Chapter 9: Momentum, Work, Power Flashcards
What does area under a graph of force-time give?
Impulse (change in momentum)
*Momentum equation
momentum = mass x velocity
units: kgms-1
What would happen when a ball(1) of velocity v with mass m hits a stationary ball(2) of the same mass
Ball(1) would stop on impact, ball (2) would move off with the same velocity v, conserving momentum
What would happen when a ball(1) of velocity v with mass m hits a stationary ball(2) that is much heavier
Ball(1) would rebound off of it, while ball(2) would move only a bit slowly as a response
How is momentum conserved in collisions and explosions
The momentum before is the same as the momentum after.
mass before * velocity before = mass after * velocity after
Is momentum a vector or scalar
Vector, the equation for momentum contains velocity, which is a vector
use the equation ‘mv’ to show conservation of momentum between a ball of velocity v hitting a stationary ball, both have same mass
mv + 0 = mv
=> 0 + mv = mv
State Newton’s First Law - the Law of Inertia
A body at rest will stay at rest (and a body in constant motion will stay in constant motion) unless a resultant external force acts on it.
State Newton’s Second Law.
The acceleration of an object is directly proportional to the resultant force applied to it (F = ma).
How does Newton’s second law apply to momentum?
The rate of change of momentum is directly proportional to the force F = Δp / Δt = ma
Δp = mΔv
What is impulse of a force?
The force multiplied by the time the force is applied for, so impulse is equal to the change in momentum Δp = FΔt
How do you increase impulse?
Increase the force, or the time it acts for (or both)
How are crumple zones in cars used for improved driver safety
They reduce the force on the driver as momentum is constant, and Δp = FΔt crumple zones increase the duration of the crash, so change in time increases, but to keep change in momentum constant, the force decreases so the force on the passenger decreases, improving their safety
How do seat belts airbags improve safety?
They reduce the force on the driver as momentum is constant, and Δp = FΔt seat belts stretch slowly and air bags deflate gradually, increasing how long it takes for a person to come to a halt if the car comes to a halt
How do you find impulse from a force-time graph?
The area under a force time graph between 2 time points on the X-axis give the impulse
What does area under a graph of force-time give?
Impulse (change in momentum)
What does the peak of the force-time graph give?
Maximum deformation of an object
State Newton’s third law
If body A exerts a force on body B then body B exerts an equal and opposite force on body A
Equation of force for free falling object near earth’s surface?
F = m g
m is mass in kg
g is acceleration usually 9.81 ms-2
What is the equation for work done or change in energy?
Work done ΔE (J) = Force x displacement in direction of force
Force in N
Displacement in m
What is the conservation of energy?
Energy is never created or destroyed, only transferred between different forms and stores of energy
How do you calculate kinetic energy gained?
KE =½ mv2
How do you calculate gravitational potential energy?
GPE = mgh
How do you combine kinetic energy with GPE?
kinetic energy gained = change in gravitational potential energy
Define projectile and give example
Object projected outwards such as a cannonball
How do you do calculations for a force acting at angles?
How would you do it for a weight, mg, acting at angle theta
- You need to resolve the weight into vertical and horizontal components
- Use the component acting in the direction of the motion i.e horizontal component mg cos theta = mg * cos theta
Define power
Rate at which work is done
Rate at which energy is transferred
Equations for power
P = work done / time
P = ΔE / t
P = Force * velocity
What are the five rules for Newton’s Third Law Pairs of Forces?
- Same type of force
- Same magnitude
- Act along same line of action
- Act in opposite directions
- Act on two different bodies
What is a perfectly elastic collision?
One where momentum is conserved and kinetic energy is conserved
What is an inelastic collision ?
One where some of the kinetic energy is converted into other forms during the collision. But momentum is always conserved
What are the two types of friction? What are the differences?
Contact friction between solid surfaces
Fluid friction, drag or fluid resistance or air resistance
Three things you need to know about or frictional forces:
Their direction?
Their affect on the speed of the object?
Which types of energy do they convert?
They always act in the opposite direction to the motion of the object
They can never speed things up or start something moving
They convert kinetic energy into heat
You will reach your terminal velocity at some point, if you have…
A driving force that stays the same all the time e.g. weight
A fictional or drag force that increases with speed
When does something reach terminal velocity?
When the frictional force equals the driving force e.g. when weight = drag due to air resistance
Describe the graph of velocity against time for an object reaching terminal velocity
Curve, where the gradient decreases, eventually turning into a horizontal line. Graph starts at the origin and increases
Describe the graph of acceleration against time for an object reaching terminal velocity
Acceleration starts off high then decreases. The rate of decrease of acceleration starts slow then speeds up then slows again. The acceleration finally reaches zero. The graph looks like an unexaggerated S shape
Describe the graph of the velocity against time for the parachutist
First half of the graph looks like the normal velocity against time for an object reaching terminal velocity. Then the graph suddenly drops to a lower velocity and flattens out, where it reaches a new terminal velocity
When is work done?
Whenever energy is transferred
What is power?
The rate of doing work – it’s the amount of energy transferred from one form to another per second
How do you answer a question where somethings projected at an angle
- resolve initial velocity into horizontal and vertical components
- use vertical component to find how high it goes and and to work out how long it’s in the air for
- use horizontal component to find distance travelled horizontally while in air
How do you use vertical component to find highest point of projectile’s motion and how long it’s in the air for?
If the graph is symmetrical: at the halfway point, vertical velocity is 0 for an instantaneous time, so the value of vv must be multiplied by 2
To get the second time vv = 0 which is when it will hit the ground
so vv = 0, uv = resolve into vertical and horizontal to find out
a = g = -9.81 (upwards as neg)
t = ?
use v = u + at to get time
This is time taken to get to highest point; multiply by 2 to get the time to reach ground again
How do you use horizontal component to find distance travelled after you have found time before it hits the ground again using vertical component
There is no acceleration horizontally so
a = g = 0
this means that uH = vH (speed)
time for it to hit ground found from vertical component = t
use this to find s, distance travelled
you can use speed = distance / time
distance = speed * time
how to answer question where projectile is thrown horizontally, you want how long it takes to hit ground and how far it travelled
break it into vertical and horizontal
vertical: thrown horizontally with speed Vh so
for vertical u = o
a = g = (-) 9.81
if done above ground level s = xm
so use s = ut + 1/2 at^2
usually just goes to s = 1/2 at^2
use this to find time
horizontal: Vh isnt affected by gravity so Uv = Vv and a = N/A
use time t from vertical component
usually can use speed = distance / time
distance = speed * time
s = Vv (Uv) * t
What are the forces acting on a person falling at constant speed
if falling at constant speed, forces are equal, drag = mg
Key points to remember for work done
Work done is not necessarily the total energy. If you move an object higher up you have increased its potential energy, but it already had some potential energy to start with
Force, F, will usually be fixed.
Equation assumes force is in same direction as direction of movement
Equation for work done at an angle
Work done = force * distance * cos theta
Equation linking power, force and velocity
Equation linking power, force at an angle and velocity
Power = Force \* velocity P = Fv
Power = Force cos theta \* velocity P = F cos theta \* velocity
