Mechanics Flashcards
What are scalar quantities?
Scalar quantities have magnitude only.
What are vector quantities?
Vector quantities have a magnitude and a direction.
Scalar or Vector?
- Distance
- Mass
- Velocity
- Energy
- Weight
- Acceleration
- Temperature
- Displacement
- Force
- Speed
- Scalar
- Scalar
- Vector
- Scalar
- Vector
- Vector
- Scalar
- Vector
- Vector
- Scalar
What should an appropriate scale look like?
An appropriate scale should maximise the amount of graph space available.
Calculating the final vector can be done in two ways:
- By measurement of the diagram, if it is drawn to scale
- By using Pythagoras/trigonometry
How would you work out the magnitude of a vector?
[Use the following question as an example]
A 3N northwards force and a 4N eastwards force act on a mass. What is the magnitude of the resultant force?
√3² + 4²
=√9 + 16
=√25
=5N
How would you work out the direction of a vector?
[Use the following question as an example]
A 3.0N northwards force and then a 4.0N eastwards force act on a mass. What is the direction of the resultant force?
- Draw Triangle.
(AB=3, BC=4) - Lable angle required.
(BAC) - Lable sides of the triangle with opposite-adjacent-hypotenuse.
- Choose the correct equation from SohCahToa.
(In this case Toa) - Write out the formula with know values.
(Tan(θ) = 4/3) - Rearrange and solve, giving the answer to an appropriate s.f
(Tan⁻¹(4/3) = θ, θ = 53⁰) - Write the answer in relation to the direction.
(53⁰ East from North/the verticle)
How would you resolve a vector?
- Sketch the vector.
- Lable sides of the triangle with opposite-adjacent-hypotenuse.
- Choose the correct equation from SohCahToa.
- Write out the formula with know values.
- Rearrange and solve, giving the answer to an appropriate s.f
- Repeat the same steps for the other axis.
What are the suvat quantities?
s: distance
u: initial velocity
v: final velocity
a: acceleration
t: time
What is instantaneous velocity?
Velocity at a given point
What is average velocity?
Can be found using (u + v)/2
if acceleration is constant
What is rectilinear motion?
Moving in a straight line.
What is the vertical acceleration due to gravity?
9.81ms⁻²
Displacement-time graphs:
What does the gradient show?
Velocity (not speed because a direction is shown)
Velocity-time graphs:
What does the gradient show?
What does the area under the graph show?
Gradient: Acceleration.
Area: Displacement.
What is newtons first law?
An object at rest will remain at rest…
An object in motion will remain in motion…
…unless acted on by an unbalenced force.
What is newtons second law?
The acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object.
What is newtons second law?
quantativly
∑F = ma
What is newtons third law?
Every action has an equal but opposite reaction.
Is momentum scalar or vector?
Vector.
How do you calculate momentum (p) given the mass and velocity of an object.
p = mv
What is the law of conservation of momentum?
The total momentum before must be the same as the total momentum after, because linear momentum is always conserved (provided no external force acts on the bodies).
How do you quantitivly show conserved momentum when the masses move off together?
mₜ₁vₜ₁ + mₜ₂ vₜ₂ = (mₜ₁ + mₜ₂) vₜ₁₂
How do you quantitivly show conserved momentum when the masses move off separately?
mₜ₁vₜ₁ + mₜ₂ vₜ₂ = mₜ₁vₛ₁ + mₜ₂ vₛ₂
Using newton’s second law, derive the equation of resultant force.
F=ma
Using Newton’s 2nd law:
a= Δv / Δt
∴
F=mΔv / Δt
or as…
F= Δ(mv) / Δt
∴ resultant force = change itn momentum / time interval
What is impulse?
Where the change in momentum is equal to the resultant force multiplied by time
What is impulse?
quantitivly
F= Δ(mv) / Δt
or as…
FΔt = Δmv
When is the impulse on two objects the same?
When two objects move apart in opposite directions the force on each must be the same (2nd law) and the time must also be the same.
What is the unit for impulse?
Ns
Newton seconds
What is the moment?
The turning effect of a force.
What factors effect moments?
The moment of a given force depends on…
…The size of the force.
…The perpendicular distance between the line of the force and the axis of rotation.
Relate moments to the force exerted.
moment of force = Fx
State the principle of moments.
The sum of the clockwise moments must be equal to the sum of anticlockwise moments if an object is in equilibrium (not accelerating).
Quantitivly show the principle of moments.
F₁x₁ = F₂x₂
Cranes lift heavy building materials using a horizontal arm called a jib. A hook moves up and down the jib and can lift loads from different points. Cranes have a counterweight balanced at the other end of the jib.
Use your understanding of moments to explain why cranes need to have a counterbalance. Why is it useful to be able to lift loads from different points on the jib?
- Without the counterweight, the crane would topple over.
- The counter-weight creates a moment that opposes the moment from the load.
- In order to balance the crane, you need to make the clockwise moment, and anticlockwise moment, equal.
- Heavier masses can be lifted closer to the pivot in order to equal the moment of smaller masses lifted further away from the pivot.
- This will ensure that the clockwise and anticlockwise moments are equal.
What is a couple?
- When you apply two moments to an object.
- For example when turning a tap.
What is torque?
The overall turning effect.
How do you calculate torque?
clockwise torque = Σclockwise forces.
anticlockwise torque = Σanticlockwise forces.
Define kinetic energy.
The ability of an object to do work due to its motion.
Define gravitational potential energy.
The potential that an object has due to it being elevated in a gravitational field.
Define work done.
Where energy is transferred to or from an object.
Define power.
The energy transferred per unit time.
Define the law of conservation of energy.
Energy can never be created or destroyed. It can only be transferred from one store or location to another.
Define efficiency.
The ratio of useful energy transferred to total energy supplied.
Define a joule.
The standard unit for one Newton metre.
Quantitivly show workdone in relation to a change in distance.
ΔW = FΔs
When does an object have potential energy?
When an object is able to do work due to its position or state.
Quantitivly show:
The increase in GPE is equal to the work done to lift the object to a height, h.
The increase in EPE is equal to the work done to stretch the object by an extension, x.
W = mgΔh
W = FₐᵥΔx
What does a distance-time graph describe?
The journeys of different objects.
What does a velocity-time graph describe?
The speed of an object changes.
What does a flat horizontle line show in a distance-time graph?
When an object is stationary.
What does a flat horizontle line show in a velocity-time graph?
Constant speed.
What does a steep, diagonal line show in a distance-time graph?
When an object is travelling quickly.
What does a steep, diagonal line show in a velocity-time graph?
Constant acceleration.
What do lines moving away from the x-axis in a distance-time graph show?
Moving away from the starting point.
What do lines moving towards the x-axis in a displacement-time graph show?
Moving towards from the starting point.
What do lines moving towards the x-axis in a velocity-time graph show?
Slowing down.
What do lines moving below the x-axis in a velocity-time graph show?
Changing direction.
What does the area under the graph show in a velocity-time graph?
Distance travelled.
