====== AP Physics 1 Study Guide ====== * Also refer to our [[AP Physics C Mechanics]] Study Guide, it has very similar topics for the most part and prettier formatting Credit goes to u/OldFlyingHat - 1D motion - Distance is d - D=sum of lengths - Distance is all negative and positive - Displacement is final position minus initial - $\Delta X = X_f -X_i $ - Speed is scalar, so not a vector - Distance/time - S=d/$\ \Delta t$ - Average speed is over long period of time - Savg=total d/total t - Instantaneous Is at a particular moment in time - Speed can never be negative, only zero or positive - Velocity is displacement per time - V=$ \frac{\Delta X}{\Delta t}$ - Can be negative or positive - Generally if pointed left its negative - Generally if pointed right its positive - Acceleration - $\frac{m}{s^2}$ - is a vector - points in the direction of the net force - if velocity is changing acceleration is present - a= $ \Delta $ v/t or ($v_f$-$v_i$)/t - position vs time graph - y axis is x or position (m) - x axis is time - slope is velocity - curvature means there’s acceleration - concave up means positive acceleration - concave down means negative acceleration - Velocity vs time graph - Y axis is velocity (m/s) - X axis is time - Slope is acceleration - Area under the curve is displacement or $ \Delta $ X - Acceleration vs time graph - Y axis is acceleration (m/s^2) - X axis is time - Slope is Jerk or Jolt (not needed) - Area under graph is change in velocity - Kinematic formulas: ACCELERATION **HAS** TO BE **CONSTANT** {{:pasted:20240406-033657.png}} - Free Falling Object/ Flying Object - Acceleration is G (9.8m/s^2), but in a free falling occurrence the acceleration due to gravity is negative - “Dropped” means $v_i$ is 0 - Time after a drop is t=sqrt(2h/g) - At maximum height means $V_f$=0 - 2D motion - Vector components can be broken down into perpendicular pieces - Along x and y directions > - $V_x$= Vcos($\theta$) - $V_y$=Vsin($\theta$) - DON’T FORGET SIGNS OF THE VECTORS YOU NERDS - Tip to tail vector addition - Place the tail of the next vector on the tip of the previous one - Then draw total vector form the first tail to the last head - If the vector is subtracted flip its tail and head - Component Vector addition - Add vectors together by adding their components to find the total vector > - To subtract a vector, multiply its components by -1 then add, or….ya know…..just subtract - 2D kinematics and projectiles - Vertical Equations - Vf=Vi+(-9.8)t - $ \Delta $X=vi*t+(1/2)(-9.8)^2 - $v_f^2=v_i^2+2(-9.8)(x_f-x_i)$ - (vf+vi)/2=(xf-xi)/t - Horizontal equation note: no horizontal acceleration - $ \Delta $ x=vt - X and y velocities behave independently - Graphing data to a linear fit - If the data is a parabola (exponentially rising) then make the x value squared - Forces and Newton’s laws - Newton’s first law - “Objects will maintain a **constant** **velocity** (which could be zero), unless acted upon by an unbalanced force” - a=0 if Sigma F=0 (ie no net force) - there does not need to be force in order for motion to occur but there needs to be a force if there is acceleration - works on systems too - the Center of mass will stay at constant motion unless an outside force acts on the system - Newton’s Second Law - “The acceleration of an object is proportional to the **net force** on the object, and inversely proportional to the mass of the object” - Unbalanced net forces cause acceleration (speed up slow down or change directions) - Equations - A=(sigma force)/m - Ax=(sigma force in the x direction)/m - Ay=(sigma force in the y direction)/m - Newton’s Third Law - “For every action, there is an equal and opposite reaction” - Basically If object A exerts a force on an object , then object B must exert an equal and opposite force back on Object A - Fab=-Fba - Force of Gravity - Is a vector - Always downwards - Synonymous with weight - Weight is NOT mass, mass times g - Fg=mg - Normal Force: N - It is a vector - The outward perpendicular force exerted on an object by a surface - Always pushes, cannot pull an object - Fn=? No set equation. Need to use newton’s second law to find - If there is acceleration in the direction of the normal force, then fn is not mg, acceleration y= (Sigma Fy/m) - Tension: N - Is a vector - Always pulls an object, a rope can’t push an object - Use newton’s second law to find (a=sigma/m) - Kinetic friction: N - Is a vector - Stops surfaces from sliding - Fk=Uk*Fn - Static friction: N - Is a vector - Will eb equal to the force trying to move the object until it reaches its maximum - Fsmax=UsFn - Fs - Ignore internal forces - Centripetal Forces - Period and Frequency - Period (t) can’t be neg - Number of seconds it takes for one entire revolution or circle - T=seconds/cycles second per cycle - Measured in seconds - Frequency (f) can’t be neg - Number of cycles completed by an object in one second - F=cycles/seconds cycles per second - Unit is 1/seconds which is Hz - Velocity - 2piR/T - 2piR*f - Centripetal acceleration ac - Measured in m/s^2 - Is a vector - ALWAYS POINTS TOWARDS MIDDLE OF THE CIRCLE - Only changes direction of velocity does not speed up or slow down - Ac=v^2/r or (4*pi^2*r)/T^2 or 4pi^2*f^2*r - If it is speeding up there needs to be a tangential acceleration, which points in the direction of motion - Centripetal forces - Measured in N - Is a vector - Any regular force that make something move in a circular path - For satellites and planets, it’d be Fg - Yoyo going around on a string or anything like that its Ft - Skateboarder or roller-coaster in a loop de loop Fn - Car going around a roundabout itd be Fs (force static friction) - Ac=Sigma Fc/m where ac=v^2/r - V^2/r=Sigma Fc/m - If the Fc points inward its positive as it points in the direction of the centripetal acceleration - If the Fc is pointed outwards, then it will be negative as it points in the opposite direction of the centripetal acceleration - Only plug in centripetal/radial force for Fc - Forces that are tangential are not included they go into a separate newton’s second law equation, tangential changes speed, centripetal changes direction - Example, ball rolling over hill would be Fn=Mg-Force centripetal, so Fn=Mg-M(s^2/r) - Newton’s universal force of gravity - Fg - Measured in N - All masses in the universe pull/attract every other mass with a gravitational force Fg - Force Fg is proportional to the masses - Fg=GM1m2/R^2 - G is the universal gravitational constant - 6.67*10^-11 Nm^2/kg^2 - **EVEN IF THE MASS IS DIFFERENT THEY EXERT THE SAME FORCE ON EACH OTHER SO FG IS EQUAL TO EACH OTHER** - i'm going to talk about this again in energy as it relates to kinetic - Acceleration due to gravitational field - Gravitational field is just another word for acceleration due to gravity - All masses create a gravitational field that points radially in towards them - The strength is affect by 1/r^2 meaning the further away the less strong - g(acceleration due to gravity)=G(6.67*10^-11)M/R^2 - measured in m/s^2 or N/kg - g=Fg/m and Fg=g*m - Density - P(density)=M/v - Density is mass per volume - We can use density to determine the mass of an object if we also know the volume - Gravitational orbits - When object orbits due to gravitational force - If the orbit is circular we can relate the speed, radius of the orbit, and the mass - A=sigma F/m so newtons second law - V^2/r(or ac)=Fg/m - V^2/r=(G(Mm)/d^2)/m - V^2=GM/r - (Big m is the mass of the object that is being orbited around, so not the satellite) mass in orbit doesn’t matter - **MAKE SURE TO COUNT RADIUS OF THE PLANET IN YOUR R COUNT SO IF AN OBJECT IS ORBITING 3R AND THE PLANET HAS A RADIUS OF R THEN THE VALUE IN THE EQUATION SHOULD BE 4 R. GRAVITATION STARTS AT THE CENTER OF AN OBJECT** - Energy and Work - Energy J, joules - Objects and systems can have, transfer, or transform energy - Energy being transferred between systems is called work - Works equation is w= $ \Delta $ E - Energy is conserved so it can’t be created nor destroyed, however energy can leave the system if the earth isn’t included - **Side note potential gravitational energy doesn’t exist when the earth isn’t included in the system** - If there is no external work then energy is constant - Types of energies: - K=kinetic energy= (½)mv^2 (energy due to motion) - Ug= Gravitational potential energy= mgh (energy due to height) - Us= spring potential energy= (½)kx^2 (energy in a spring) (x is the length of compression r stretch from x=0) - $ \Delta $ E thermal=thermal energy=FkD (heat energy from friction/air resistance) - E mechanical= mechanical energy= K+Ug+Us (does not include thermal) - Work W joules - Not a vector - Work is the transfer of energy from one object or system to another - W=$ \Delta $ E=Fdcos(theta) so force applied times displacement of object times the cos of the angle - If the force is perpendicular to the movement of an object then it provides zero work unless it points towards the surface the object is moving on and there is friction present as it would increase the normal force which affects Ff - Work energy principle NET WORK - Wnet=$ \Delta $ W - W1+w2+w3=Kf-Ki=1/2mvf^2-1/2mvi^2 - **Work is always negative if it moves against the motion don’t forget to square the v, v does not become negative if its moving in a new direction** - Force vs. x graph force position graph - Work is area bound by the curve or under the curve - Above x axis is positive work done - Below x axis is negative work - **IF IT IS A FORCE VS TIME GRAPH THE AREA IS ACTUALLY IMPULSE, NOT WORK** - Power - Power is the amount of work done per time - Amount of energy transferred per time - Measured in watts - Pavg=W/t=$ \Delta $ E/t - **Gravitational potential energy when the gravitational field is not constant** - If the gravitational field is varying (like two planets acting on each other or some similar situation) then you cannot use ug=mgh - Instead use Ug= -G%%((%%m1+m2)/d) where G is the gravitational constant (6.67*10^-11) - **key point: while Ug will always be negative, it can still be transferred into kinetic as it gets lower and lower due to it being defined as a perpetual negative** - **in order for the ug to be transferred into kinetic the distance between planets needs to decrease** - Momentum and Impulse - Momentum (p) - Is a vector - Momentum is mass times the velocity p=mv - note: p is lower case, capital is power - momentum will be conserved if there is no external force on the system **