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# Physics 1 Exam 1 Study Guide PHYS1301

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This 6 page Study Guide was uploaded by Aishwarya Juttu on Friday September 30, 2016. The Study Guide belongs to PHYS1301 at University of Houston taught by Rene Bellwied in Fall 2016. Since its upload, it has received 8 views. For similar materials see Intro General Physics I in Physics at University of Houston.

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Date Created: 09/30/16

Physics 1 Exam 1 Review Chapter 1 Introduction to Physics - Units of length, mass, and time - length= meters (m) - mass= kilogram (kg) - time= seconds (s) - Dimensional analysis- any valid physical formula must be dimensionally consistent, each term has the same dimension - Ex: distance= velocity x time - velocity= acceleration x time - energy= mass x (velocity)^2 - Dimensional consistent- each term in the equation must have the same dimensions - Ex: Correct (apples + apples), (time + time) - Ex: Incorrect (apples + oranges), (time + distance) - Significant figures- defining the number of digits that are known with certainty - Adding/Subtracting: count how many number of sig figs are present after the decimal, the lowest sig fig is used in the final answer - Ex: 2.987+2.8= 5.787 The lowest number of sig figs present after the decimal point is 1 in 2.8 compared to 3 in 2.987 so the final answer should only have 1 sig fig after the decimal point.Answer= 5.8 - Ex: 8.012-8.9808=-0.9688 The lowest number of sig figs present after the decimal point is 3 in 8.012 compared to 4 in 8.9808 so the final answer should only have 3 sig figs after the decimal point.Answer= -0.969 - Multiplying/Dividing: count the total number of sig fits present and the lowest sig fig is used in the final answer - Ex: 2.98x9.203=27.424 The lowest number of sig figs present 3 in 2.98 compared to 4 in 9.203 so the final answer should only have 3 sig figs after the decimal point.Answer= 27.4 - Ex: 4.00/6.1= 0.6557 The lowest number of sig figs present 2 in 6.1 compared to 3 in 4.00 so the final answer should only have 2 sig figs after the decimal point. Answer= 0.66 - When calculating multiple steps, always keep an extra digit and ROUND IN THE FINAL STEP - Ex: (3.00-1.4832)x3.1= 1. 3.00-1.4832=1.516 2. 1.516x3.1=4.699 Round in final step soAnswer has to have 2 sig figs: 4.7 - Scalar- number value with units, it can be negative, positive or zero, does not have a direction - ex: temperature, speed or magnitude - Vector- number value with units and a direction; in other words quantity magnitude and direction - ex: velocity - | velocity | = speed/magnitude Chapter 2 One - Dimensional Kinematics - Coordinate system- a diagram that defines the position and the motion of a particle - Distance = total length traveled; units: meters (m) - Displacement (meters) = change in position = final position - initial position - Δx = xf- xi - Average speed= distance / elapsed time units: meters/sec (m/s) - Avg. speed = distance/Δt - Average velocity= displacement / elapsed time units: meters/sec (m/s) - Avg. velocity =Δvelocity /Δt - Instantaneous velocity- velocity at an instant time - When velocity is constant, the average velocity over any time interval is equal to the instantaneous velocity at any time - - Instantaneous speed- the magnitude of the instantaneous velocity, remember | velocity | = speed/magnitude - Acceleration- rate of change of velocity with time - Acceleration = velocity / time units: m/s^2 - Avg.Acceleration =Δv /Δt units: m/s^2 - InstantaneousAcceleration- acceleration at that moment - When acceleration is constant, the instantaneous and average accelerations are the same - Acceleration and Velocity can be either positive or negative - Deceleration- an object whose speed is decreasing is said to be decelerating; occurs when velocity and acceleration have opposite signs - When velocity and acceleration of an object have the same sign, the speed of the object increases - When velocity and acceleration of an object have the opposite sign, the speed of the object decreases - Constant acceleration- same acceleration at every instant of time - When acceleration is constant, the instantaneous acceleration is equal to the average acceleration - Velocity as a function of time v = v0 + at - Position as a function of time x = x0 + 1/2(v0 + v)t - Position as a function of time x = x0 + v0t + ½at^2 - Velocity in terms of displacement v^2 = v0^2 + 2a(Δx) - Average VelocityAvg. v = ̅(v + v0) - Free fall - the motion of an object falling freely under the influence of gravity; means free from any effects other than gravity - It is free fall when an object is released, whether it is dropped from rest, thrown downward, or thrown upward - Galileo showed that objects of different weight fall with the same constant acceleration in absence of air resistance - Gravitational acceleration = g = 9.81m/s^2 - Positive upward direction a = -g - Negative downward direction a = +g - Special circumstances whether x = 0 and positive is downward then the following formulas can apply: - x = 1/2 gt^2 - v = (2gx)^(1/2) Chapter 3 Vectors in Physics - Scalar components of a vector (V) are Vx and Vy - I’m using V as the vector - To calculate Vx = Vcosθ - To calculate Vy = Vsinθ - V = Vx^2 + Vy^2 - V= (initial v)t - To find the angle given both rx and ry: - θ = sin ^-1(Vy/V) - θ = cos ^-1(Vx/V) - θ = tan ^-1(Vy/Vx) - To determine sign of x and y components: - Start at the tail of vector and move along the x axis toward the right angle, if you are moving in the x axis positive direction, then x component is positive. If you are moving in the x axis negative direction, then x component is negative. - Start at the tail of vector and move along the y axis toward the tip of the arrow, if you are moving in the y axis positive direction, then y component is positive. If you are moving in the y axis negative direction, then y component is negative. - When calculating angles consider in which quadrant the direction of angle is in: - Quadrant 1: θ - Quadrant 2: -θ +180 - Quadrant 3: θ +180 - Quadrant 4: -θ +180 - Remember θ can be calculated using sin, cos, or tan given x and y components, and the vector - Given angle between vector and y axis, angle is called θ’: - θ+ θ’= 90 therefore 90-θ = θ’ - Vx = Vsin θ’ - Vy = Vcos θ’ - Adding vectors: simply add - Cx =Ax + Bx - Cy =Ay + By - C^2 = Cx^2 + Cy^2 - Subtracting vectors: minus sign comes from a negative x or y component meaning the component is pointing in the opposite direction - Cx =Ax + (-Bx) - Cy =Ay + (-By) - Unit vectors- x and ŷ are defined to be dimensionless vectors of unit magnitude pointing in the positive x and y directions; these are used to specify directions only - Vector addition C=A+B= (Ax+Bx) x + (Ay+By) ŷ - Vector subtraction C=A-B= (Ax-Bx) x + (Ay-By) ŷ - Position vector = hypothenuse vector - Displacement vector = Δr = final r - initial r - Velocity vector- displacement vectorΔr divided by the elapsed timeΔt; gives direction and magnitude of motion Avg v=Δr/Δt - Acceleration vector- change in velocity vectorΔv divided by theΔt; Avg a=Δv/Δt - Change in velocity= Δv= final v - final v - Velocity vector is always in the direction of a particle’s motion, but acceleration vector can point in directions other than the direction of motion Chapter 4 Two - Dimensional Kinematics - Projectile- an object that is thrown, kicked, batted, or launched into motion and then allowed to follow a path influenced by gravity - Earth’s rotation and air resistance is ignored. - Gravity acceleration if thrown downward is 9.81m/s^2 - Gravity acceleration if thrown upward is -9.81m/x^2 - Gravity acceleration in the x axis is 0 - Horizontal and vertical motions in projectile motion are independent. - Zero launch angle - x=v0(t) - y=h-1/2gt^2 - vx=v0=constant - vy=-gt - vx^2=v0^2=constant - vy^2=-2gΔy - General launch angle where θ is a nonzero number - Basic equations for projectile motion: - x=(v0cosθ)t - vx=v0cosθ - vx^2=(v0^2)cos^2θ - y=(v0sinθ)t-1/2gt^2 - vy=v0sinθ-gt - vy^2=v0^2sin^2θ-2gΔy - Range of a projectile- horizontal distance it travels before landing - Landing site- a projectile launched horizontally - Parabolic path- path followed by a projectile launched horizontally with an initial speed Chapter 5 Newton’s Laws of Motion - Force- a push or pull; units: Newton (N) or (kg*m/s^2) - Magnitude- strength of force - Direction- direction of which you are pushing or pulling - Newton’s First Law of Motion- an object at rest remains at rest as long as no net force acts on it; also called law of inertia - if the net force is zero, its velocity is constant - Newton’s Second Law of Motion- an object of mass m has an acceleration a given by the net force F divided by m; F=ma - the greater the acceleration is promotional to the force- the greater the force, the greater the acceleration - if the mass of an object is doubled but the force remains the same, the acceleration is halved meaning acceleration is inversely proportional to mass - if the net force on an object is zero, the object moves with constant velocity - When working a problem, remember that if acceleration is negative so will the force - Free-body diagram- sketch indicating each and every external force acting on a given object - W is weight which is a downward force of gravity - F is upward force that is exerted - Newton’s Third Law of Motion- for every force that acts on an object, there is a reaction force acting on a different object that is equal in magnitude and opposite in direction - Contact forces- when objects are touching one another - the same net force acts on the total mass, so both boxes have the same acceleration - If more than one force acts on an object, acceleration is in the direction of the vector sum of the forces - Weight (W)- gravitational force exerted on it by the Earth; W=mg - Apparent weight- force that pushes upward on your feet and gives you the sensation of your weight pushing down on the floor; - F= Wa-W force is positive if elevator is going upward b/c is positive - -F= Wa - W force is negative if elevator is going downward b/c a is negative - Remember F=ma - If surface is angled: Wx= Wsinθ = mgsinθ - Wy=-Wcosθ=-mgcosθ - Normal force-when downward force of gravity is being opposed by an upward force exerted by the counter; force is called normal because it is perpendicular to the surface; normal = perpendicular - F= F+N+W

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