Physics 152 - Final Exam Cram Sheet PDF

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Summaries for every section covered in class and the textbook. ...

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PHYSICS MIDTERM STUDY GUIDE CHAPTER 1: The Science of Physics 1.1 What is Physics? - Areas within Physics: Mechanics, Thermodynamics, Vibrations and wave phenomena, Optics, Electromagnetism, Relativity, Quantum Mechanics - Scientific Method: Question→Test hypothesis→Analyze/revise→Conclusion/spread - System - need to define a system in situation. An object and items around it = simple model. 1.2 Measurements in Experiments - 3 dimensions (physical quantity measured) - length, mass, time. - SI Units: Length=meter, mass=kilogram, time=second - Prefixes: pico(p)(-12), nano(n)(-9), micro()(-6)(μ), milli(m)(-3), centi(c)(-2), deci(d)(-1), kilo(k)(3), mega(M)(6), giga(G)(6), tera(T)(12) - Accuracy - how close to accepted value, Precision - degree of exactness(limit of measuring instrument) - Sig Figs - Decimal point present (pacific) count non zero from left. Decimal point absent (atlantic) count non zero from right. Multiplication use least present in measurements. Addition use the least amount of decimal places. 1.3 The Language of Physics - Dimensional analysis can weed out invalid equations. - Order of magnitude to check answers - determine power of 10 close to numerical value - Percent Error - 100x ((measured-accepted)/accepted) CHAPTER 2: Motion in One Dimension 2.1 Displacement and Velocity - Motion takes place over time and depends on frame of reference (where you refer motion from. Ex: fixed or moving frame) - Displacement - distance from the initial position to the final position. ∆x = xf-xi. Not always total distance travelled. Positive or negative. - Average velocity = displacement/time vavg = ∆x/∆t. (Positive or negative) - Instantaneous velocity - use tangent line for slope at that exact point. 2.2 Acceleration - Avg Acceleration = change in velocity/time aavg = ∆v/∆t = (vf-vi)/(t) - Has direction and magnitude. - Displacement with constant acceleration - ∆x = ½(vi+vf)t - Velocity with constant acceleration - vf = vi + at - Displacement with constant acceleration - ∆x = ½at2 + vit - Final velocity after any displacement - vf 2 = vi2 + 2a∆x

Formula

d

t

a

v1

v2

d = ½(v1 + v2)t

d

t

--

v1

v2

d = ½at2 + v1t + h

d

t

a

v1

--

v2 = at + v1

--

t

a

v1

v2

v22 - v1 2 = 2ad

d

--

a

v1

v2

2.3 Falling Objects - Free fall: Object has nothing touching it. Only force is gravity (constant) - Acceleration is constant during upward and downward motion. - The acceleration is independent of position, velocity, mass - Acceleration by Gravity: -9.8 m/s2 (use - if displacement down is also -) CHAPTER 3: Two-Dimensional Motion and Vectors 3.1 Introduction to Vectors - Vectors indicate direction and magnitude. - Resultant vectors - represent the sum of two or more vectors. Have to have same units and describe similar quantities. Can be added graphically tip to tail. - Properties: Vectors can be moved parallel to themselves in a diagram. Vectors can be added in any order. To subtract a vector, add its opposite (opp direction). Multiplying or dividing vectors by scalars results in vectors. 3.2 Vector Operations - Resultant magnitude and direction of perp vectors- Use pythagorean thm to find magnitude of resultant. C = √(A2 + B2 ). Use tangent function to find direction of resultant. Angle = tan-1  (opp/adj) - Resolve vectors into components. x and y component. - Resultant of vectors that are not perp - Resolve into components and add those and then find resultant. 3.3 Projectile Motion - Use components of projectile. x and y. - Projectile motion - when objects are thrown or launched in the air and are subject to gravity. Follows parabolic trajectory. Basically free fall with horizontal velocity. - Launched Horizontally: - Horizontal Motion: vx = vxi = constant x = vxt - Vertical Motion: vyf = gt y = ½gt2 vyf 2 = 2gy - t = √(2h/g)

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Launched at an angle:

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v x = vxi = vicos = constant x = (vicos )t

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v yf = gt + visin y = ½gt 2 + (visin )t v yf2 = vi2(sin )2 + 2gy

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t = (2vsin )/g x = (v2sin(2 )) / g

3.4 Relative Motion - In different frames of reference, velocity differs. - Can be relative velocity with respect to another moving object - If same direction, vac = vab + vbc - Ex. if diff directions. Velocity of river in relation to earth given and velocity of boat crossing in relation to water. Find velocity of boat relative to earth. Forms right triangle where velocity of boat in relation to earth is hypotenuse. CHAPTER 4: Forces and Laws of Motion 4.1 Changes in Motion - Force - push or pull, vector quantity, can cause acceleration and change in direction. - SI Unit - Newtons (N) or kg*m/s^2. - Contact forces or Field forces - Ex. A push vs gravity - Force diagrams - Free-body-diagrams - Force is vector. Draw from center point. 4.2 Newton’s First Law - If net force is 0, can be at rest or at constant velocity. - First Law - Obj at rest stays at rest, obj in motion stays in motion unless it experiences a net external force. - Inertia - tendency of an object not to accelerate. Resistance to change in velocity. Continue in same direction of motion as before. - Mass is a measure of inertia. Inertia is proportional to an object’s mass. Greater the mass, the less the body accelerates under applied force. - Sum of forces acting on an object is net force. Sum of all vectors. - Equilibrium - at rest or at constant velocity. Net force and acceleration is 0. 4.3 Newton’s Second and Third Laws - Second Law - Force is proportional to mass and acceleration. F  NET = m*a - Third Law - Forces always exist in pairs. For every action, there is an equal and opposite reaction. Action and reaction forces each act on different objects. - Field forces also exist in pairs like gravity. 4.4 Everyday Forces - Weight - earth’s gravitational force directed to the center of the earth. - Fg =m*g. g = 9.8 m/s^2

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Normal Force - Fn. Force exerted by ground up, perpendicular to surface that object is on. Usually equal and opposite to Fg. - If incline surface, Normal force is perpendicular to surface so not directly opposite gravity. Gravity can be made into vector quantities. N =

mgcos . -

Force of Friction - friction opposes the applied force. - Static friction Fs- resistive force that keeps object from moving with applied force. Fs = - Fapplied. - Kinetic friction - retarding frictional force on an object in motion.

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FNET = F applied - Fk

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Coefficient of friction - Force of friction is proportional to the normal force. Coefficient depends on composition of surface. Coeff. Of kin friction: Ratio of kinetic friction to the normal force. Coeff. Of static friction: Ratio of static friction to the normal force.

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Ff = μN = μmgcos

Air resistance is also a force of friction

CHAPTER 5: Work and Energy 5.1 Work - Work is done when force causes a displacement of the object. Measured in Joules. - Work - The product of the component of a force along the direction of displacement

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W = Fd

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FORCE MUST BE DONE PARALLEL TO DISPLACEMENT. If object has force applied that is not in direction of displacement then use the component that is. Use angle between force and displ. W = Fdcos - If work is positive then force and displacement in the same direction. If negative then force and displacement in opposite directions. 5.2 Energy - Kinetic Energy - the energy of an object that is due to the object’s motion. - KE = ½mv2 -

SI Unit is Joule. Work-Kinetic Energy Theorem - Net work is the change in kinetic energy.

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WNET =

KE = ½mvf 2 - ½mvi2

Potential Energy - the energy associated with an object because of the position, shape, or condition of the object. Stored energy. Gravitational Potential Energy - depends on height from a zero level.

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PEg = mgh

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Elastic Potential Energy - In a spring, depends distance compressed or stretched. - PEelastic = ½kx2 . - x is distance compressed or stretched. k is the spring constant or force constant. - Spring constant - if flexible, constant is small, if stiff, constant is large. Unit - N/m. 5.3 Conservation of Energy - Conserved means it stays constant throughout. - Mechanical energy - the sum of kinetic energy and all forms of potential energy. Could include elastic potential energy like in a pendulum clock.

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ME = KE + PE

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-

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Other energy - nuclear, chemical, internal, electric is nonmechanical energy. Conservation of Mechanical Energy - MEi = MEf (in absence of friction) - Alternate - ½  mvi2 + mghi = ½mvi2 + mghf - If starts with height and ends with velocity  E = KE mgh = ½mv 2 v = √(2gh) P

If on incline and KE at the end does not equal PE at the beginning then the difference in the work done by friction. 5.4 Power - Power - rate at which work is done or rate of energy transfer.

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P = W/ t Also P  = Fv SI unit is the watt (W) or sometimes horsepower (hp). Machines with different power ratings do same amount of work but in different time intervals

CHAPTER 6: Momentum and Collisions 6.1 Momentum and Impulse - Momentum - product of mass and velocity. p = mv -

Momentum is a vector quantity with direction matching the direction of velocity. SI Unit - (kg*m)/s Impulse - the product of the force and the time over which the force acts on an object. Impulse Momentum Thm - F t = p = mv f - mv i In an impact (change in momentum to 0) the force is reduced when time interval is increased. 6.2 Conservation of Momentum - Momentum is conserved. Total momentum of all objects interacting with one another stays the same regardless of the nature of the forces between the objects.

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m 1v1, i + m2v2, i = m 1v1, f + m2v2, f

pinitial = pfinal

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Conserved in collisions, and in objects pushing away from each other Forces in real collisions are not constant during the collisions. So impulse problems use avg force. 6.3 Elastic and Inelastic Collisions - Perfectly Inelastic collision - a collision in which two objects stick together after colliding. - Essentially becomes one object after the collision. ⚪ → ⚫ = ⚪⚫ →

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m 1v1, i + m2v2, i = (m 1 + m2)vf

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Momentum is conserved but Kinetic Energy is not conserved in inelastic collisions. KEi ≄KE  f - You can find decrease in total kinetic energy. Elastic collisions - two objects collide and return to their original shapes with no loss of kinetic energy. Bounce back. ⚪ → ←⚫ = ←⚪ ⚫ → or ⚪ → ⚫ = ⚪ ⚫→ - Kinetic energy is conserved. KEi = KEf - Momentum is conserved: m  1v 1, i + m2v2, i = m 1v1, f + m 2v2, f . Kinetic Energy is

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conserved: ½  m 1v21, i + ½m2v 22, i = ½m 1v21, f + ½m2v22, f Difference in final velocities of two objects after collision is the negative difference between the initial velocities. ( V A, f - V B, f) = -(VA, i - V B, i)

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Most collisions are neither elastic nor perfectly inelastic.

CHAPTER 7: Circular Motion and Torque 7.1 Circular Motion - Circular motion is moving about an axis of rotation.

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Tangential speed (vt) - speed of an object in circular motion. Along an imaginary line drawn tangent to the circular path. If tangential speed is constant then motion is uniform circular motion. Depends on distance from the object to the center (so radius). Acceleration can be produced by changing magnitude of velocity or the direction. Bc circular, the direction is changing. Centripetal Acceleration - a  c = v2/r.

- Is a result of a change in the direction of the tangential velocity. - The direction of the centripetal acceleration is to the center. - Tangential acceleration is due to a change in speed. - Centripetal force - F  c = (m*v2)/r - The net force on an object in uniform circular motion. Any type of force or combination of forces can provide this force. Ex. Friction, Normal force - Acts at a right angle to the motion (to the center). 7.4 Torque - A quantity that measures the ability of a force to rotate an object around some axis. Ex. door on hinge, cat flap, etc. - The lever arm is the perpendicular distance from the axis of rotation to a line drawn along the direction of the force. So rsinθ. -

Theta is angle between radius and line drawn along direction of the force.

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𝛕 = Frsin

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Maximum torque is when the force acts furthest from the center. Units - Nm (Newton meters)...