Mometrix OATs prep: Physics

Meter

Standard unit of length, represented by m.

Kilogram

Standard unit of mass, represented by kg.

Second

Standard unit of time, represented by s.

Unit of Velocity

m/s

Units of acceleration

m/s²

Units of force

Newtons or kg • m/ s²

Units of energy

Joules (J) or kg • m² / s²

Units of pressure

Pa or kg/m²

Units of frequency

Hz or s^-1

How is a vector represented?

By the magnitude and angle associated with its x and y components

How to calculate the x component of a vector?

v cos (angle)

How to calculate the y component of a vector?

v sin (angle)

Magnitude of a vector can be calculated by?

$$\sqrt{v_{x}^2}+v_{y}^{2_{}}$$

How to calculate the angle of a vector l?

$$\tan\theta=\frac{v_{y}}{v_{x}}$$

Define velocity

Rate of change of position over time.

How to calculate average velocity?

$$\frac{\left(x_2-x_1\right)}{t_2-t_1}$$

How to determine instantaneous velocity?

Is equal to the slope at the particular point on a position vs time graph.

Define acceleration

Rate of change of velocity over time

How to calculate average acceleration?

$$\frac{\left(v_2-v_1\right)}{t_2-t_1}$$

How to determine instantaneous acceleration?

Can be found from the slope of a velocity vs time graph.

How to find change in velocity?

Using acceleration vs time graph, adding up the area between the x axis and the line.

How to determine the change in position?

Using a velocity versus time graph, adding up the areas between the x axis and the line.

How to calculate the absolute position?

Add the change in position to the initial position.

How to determine absolute velocity?

Add the change in velocity to the initial velocity.

Newton’s 1st Law / Law of Inertia

An object at rest tends to remain at rest, and an object in motion tends to remain in motion, unless acted on by an outside force. (Only applies if the frame of reference is stationary or moving at a constant velocity)

Newton’s 2nd Law

The net force on an object is equal to the product of the objects mass and its acceleration. ($F=ma$ )

Newton’s 3rd Law

For every action, there is an equal and opposite reaction.

Common example of Newton’s 3rd Law

The force gravity the Earth exerts on you is equal to the force you exert on the earth.

when is Friction force present?

Whenever there are two objects in contact and there exists a normal force between them

Define kinetic friction

If the two objects are in motion relative to each other - like a block sliding across a table.

Define static friction

If the two objects aren’t in relative motion - like a book resting on a shelf.

Define the coefficient of friction $\left(\mu\right)$

A value that characterizes the frictional force between two objects depending on their material and texture.

What is an important difference when considering static and kinetic friction?

That the coefficient of static friction between two objects is always greater than the coefficient of the kinetic friction.

how to calculate the force of kinetic friction?

$$f=\mu n$$

How to calculate the amount of force for friction to be overcome and an object to move?

$$f_{s}\le\mu n$$

If net force excluding friction is less than this value, then the object will stay still

How to calculate center of mass?

$$\frac{\Sigma m_{i}x_{i}}{\Sigma m_{i}}$$

Free body diagram

Shows all the forces acting on an object with their magnitude and direction. Useful to write a formula for the net force.

Define equilibrium

When the net force on an object equals zero

Define static equilibrium

When an object is not moving and its velocity equals zero

Define dynamic equilibrium

When an object is moving but its velocity is constant.

Define Translational equilibrium

If the forces on an object are balanced (net force = 0)

Define rotational equilibrium

When the torques on an object are balanced or net torque on the object os zero

True or false: it is possible for an object to be in translation and rotational equilibrium

True

Define Net Force

The total force on an object. That is, the sum of all the individual forces

True or False: if the net force on an object is zero, the object is motionless.

False

What is important to remember when calculating Net Force?

That forces are represented by vectors. Direction affects how the magnitudes are added up.

If net force on an object is zero, then the object can’t be?

Accelerating

Define Torque

(Kinda) a rotational analogue of force.

How to calculate torque?

$$\tau=rF\sin\phi$$

r = lever arm

F = force

$\phi$ = angle between force and lever arm

What is a lever arm? A vector pointing from the axis to where the force is exerted

The distance between the axis of rotation and the point at which the force is exerted.

What equation shows the relationship between torque and acceleration?

$$\tau=Ia$$

I = the moment of inertia

a = angular acceleration

What are the units of Torque?

N • m

Equation for Kinetic energy?

$$K=\frac12mv^2$$

A 2000 kg car moving at 30 m/s has a kinetic energy of what?

900,000 J

What is the acceleration of gravity?

9.8 m/s²

How to calculate gravitational potential energy?

$$U=mgy$$

m = mass

g = gravitational acceleration

y = is the altitude of the object

10 kg weight at the top of a 2.0 m ladder has a potential energy of?

196 J

What does a spring constant tell you?

How hard it is to stretch the spring. The higher the spring constant, the harder it is.

Hooke’s law equation

$$F=-k\Delta x$$

The spring constant is always

Positive

Units of the spring constant?

N/m or kg/s²

What equation can the units of the spring constant (k) be determined?

$$k=-\frac{f}{\Delta x}$$

Equation for the potential energy of a spring?

$$\frac12k\left(\Delta x\right)^2$$

$\Delta x$ = displacement of the end of the spring from its equilibrium position

k = the doing constant

True or False: A spring in its equilibrium state has no potential energy

True

The more a spring is stretched or compressed, the

Higher its potential energy

If a spring with a spring constant of 10 N/m is compressed by 20.0 centimeters, what is its potential energy?

0.200 J

Conserved energy means?

Energy may change form, but the total amount of energy in a system does not change.

What does mechanical energy refer to?

Kinetic and potential energy

True or false: mechanical energy is conserved only when the forces acting on the system are conservative forces

True

What are the Units of power?

Watts (W) or kg • m² / s²

Define Power

Change in energy over time

Equations to calculate power?

$P=\frac{\Delta E}{\Delta t}$ or $P=\frac{W}{\Delta t}$

How to calculate power exerted by a constant force?

$$P=Fv$$

If an object is moving in the same direction as the force that is acting on it, the work is calculated by?

$$W=F\cdot d$$

If the motion of an object is not in the same direction as the force acting on it, then how is work calculated?

$$W=F\cdot d\cos\theta$$

Define Mechanical advantage

The factor by which a machine decreases the necessary force to perform a task. It is a ratio of the force produce to the force applied.

What is the mechanical advantage for a lever?

The ratio of the distance from the fulcrum to the point where the force is applied to the distance from the fulcrum to the point where force is exerted.

How to determine the mechanical advantage of a pulley system?

Equal to the number of rope systems that hold up the object being lifted

The Work Kinetic energy theorem

states that the work done on an object by the net force on that object is equal to the change in the objects kinetic energy.

Define conservative force

A force that only requires the starting and end positions to calculate work. The path the object takes does not matter.

List some example of conservative forces.

Gravity, electric force, and elastic force

List examples of non-conservative forces.

Friction, tension, and air drag

What are the Units of momentum?

Kg • m /s

How to calculate momentum?

$$P=mv$$

m = mass of a particle

v = velocity of a particle

the rate of change of momentum is proportional to

The force exerted and is in the same direction

define Impulse

Application of force over a period of time

Equation showing the relationship between impulse and momentum?

$$Ft=\Delta mv$$

True or False: We can assume that momentum of a closed and isolated system will neither increase or decrease

True

What is a closed and isolated system?

A system in which no particles are leaving or entering and the sum of external forces is 0.

Define a perfectly elastic collision

A collision in which both total momentum and kinetic energy are conserved.

Define a perfectly Inelastic collision

A collision in which only momentum is conserved, as the two bodies combine to form a single object.

Polar coordinates were designed for?

Situations in which circular arcs are more common than straight lines and angles. An object is described by its distance from the origin ( r) and the angle between its position and the positive x-axis.

Equations for converting to or from polar coordinates?

$$x=r\cos\theta$$

$$y=r\sin\theta$$

$$r=\sqrt{\left(x^2+y^2\right)}$$

$$\theta=\tan^{-1}\left(\frac{y}{x}\right)$$

For uniform circular motion?

r = 0 and rate of change for $\theta$ is constant

Equation for centripetal acceleration?

$$a_{c}=\frac{\left\vert v\right\vert^2}{r}=r\omega^2$$

r = distance from origin

w = rate of change in angle

Equation for centripetal force?

$$F=ma_{c}=\frac{m\left\vert v\right\vert^2}{r}=mr\omega^2$$

define translation

When something is moving in a straight line

Define rotation

When something is moving around a fixed axis

A full rotation is equal to?

360 degrees, $2\pi$ radians or 1 revolution

What equations are used to relate rotational movement to translational movement?

$$x=r\theta$$

$$v=rw$$

$$a=ra$$