Mechanics Flashcards
What is a scalar
A quantity which only has magnitude (size)
What is a vector
A quantity which has both a magnitude and a direction
Displacement
Describes how far an object is from where it started and in what direction
Examples of scalars
Distance
Speed
Mass
Time
Energy
Temperature
Examples of vectors
Displacement
Velocity
Acceleration
Force
Momentum
What are vectors represented by
An arrow
Length represents magnitude and arrowhead indicated direction
When can you use calculation to add vectors
IF the vectors are perpendicular, so you can use pythagoras theorem
When can you use scale drawings to add vectors
When the vectors are not perpendicular
How can coplanar forces be represented
By vector triangles
When are forces in equilibrium
If the object is at rest or moving at constant velocity
Moment
Force x perpendicular distance from the point to the line of action of the force
Couple
Pair of equal and opposite coplanar forces
Moment of couple
Force x perpendicular distance between the lines of action of the forces
SI unit for moment
Nm
Principle of moments
For a system to be in equilibrium, the sum of clockwise moments about a point must be equal to the sum of the anticlockwise moments (about the same point)
Forces up =
Forces down
Coplanar forces
Pair of forces that are :
Equal in magnitude
Opposite in direction
Perpendicular to the distance between them
NOT IN THE SAME LINE OF ACTION !!
Why do objects with a couple not accelerate
Couples produce a resultant force of zero, so, due to Newton’s second law, the object does not accelerate
Centre of mass
The point at which the the weight of the object may be considered to act
Where is the position of the centre of mass of a uniform regular solid
At the centre e.g for a person standing up it is behind the navel
Where is the centre of mass for symmetrical objects with uniform density
At the point of symmetry
What does the position of the centre of mass of an object affect
Its stability
What happens to the centre of mass and the stability of an object if the base is wider
Lower centre of mass
More stable
What happens to the centre of mass and stability of an object if the base is narrower
Higher centre of mass
Less stable (more likely to topple over)
What does the centre of GRAVITY depend on and why
The gravitational field because weight = mass x acceleration due to gravity.
Therefore an object in spaces’ centre of gravity will be more towards object with larger gravitational field
Instantaneous velocity/speed
The speed/velocity of an object at any given point in time
How to find instantaneous velocity on a displacement-time graph
Draw a tangent to the curve and calculate its gradient
Average speed
The total distance divided by the total time
Gradient of a displacement-time graph
Velocity
Y intercept on displacement-time graph
Initial diplacement
What does a diagonal straight line represent on a displacement-time graph
Constant velocity
What does a curved line represent on a displacement-time graph
Acceleration
What does the horizontal slope represent on a displacement-time graph
State of rest
What does the slope on a velocity-time graph represent
Acceleration
What does the y-intercept on a velocity-time graph represent
Initial velocity
What does a straight line on a velocity-time graph represent
Uniform acceleration
What does a curved line on a velocity-time graph represent
Non-uniform acceleration
What does a horizontal line on a velocity-time graph represent
Motion with constant velocity
What does the area under a velocity-time graph represent
Displacement/distance travelled
What does the slope on an acceleration-time graph represent
Nothing
What does the y-intercept on an acceleration-time graph represent
Initial acceleration
What does a horizontal line on an acceleration-time graph represent
An object undergoing constant acceleration
What does the area under an acceleration-time graph represent
Change in velocity
Time of flight
How long the projectile is in the air for
Range
The horizontal distance travelled by the projectile
What is the v when the projectile is at max height
0
What displacement is used when calculating time of flight when the projectile leaves and stops at the same height
0
How do we calculate the vertical and horizontal components of velocity
vertical - SUVAT
horizontal - distance = speed x time
Drag forces
Forces that oppose the motion of an object moving through a fluid e.g. friction and air resistance
Properties of drag forces
Always in OPPOSITE direction to motion of the object
Never speed an object up or start them moving
Slow down an object or keep them moving at constant speed
Convert KE in heat and sound
What happens to drag forces as speed increases
Drag forces also increase
What happens to the range and maximum height of a projectile when there is air resistance
It decreases
Describe how terminal velocity is achieved
For a body in free fall, the only force acting is its weight and its acceleration is only due to gravity.
Weight is initially greater than drag/friction and the resultant force causes acceleration
Drag force increases as velocity increases.
Due to Newton’s Second Law, this means the resultant force and therefore acceleration decreases. F=ma
When the drag force is equal to the gravitational pull on the body, the body will no longer accelerate and will fall at constant velocity - the terminal velocity.
What is the aim of the experiment
To calculate the value of the acceleration due to gravity, g
What is the independent and dependent variable in the determination of g practical
Independent - Height
Dependent - Time
What are the control variables in the determination of g practical
Same steel ball-bearing
Same electromagnet
Distance between ball-bearing and top of glass tube
What is the resolution of the measuring equipment in the determination of g practical
Metre ruler - 1mm
Timer - 0.01s
Describe the method in the determination of g practical
Set up the apparatus by attaching the electromagnet to the top of a tall clamp stand. Do not switch on the current till everything is set up.
Place the glass tube directly underneath the electromagnet, leaving space for the ball-bearing. Make sure it faces directly downwards and not at an angle.
Attach both light gates around the glass tube at a starting distance of around 10 cm.
Measure this distance between the two light gates as the height, h with a metre ruler.
Place the cushion directly underneath the end of the glass tube to catch the ball-bearing when it falls through.
Switch the current on the electromagnet and place the ball-bearing directly underneath so it is attracted to it.
Turn the current to the electromagnet off. The ball should drop.
When the ball drops through the first light gate, the timer starts.
When the ball drops through the second light gate, the timer stops.
Read the time on the timer and record this as time, t
Increase h (eg. by 5 cm) and repeat the experiment. At least 5 – 10 values for h should be used
Repeat this method at least 3 times for each value of h and calculate an average t for each
What is the equation in the determination of g practical
2h/t = gt + 2u
What are the systematic errors in the determination of g practical
Residue magnetism after the electromagnet is switched off may cause t to be recorded as longer than it should be
What are the random errors in the determination of g practical
Large uncertainty in h from using a metre ruler with precision of 1mm
Ball may not fall accurately down the centre of each light gate
Random errors are reduced through repeating the experiment for each value of h at least 3-5 times and finding an average time
Safety considerations in the determination of g practical
Only switch current on the electromagnet once everything is set-up to reduce risk of electrocution
A cushion must be used to catch the ball-bearing so it doesn’t damage the surface
The tall clamp stand needs to be attached to a surface with a G clamp so it stays rigid
Newtons first law
A body will remain at rest or move with constant velocity unless acted on by a resultant force
Newtons second law
The resultant force on an object is equal to its rate of change in momentum
F=ma
What happens if the resultant force is along the direction of motion
It will speed up or slow down the body
What happens if the resultant force is at an angle
It will change the direction of the body
Newtons Third Law
If body A exerts a force on body B, then body B will exert a force on body A of equal magnitude but in the opposite direction
Conditions for 2 forces to be a newtons’ third law pair
Forces must act on 2 DIFFERENT objects
Forces must be of the same type
Forces must be the same size
Forces must act in opposite directions
momentum
mass x velocity
Unit for momentum
kg ms^-1
Principal of conservation of linear momentum
The total momentum before a collision = the total momentum after a collision provided no external forces acts
What are closes or isolated systems
Systems with no external forces
Change in momentum =
Force x (change in)Time where F is constant
Impulse
Change in momentum (Ns)
What does the area under a force- time graph represent
The impulse
How can impact forces be reduced
Increasing the contact time
What happens to change in momentum as the contact time increases
Change in momentum is greater
What happens to KE in an elastic collision
Kinetic energy IS conserved
What happens to KE in an inelastic collision
Kinetic energy IS NOT conserved
What happens to the objects in an elastic collision
Objects collide and DO NOT stick together and then move in opposite directions
What happens to the objects in an inelastic collision
Objects collide and stick together after the collision
How do seatbelts, crumple zones and airbags generally work as safety features
They absorb the energy from the impact and increase the time over which the force takes place.
This, in turn, increases the time taken for the change in momentum of the passenger and the vehicle to come to rest.
The increased time reduces the force and risk of injury on a passenger
How do seatbelts reduce the force in a collision
Seat belts are supposed to keep people fixed to their seat in an abrupt stop.
They stretch slightly to increase the time for the passenger’s momentum to reach zero and therefore reduce the force
How do airbags reduce the force in a collision
They act as a soft cushion
How are crumple zones used to reduce the force in a collision
They increase the time over which the vehicle comes to rest, lowering the impact force on the passengers
Work
The amount of energy transferred when an external force causes an object to move over a certain distance.
Work done =
Average force applied parallel to direction of displacement x Displacement
How is work done when a force is used to move an object over a distance
When pushing a block, work is done against friction to give the box KE to move.
The KE is then transferred to other forms of energy e.g. sound, heat
Work done when direction of motion is not parallel to direction of force =
Force x displacement x cos/sin0
Power
Rate of energy transfer
Power =
change in work done / change in time
Power if an object is moving at constant velocity with constant force
P = F x V with the force acting in the direction of the velocity
What does the area under the force-displacement graph represent
Work done
How to calculate work done when there is a variable force
Using the area under the graph
Loss/change in KE
work done
Conservation of energy
Energy cannot be created or destroyed, it can only be transferred from one form to another
