Physics equations - MCAT
These are some common Physics equations that will probably need to be memorized and understood for the MCAT
vectors
Pythagorean Theorem: a^2 + b^2 = c^2
**Remember the common 3-4-5 and 5-12-13 triangles**
sin(theta) = (opposite / hypotenuse)
cos(theta) = (adjacent / hypotenuse)
tan(theta) = (opposite / adjacent)
Distance, Displacement, Velocity, and Acceleration
Displacement d = change in position
Speed = (distance) / (time)
Velocity v = (displacement) / (time) — this is a vector
**Note that displacement is the NET distance from the starting point**
Acceleration a = (change in velocity) / (time) — this is a vector
**Because acceleration is a vector, a change in velocity or a change in direction means the object has accelerated**
Linear Motion
v = v0 + at
d = v0t + 0.5at^2
v^2 = V0^2 +2ad
vavg = 0.5(v + v0)
**Note that these equations are under the assumption that the objects are moving with constant acceleration**
Objects shot into projectile motion
dx = v0xt
V0x = V0xcos(theta) V0y = V0sin(theta)
ax = 0 ay = -10 m/s^2 (acceleration due to gravity)
Peak height of an object: V0 x sin(theta) = sqrt(2gh)
Range of object = Vicos(theta) x (time)
Newtons Law and the Law of Universal Gravitation
Force = mass x acceleration or F = ma
F = (Gm1m2) / r^2 where G = 6.67 x 10^-11 m^3 kg^-1 s^-2 (do not memorize this constant!)
**m1 and m2 are the masses of the objects while r is the distance between the center of masses of the two objects**
**Note that both objects described feel forces of the same magnitude**
**Note that combind these two equations we get**:
F = (Gm1m2) / r^2 = ma –> from here we can find the acceleration of either object just by plugging in the mass of the other object
Inclined Planes
F = mgsin(theta)
**this is the force causing an object to move up or down the incline plane**
Fn = mgcos(theta)
**this is the force being applied on the object that continuously changes the direction of velocity by creating a continuous centripetal acceleration**
Circular Motion
Centripetal Acceleration = ac = (v^2) / (r) *r = radius of circle*
**Note that this acceleration ALWAYS points toward the center of a circle**
Centripetal Force = F(c) = mv^2 / r
Frictional Forces
**Static friction — Force opposing motion when two objects are not moving relative to each other**
f(s) = mus x Fn where mu(s) is the fraction of the Normal Force (Fn)
**Kinetic Friction — Force opposing motion when two objects are moving relative to each other**
f(k) = mu(k) x F(n)
**mu(s) > mu(k)**
Hooke’s Law
F = -k(x)
k is a constant for a particular object
x is the deformation or the change in position of the object
Equilibrium
Means no linear or angular acceleration applied the an object (object moves and rotates at a constant velocity or zero velocity). The sum of all forces acting on such objects is zero
F(upward) = F(downward)
F(rightward) = F(leftward)
Torque
Tau = (force) x (moment arm)
Tau(clockwise) = Tae (counterclockwise) for static problems
Center of mass = x = (m1×1+m2×2+….) / (m1+m2+….)
**Note the equation is dependent on the number of objects**
Energy
Kinetic Energy = K = .5(mv^2)
Gravitational Potential Energy = U(g) = mgh
**this equation is used for objects near the earth’s surface**
Elastic Potential Energy = U(e) = .5(k)(x^2)
**this shows the potential energy for objects following Hookes Law**
Work
W = Fdcos(theta)
**Work is done by all forces except that of FRICTION**
W = (delta)K + (delta)U
**this equations can also be written:
.5(mv(f)^2) + mgh(f) = .5(mv(i)^2) + mgh(i)**
Power
P = (work) / (time) — measured in watts
P = Fdcos(theta) / (time)
P = Fvcos(theta)
**sometimes power is defined by transferred energy (E) which is Work + heat(q)** P = (delta)E / (time)
momentum
p = mv — mass and velocity of an object
**Momentum is always conserved**
Collisions
Elastic collisions: U(i) + K(i) = U(f) + K(f)
** Mechanical energies before and after collision are equal
Inelastic collision: Use the conservation of momentum to solve inelastic collision problems since mechanical energy is converted internal energy
**p(i) = p(f)
Impulse
Is the change in momentum: J = (delta)p
F(avg) = m(vf-vi) / (change in time)
mass defect
Nucleus of an atom has less mass than the sum of its individual parts. The difference of the mass is the mass defect. Binding energy holding protons and neutrons can be found using the defect
E = mc^2 where m is the mass defect
Density of and Specific Gravity
Density = mass / volume (kg/m^3)
S.G. = (density of a particular substance) / (density of water)
Fluid Pressure on objects
P = Force / area
P = (density)(g)(y)
**where g is gravity and density and y is the density and depth of the fluid the object can be found respectively**
if a fluid is open to the atmosphere, the pressure is:
**Pressure = (density)(g)(y) + P(atm)
Pascal’s Principle
Any change in pressure applied to an enclosed fluid is transmitted undiminished to all parts of the fluid and the enclosing walls
**Principal seen in the Hydraulic Lift where: F(1)/A(1) = F(2)/A(2)
Archimedes Principle
Any fluid applies a buoyant force to an object that is partially or completely submerged in it — this force is equal to the weight of the fluid that the object has displaced.
**F(b) = W(fluid)** — can also be written
**F(b) = (density of fluid)(g)(Volume of fluid displaced)
Ideal Fluids
The equation of continuity: The mass flow rate of a fluid has the same value at every position along a tube that has a single entry and a single exit point for fluid flow –> for two positions along a tube:
**(density)(A1)(v1) = (density)(A2)(v2)**
A= cross sectional area of tube
v = fluid velocity
Since density is constant in an imcompressible fluid, it does not change during flow: A1v1 = A2v2
volume flow rate = Q = Av
Bernoulli’s Equation
In a steady flow of nonviscous, imcompressible fluid of a cetain density, the pressure, the speed, and the elevation at two points are related by the following equation:
P1 + .5(density)(v1^2) + (density)(g)(y1) = P2 + .5(density)(v2^2) + (density)(g)(y2)
