Mechanics Flashcards
When does an object accelerate?
An object accelerates when its velocity changes
- When velocity is positive > the object is speeding up > positive acceleration
- When velocity is negative > the object is slowing down > negative acceleration > deceleration
Terminal Velocity Question
1 • At the instant the diver leaves the plane, air resistance = 0N and the acceleration will be 10ms^-2 (acceleration of gravity).
2 • The weight of the diver remains constant, but the opposing force (air resistance) will increase as the diver falls. There is a resultant force acting downwards because the air resistance is less than the weight force of the diver. This means the forces are unbalanced and the diver will accelerate.
3 • The velocity of the diver will increase and they will continue to accelerate, but at a smaller rate (due to increased air resistance). This means the resultant force acting on the diver will decrease and the acceleration of the diver will decrease, until the resultant force = 0N, where weight = air resistance. At this point, the change in velocity will be 0ms^-1.
4 • This means the diver no longer accelerates (the velocity does not increase). This corresponds to its maximum velocity, called ‘terminal velocity’. Terminal velocity occurs when the resultant force acting on an object is 0.
Force and pressure question
(If the two objects being compared have the same weight, but exert a different pressure)
1 • The pressure exerted by the object with the smaller surface area is greater than the pressure exerted by the object with the larger surface area, because although the weight force exerted by the object remains the same, the surface area for which that force is applied is smaller for the object with the smaller surface area.
2 • As P = F/A, (and the weight force remains constant) pressure is inversely proportional to surface area. Therefore, when surface area decreases, pressure increases.
3 • The object with greater pressure will have increased friction, as it will sink into the ground more and enable a better grip and have more stability.
4 • The object with the lower pressure will have decreased friction, as it will not be able to sink into the ground. And therefore, it will likely slip and lose traction.
Gravitational potential energy question
1 • Work done is equal to the amount of energy an object possesses. Therefore, the work done = the gravitational potential energy gained.
2 • There is an energy difference because some of the energy used is converted to heat and sound due to the friction between the moving parts of the object.
3 • This means the gravitational potential energy the object gains is less than the total energy it uses.
Units for power
Watts (W)
Formula for area of a trapezium
Sum of parallel sides / 2
X the perpendicular height
Units for pressure
Pascals (P)
Units for work and energy
Joules (J)
Distance over time graph question
/ - ) (
/ A. The object moves at a constant speed of ___ for the first ___ seconds.
• The gradient is constant > The rate of change of distance is constant > The velocity is constant > The object is traveling at a constant speed
(This means the forces acting on the object are balanced, they are equal and opposite. The net force is 0.)
- B. The object is stationary at ___m for the next ___ seconds.
• The gradient is 0 > The rate of change of distance is 0 > The velocity is 0 > The object stops moving
) C. The object travels ___m in the next ___ seconds at an increasing speed.
• The gradient is increasing > The rate of change of distance is increasing > The velocity is increasing > The object is speeding up (experiencing a positive acceleration)
( D. The object travels ___m in the next ___ seconds at a decreasing speed.
• The gradient is decreasing > The rate of change of distance is decreasing > The velocity is decreasing > The object is slowing down (experiencing a negative acceleration)
Velocity over time graph question
(When line on graph has an increasing gradient / )
A. The object accelerates at a constant ___ for the first __ seconds.
• The gradient is constant (positive) > The rate of change of distance is increasing > The velocity is increasing > The object is speeding up (experiencing a positive acceleration)
(When line on graph has a gradient of 0 - )
B. The object remains at a constant velocity of ___ for the next ___ seconds.
• The gradient is 0 > The rate of change of distance is constant > The velocity is constant > The object is traveling at a constant velocity, with no acceleration
(When line on graph has a decreasing gradient \ )
C. The object negatively accelerates at a constant ___ for the final ___ seconds.
• The gradient is constant (negative) > The rate of change of distance is decreasing > The velocity is decreasing > The object is slowing down (experiencing a negative acceleration)
Dropping objects question
(work, power and energy)
PRESSURE
How far the object sinks into the ground is determined by the pressure they exert on the surface when they land.
- P = F/A. As the (object 1) has a greater mass than the (object 2), its weight force (F = mg) will be higher.
- As pressure is directly proportional to force, as the weight force increases, the pressure increases. Therefore, the (object 1) will exert more pressure on the ground and therefore sink more into the flour than the (object 2).
Dropping objects question
(work, power and energy)
ENERGY
Both objects are at the same height, but the (object 1) has a bigger mass and therefore greater gravitational potential (GPE = mgh) energy than the (object 2).
- When the objects fall to the ground, all the gravitational potential energy is converted into kinetic energy. Therefore assuming the conservation of energy, initial GPE = final Ek.
- Because the (object 1) has a larger initial gravitational potential energy and therefore larger final kinetic energy when it hits the ground, it has a greater impact and causes a deeper crater to be created.
Conservation of energy
Total energy is conserved through being transformed into other form(s).
Eg. Kinetic energy is converted into thermal energy (heat) or friction force that does work on an object.
Define mass vs. weight
Mass is the fundamental measurement of matter which an object has
(constant)
Weight is the downward force that an object experiences due to gravity
(not constant because it is influenced by location, as to how much gravity there is)
How power is affected by speed and time
If an object is lifted at twice the speed, the power needed to lift it will increase. This is because if the speed is doubled, the time taken to lift the load is halved.
As P = W/t, (power is a measure of the amount of work done per second) and since the amount work done does not change, if the time is halved the power is doubled.
What does a constant speed indicate?
A constant speed means that the forces acting upon the object are balanced and that they are equal and opposite.
(there is no resultant force)
Velocity over time graph
What does the gradient of the graph and area under the graph indicate?
- The gradient of a velocity over time graph indicates the acceleration of an object. A steeper slope indicates a greater acceleration.
- The area under a velocity over time graph indicates the distance traveled by an object.
The formula for the area of a trapezium
(sum of parallel sides / 2) x perpendicular height
Speed and velocity of a bouncing ball when it is dropped onto the ground
SPEED
(From when the ball leaves the hand of the person dropping it )
• The ball is speeding up and experiencing a positive acceleration, due to the influence of gravity applying 10ms-2 to the ball in a downwards direction, aiding the movement of it. ˅ ˅
(From when the ball is bouncing back from the ground into the air)
• The ball is slowing down and experiencing a negative acceleration, due to the influence of gravity applying 10ms-2 to the ball in a downwards direction, opposing the movement of it. ˅ ^
VELOCITY
(The instant the ball is in contact with the ground)
• The ball experiences maximum velocity on impact, and changes direction.
Distance and Displacement
• Distance is how far has been traveled in total by the object
(Area A + Area B)
• Displacement is how far has been traveled from the start to the endpoint of an object
(Area A = Area B)
Average speed formula
Distance / time
Vector quantities and the resultant vector
A vector quantity has both size and direction
(Eg. displacement, velocity, acceleration)
- Vectors quantities of the same quantity type (displacement + displacement etc.) can be added by placing the tail of the next vector on the head of the first vector
- The resultant vector is then represented by the arrow joining the tail of the first vector to the head of the last vector. This is equivalent to the vector sum of the forces.
Force, mass and acceleration
F = ma
Acceleration is directly related to force and indirectly related to mass. Therefore, as force increases, acceleration increases and as mass increases, acceleration decreases.
• The acceleration of an object is directly proportional to the resultant force and inversely proportional to its mass.
(See terminal velocity question)
Define net force
The net force is that single force that has the same effect as the sum of all force added head to tail.
If the forces are acting in the same direction, they add to give a larger net force.
If the forces are in the opposite direction, they subtract to give a smaller net force.
Net forces determine whether an object is experiencing a positive acceleration, negative acceleration or maintaining a constant speed.
If the net force is pointing in the same direction as the direction of motion, the object positively accelerates.
If the net force is pointing in the opposite direction to the direction of motion, the object negatively accelerates.
If the net force is 0, the object is either maintaining a constant speed or is stationary.
Final velocity formula (without time)
Vf = Vi + 2ad
• Can be used to find acceleration or distance if initial and final velocity is given, through substitution
Distance formula
(Vi + Vf / 2) t
Time formula
Vf - Vi / a
Acceleration formula
Vf - Vi / t
Distance formula (without final velocity)
1/2 at^2 + Vit
Define work
Work is a measure of the amount of energy an object possesses.
Define energy
Energy is a measure of the amount of work an object is able to do.
Displacement force formula
1/2 mVf^2 - 1/2 mVi^2
Kinetic energy formula
1/2 mVf^2
What does a change in kinetic energy mean?
A change in the kinetic energy of an object means the velocity of the object will change, and the object will accelerate. This means there is a resultant force acting upon the object, and the object is displaced (moves).
If the change in kinetic energy is > 0, this means the kinetic energy of the object would have increased
If the change in kinetic energy is < 0, this means the kinetic energy of the object would have decreased
What does a resultant force indicate?
A resultant force means that the forces acting upon the object are unbalanced and unequal. This means the velocity of the object will change, and the object will accelerate.
Work done to displace a trolley on a smooth surface
Work = Force x Distance
• If the change in velocity is > 0, this means the kinetic energy of the object increased. This means that work was done on the trolley, (as the kinetic energy of the trolley changed).
• The work done on the trolley = The change in kinetic energy
Work done to displace a trolley on a rough surface
Work = Force x Distance
• The useful work done on the trolley = the work done by the resultant force
Resultant force = Applied force - Friction
• To overcome the effects of friction, the applied force must be equal to the friction force over the distance. This means that work must be done on the trolley.
• The applied force must increase the Ek of the trolley AND overcome the effects of friction.
• The total work done = Applied force.
Work done to lift an object to a height of h
Work = Force x Distance
• The work done on the object = The change in gravitational potential energy
∴ The work done on the object = mg△h
• When calculating GPE (mg△h) you need a reference point from where you are measuring with respect to
Total mechanical energy formula
Ek + GPE
Total mechanical energy and velocity of an object down a ramp from point A to B, with a smooth surface
• Because the ramp is smooth, we can imply that no energy is lost in the form of heat or sound due to friction
The total mechanical energy at A with respect to B = GPE
(Because Ek = 0, as the object is stationary)
• Assuming the conservation of energy, the total mechanical energy at A = total mechanical energy at B. Because at B the GPE is 0, the total mechanical energy at B is in the form of Ek only (all GPE at A is transformed into Ek at B)
∴ From the total mechanical energy, we can calculate the velocity at B
(Calculate the Ek, then substitute Ek into formula and solve)
Force acting on an object down a ramp from point A to B with a smooth surface
Work = Force x Distance
• The total mechanical energy at B = The work done on the object
∴ From the work done on the object, we can calculate the force acting on the object as it slides down the ramp
(F x d = W, then substitute Work into formula and solve)
Velocity of an object at the bottom of a ramp with a rough surface
EXAMPLE
• A friction force of 6N over the distance of 10m removes 60J of energy from the total mechanical energy of the object.
∴ The total mechanical energy = 2,500J - 60J = 2,440J
• Assuming the conservation of energy, the total mechanical energy at A = total mechanical energy at B. Because at B the GPE is 0, the total mechanical energy at B is in the form of Ek only (all GPE at A is transformed into Ek at B)
∴ From the total mechanical energy, we can calculate the velocity at B
(Ek = 2,440J, then substitute into formula and solve)
Define power
Power is the rate of doing work.
Power required for traveling two routes
B C
| / ⁄ t = 10s
4m | / ⁄
| / ⁄\_\_\_\_\_\_\_
A
• The change in energy along AB and AC are equal because the change in GPE is the same (△h = 4m)
∴ The mgh for both routes is the same, and the total work done is the same, and this occurs in the same period of time
∴ The rate of doing work is the same (more force/shorter distance vs. less force/longer distance)
∴ The power for both routes is the same because the time taken and the work done is the same
Power required for traveling two routes
```
5s) (10s
B C
| / ⁄
4m | / ⁄
| / ⁄_______
A
~~~
• The change in energy along AB and AC are equal because the change in GPE is the same (△h = 4m)
∴ The mgh for both routes is the same, and the total work done is the same, but this occurs in a different period of time
• For AB, the change in energy occurs in 5 seconds. This means the change in energy occurs at a rate of 100J every second.
∴ Work done = 500J
∴ Power = 100W
• For AC, the change in energy occurs in 10 seconds. This means the change in energy occurs at a rate of 50J every second.
∴ Work done = 500J
∴ Power = 50W
∴ AC is easier because less power is required to travel the route.
A force of 10N enables a trolley to move at a constant speed of 5ms-1. Calculate the power needed to drive the trolley.
Power formula (using force and velocity)
Power = work / time = force x distance / time (distance / time = average velocity) = force x average velocity = 10 x 5 = 50W
_ P = FV
Efficiency formula
output (what actually happens)
/ input (what is expected to happen)
Pressure ratio of applied force and contact area
- If the contact area is doubled or the applied force is halved, the pressure is halved
- If the contact area and the applied force is doubled, the pressure remains the same
- If the contact area and the applied force is halved, the pressure remains the same
How to convert cm^2 to m^2
Divide by 10,000
Scalar quantities
A scalar quantity has only size
Eg. speed, time, mass, area, volume
Projectile motion
- Follows a parabolic curve
- Gravity is the only force acting on the projectile, applying -9.8ms^-2 to the projectile in a downwards direction. Because of this…
- As the projectile moves upwards, the force of gravity acts in the opposite direction to the vertical motion of the projectile and decreases its vertical velocity. This causes the projectile to experience a negative acceleration (deceleration), until the vertical velocity of the projectile is equal to 0.
- At this point, the motion of the projectile has covered half of its total distance, and taken half of its total time.
- As the projectile moves downwards, the force of gravity acts in the same direction to the vertical motion of the projectile and increases its vertical velocity. This causes the projectile to experience a positive acceleration.
- As there is no horizontal force acting on the projectile, the horizontal velocity of the projectile remains constant and therefore, there will be no horizontal acceleration.
Projectile motion (travel time)
Calculate the time take to reach the peak of its motion, then double it.
- Use initial vertical velocity, final vertical velocity and acceleration
(Vf = Vi + at)
Projectile motion (distance travelled)
- Use initial horizontal velocity and travel time
v = d/t
Projectile motion (height reached)
- Use initial vertical velocity, travel time and acceleration
(d = Vit + 1/2at^2)
Work done on a spring
Ep = 1/2 kx^2
Where,
Ep is the elastic potential energy
k is the spring constant
x is the distance extended
Change in momentum (with protection) question
- When the event occurs, the same change in momentum occurs. However, with the protection the stopping time is greater, than without the protection (the protection gets hit first before body).
- △p = F△t, therefore, as the impulse is the same, as the time increases, the force will decrease, and therefore the event with the protection will produce less force. This means that it is less likely that an injury will be sustained.
- This assumes that the speed is the same so the mass of the protection does not significantly affect the momentum of the body, so the impulse will be constant.
(eg. or bending knees when jumping)
Circular motion
- There is a centripetal force which acts towards the centre of the curve which causes the object to accelerate towards the centre at a constant speed along a circular path, by changing the direction of the objects velocity.
- As the net force is 0, it will continue to travel at a constant speed at a tangent to the curve in a straight line (acting at 90 degrees to the direction of travel of object, so it does not change the size of the velocity).
Calculate power to decelerate from Vf, Vi and time
Using P = △E/t
- △E is change in kinetic energy (1/2mv^2)
- Solve for kinetic energy using Vf and Vi separately
- Subtract the initial velocity solution from the final velocity solution to find △E
- Substitute back into main equation with time to solve
Using P = W/t
- Solve for acceleration (a = △v/△t)
- Solve for force (F = ma)
- Solve for distance (Vf^2 = Vi^2 + 2ad)
- Solve for work (W = F x d)
- Substitute back into main equation with time to solve
How an object on a slope can remain stationary
As the object is stationary, this means that the forces are balanced (in equilibrium). Therefore, the component of gravity down the slope is equal to the friction force, and the component of gravity into the slope is equal to the reaction force.
Equation to calculate centripetal force and acceleration
Fc = mv^2 / r Ac = v^2 / r
Where,
v is the constant speed
r is the radius of the circle
- To calculate v use v = d/t,
Where,
d is the circumference of the circle
t is the time for one revolution
Force that causes acceleration in circular motion
The tension in the cord provides centripetal force, which is the unbalanced force that causes acceleration.
Conservation of momentum
Momentum is only conserved if there is no external net force (eg. gravity or air resistance). It can be assumed that there is no friction with ice.
Unit for impulse
The unit for impulse is N s (Newton seconds)
Unit for momentum
The unit for momentum is kgms^-1
Conversion from kWh to J
Multiply kWh by 3.6 x 10^6
Conversion from mT or μT to T
- Divide mT by 1000
- Divide μT by 1,000,000
