding motion between the surfaces. Both of these frictions have what is called coefficient of friction (static value for this coefficient is generally larger) and the normal force is involved since it is the force that press up against one of the surface, therefore the equation must be Force of friction=coefficient of friction x normal force Force of friction=coefficient of friction x mgcos(theta)

What are the two equations for solids that you need to know? How are these two properties related to each other?

Stress= Force/Area and Strain=change in dimension/original dimension. These two properties are combined into the moduli of elasticity which is ME=stress/strain.

What are some examples for equilibrium?

Terminal velocity, constant velocity, objects at rest, balanced fulcrums or boards hanging from strings, objects floating in liquids.

In what direction does the angular velocity vector point?

The angular velocity vector points along the axis of rotation. Use the right hand rule to decide if it is up or down. Curl the fingers of your right hand around the axis of rotation such that your fingers point in the direction of rotation and your thumb will be pointing in the direction of the vector.

Talk about internal energy and heat energy.

The energy of the internal vibrations and random motions of molecules and/or atoms within a system. Non-conservative forces such as friction or drag acting on a moving object result in the transfer of kinetic energy into internal energy. Heat energy is energy dissipated as heat. On the MCAT, this is usually heat dissipated from a collision, or from a current carrying wire. The terms "heat energy" and "internal energy" are used almost interchangeably.

What are the equation for acceleration in circular motion? Using this information, come up with the equation for the centripetal force?

The equation for acceleration in circular motion is a=v^2/r and with this information, it is easy to come up with the centripetal force equation using Newton's 2nd law. The centripetal force equation is Fc= mv^2/r

When do you need to utilize the equation T=Frsin theta for calculating torque?

The force applied is not perpendicular to r. In most fulcrum and board-string problems the forces do act at 90 degrees, hence sin(90degrees)=1 and T=Fr.

Important note about the universal law of gravitation equation.

The formula F=gmm/r^2 gives the force due to gravity NOT gravity itself. Gravity itself, usually called "gravity", "the strength of gravitational girdled", or "acceleration due to gravity" is represented by lowercase g and is describe the formula g =Gm/r^2

Why does V = Squrt (2gh) work for either falling bodies or a mass on an inclined plane?

The formula V = √2gh is derived from conservation of energy by equating mgh to 1/2mv2 and solving for v. As long as friction, air resistance, etc. are ignored, energy will be conserved in an identical way whether the object falls directly to the ground or rolls down a plane.

In a pendulum motion, at what points do you expect the pendulum to have the greatest kinetic energy? How about potential energy? When kinetic energy is at its maximum, what assumption can you make about the gravitational potential energy of the pendulum and what can you say about the height of the pendulum?

The pendulum is at its greatest kinetic energy wise when it is at the lowest point of the arc. We can often assume that the gravitational potential energy is zero at this point and that the height is equal to zero.

Imagine that you have a spring and you want to find a way to calculate the force needed to displace the spring by a certain distance, intuitively you know that stiff spring will requires you to put in more force. From this, what can you conclude about the relationship between the spring stiffness and the force that you need to apply on the spring? Using this, can you come up with the equation of Hooke's law? What consideration you need to take into account when using this law?

The relationship between the stiffness of the spring and the force you need to use will be directly proportional since the higher the stiffness the bigger the force is. From this we can easily come up with Hooke's law equation which is F=kX where k is the spring constant/its stiffness. The main consideration we need to take into account is the fact that X is the difference in distance from the spring equilibrium position and NOT the length of the spring.

Which object has the higher ME, a marshmallow or a rock?

The rock.

Provide examples of simple harmonic motion.

There are many possible examples of SHM. A pendulum and a mass on a spring are the most common. Almost any circular motion when viewed from the side approximates simple harmonic motion. Waves sloshing back and forth in a container can approximate SHM. Molecular vibrations approximate SHM. Essentially any movement that oscillates about an equilibrium position and shows the characteristic sinusoidal pattern.

When is work positive? when is work negative?

There are two conventions for the sign of work. In physics, we say that if the force and the displacement are in the same direction, work is positive (e.g., pushing a barbell up). If force and displacement are in opposite directions we say work is negative (e.g., lowering a barbell). In both physics and chemistry a common convention is used that says: If work is done on the system it is positive; if it is done by the system it is negative.

Note about work.

Think of work as change in energy first then as a force that is applied across a displacement. For example, if a ball falls from a height h, a force (mg) has been applied across a displacement (h).

Describe how you would calculate the spring constant by hanging weights.

To calculate the spring constant, solve for k using Hooke's Law. For delta x, enter the displacement from the equilibrium point for one trial, or the difference in displacement between two trials. For F, use the force applied in one trial, or the difference in force between two trials. Caution: It is a common mistake to plug the mass in kg of a block hanging on a spring. You need to convert mass into a force F=mg

What is the equation for the potential energy stored by a capacitor? Short of similar to kinetic energy equation, strangely enough.

U=1/2 QV=1/2 CV^2

Think back to your physics 1 class in the summer and remember how Rhett said that a pretty girl would be more "attracted" toward a fat guy than a slender person. Using this example and the fact that "attraction" is involved, can you come up with the equation for the universal law of gravitation?

Well Rhett was onto something, because in physics sense, he is right that massive objects will be more attracted to each other than small objects (including human). Using this scenario, we can conclude that force of gravity is proportional with the masses of the objects. Since the force involved is an attraction force, it's intuitive to think that it will be inversely proportional with the distance. Put this all together, we can come up with the equation F=Gm1m2/ r^2 (G=6.67x10^-11 m^3/kg x s^2 or 10 m/s^2 on earth)

Important note about spring constant.

When multiple springs are attached parallel to one another and to the same bumper plate (such that each spring is compressed equally under any displacement, the effective spring constant is the sum of the individual spring constants. If the springs are attached end-to-end the springs add much like resistors in parallel, according to: 1/k effective = 1/k1 + 1/k2 + 1/k3 . . .

When you compress an elastic object (such as a spring), what form of energy do you gain from this? How would you calculate this change in energy knowing that you just perform work on this elastic object?

When you compress an elastic object, potential energy is the form of energy that you will gain. Knowing that you perform work during the compression process, we can use the equation of work along with slight modifications to calculate the Elastic Potential Energy using the equation PE=1/2 . KX^2 where x= the distance away from equilibrium of the elastic object.

How would you describe work? What is the equation for work?

Work can be described as the change in energy. The equation for work is W=F x d x cos(theta).

What are the three different type of modulus?

Young's modulus: tensile or compressive stress/strain (simultaneously pulling or pushing forces on both sides that are exactly aligned in both vertical and horizontal planes) Shear modulus: sheer stress/strain modulus (simultaneous pulling and pushing that are not aligned) Bulk modulus: bulk stress/strain modulus (simultaneous compression of all sides)

How will decreasing the following aspects of a pendulum change the frequency of oscillation? a) mass of the pendulum bob, b) length of the pendulum, c) gravity

a) decreasing the mass of the bob will have no effect; b) decreasing the length of the pendulum will increase the frequency; c) decreasing gravity would decrease the frequency.

How will increasing the following aspects of a mass on a string change the frequency of oscillation? a) mass of the pendulum bob, b) length of the spring, c) mass of the spring, d) gravity, e) the spring constant.

a) increasing the mass will decrease the frequency; b) the length of the spring has no effect as long as it is designed not to change k; c) the mass of the spring itself has no effect assuming it is far less massive than the massive object attached to it [although this would probably alter k and it would have an effect]; d) increasing gravity would have no effect; e) increasing the spring constant would increase the frequency. Encourage students to simple substitute 1/f for T in the formula for these types of problems. This will make the correct relationships easy to see. Notice that the MCAT likes to tempt you to mix up the variables that uniquely impact mass-spring systems but not pendulums.

What force equation should be set equal to the centripetal force in each situation? a) a car going around a turn in the road b) a satellite orbiting earth c) a ball on a string d) a charged particle in a magnetic field.

a) u(static)mg; b) Gmm/r2; c) tension (T); d) qvBsin theta

What is the equation for centripetal acceleration?

ac = v2/r. This can be derived by substituting the formula for centripetal force into F = ma and solving for a.

For an incline plane, it is easy to come up with the force equation for each component (horizontal=force down an incline and vertical= normal force) if you can draw the right triangle! So the task is take out a piece of paper and draw the triangle!

http://upload.wikimedia.org/wikipedia/commons/thumb/8/85/Free_body.svg/300px-Free_body.svg.png

Derive a formula for the velocity of a satellite orbiting the moon.

v = √(Gm/r); This is derived by setting mv2/r equal to the universal law of gravitation and solving for velocity.