MECHANICS AND MATERIALS Flashcards
Why is a lower centre of mass more stable?
It allows for greater angular displacement of the centre of gravity within the bounds of support.
(COM more likely to fall within base)
Rule for 3 forces acting on a point for object to be in equillibrium
Sum of any two forces must equal the third.
Line of action of each force intersects the other at a single point (otherwise there would be net turning effect)
How can the shape of a projectile cause a lift force
If the shape causes the air on top to flow faster than that on the bottom, there is lower pressure at the top so lift force is felt
Effects of drag force
Acts in opposite direction to motion
Increases with speed
Reduces horizontal range
Reduces maximum height of projectile if projected above horizontal, and makes descent steeper than the ascent
When is the tension in a lift greater/less than the weight
Greater - If lift is moving up and accelerating or if lift is moving down and decelerating
Less - If moving down and accelerating or moving up and decelerating
When can f=ma not be used
When mass isn’t constant
In non inertial (accelerating/rotating) reference frames
Energy transfers in free fall in a fluid
Potential energy transferred into Ek of fluid particles
Resultant force of falling raindrop modelled by equation
C , ΣF=0, so constant is 0, just normal square root graph
Shortcut for perfectly elastic collisions
Relative Velocity Of Approach (u1- u2) = Relative Velocity Of Separation (v2 - v1) [For perfectly elastic collisions]
Which of the following statements relating to Newton’s third law is incorrect?
A The two forces are equal in magnitude
B The two forces are equal and opposite so there is no resultant force
C The two forces are of the same type
D The two forces are equal and opposite but do not cancel
Obvs B
Which of the following statements relating to Newton’s third law is incorrect?
A The two forces are equal in magnitude
B The two forces are equal and opposite so there is no resultant force
C The two forces are of the same type
D The two forces are equal and opposite but do not cancel
Obvs B
Significance of constant velocity on Ek
No change in Ek at constant v. a = 0 so ΣF = 0 therefore no work being done on object
What is the centre of mass of an object?
The point through which a single force has no turning effect
How does a car move forwards
Friction between wheel and ground pushes back on the ground, which in turn pushes forward on the wheel
Explain how wheels skid/slip
While braking, the rotational velocity = 0, however wheel still moves forward due to momentum
Under slip when rotational velocity»_space;>linear velocity, occurs as the force being applied exceeds the frictional force.
State 2 factors that affect the usefulness of hydroelectric power for electricity production
- locations for power stations are limited
(e.g. by geographical and meteorological
factors) - continuous generation may not be
possible (e.g. times of drought) - environmental impact (e.g. population is
displaced when reservoir is built, damage to
wildlife habitats, visual intrusion)
Describe energy changes in an object at terminal velocity
No change in Ek of falling object as v is constant, so ALL of GPE is doing work against overcoming frictional forces
Alternate approaches to answering impact force questions (airbag on a driver)
Energy:
* air bag absorbs EK of the driver
* over a greater distance
* ∆ EK = force × distance
* so force is reduced
Effect of pressure:
* air bag increases contact area
* force on driver acts over a
larger area
* pressure (force per unit area)
on driver is reduced
Assuming the power output from a wind turbine is proportional to the Ek of the wind, discuss what would happen if the wind speed decreased by 1/2
- 1/2 As much mass passing through the blade each second
Ek ∝ v^2 so E reduced to 1/4 of original value x 1/2 = 1/8
Factors affecting the horizontal force on a ship being pulled by a sail
Angle of cable to horizontal
Surface area of sail
Wind speed/Ek
Acceleration of ship
Note when doing change in momentum
If velocity is in an opposite direction, add velocities
What wld happen without seatbelts
would have continued to move forward as
the car slowed down and she would have
collided with the back of a front seat or with the
front windscreen of the car
The impact time would have been much less so
the impact force would have been much
greater.
Discuss effects of reducing speed limit from 30mph to 2omph for road safety
The stopping distance would be much less at 20
mph than at 30 mph.
This is because the braking distance depends
on the square of the speed so it would be
reduced by more than half i.e. (20/30)2
.
Fewer accidents would occur because cars
travelling at 20 mph would stop in a much
shorter distance than cars at 30 mph.
Where drag force on falling projectile arises from
Friction between layers of air near the surface where air flows over the surface
Factors affecting top speed of vehicle
Engine power + shape
More streamline, lower drag force. For constant engine power
F=Fe-D so a = Fe-D/M
D increases with speed, and max speed reached when D=Fe, (terminal so a=0)
Things affecting drag force
Shape
Speed
Viscosity
Faster object greater drag force
eqs for thinking distance and braking distance
Thinking = v.reaction time
Braking = v^2/2a for constant a
Friction w cars stuff
If driver accelerates too fast, wheels skid - as there is an upper limit to the amount of friction that can be provided by road
Same for decelerating - car goes uncontrollably forward
Friction between road and tyres prevent wheel spin(slip)
https://www.youtube.com/watch?v=1UD560RQ684
Eq for calculating impact time
S=1/2(u+v)t
Deriving conservation of momentum
2 Balz - do resultant force on both, then N3L says equal and opposite, so yeah
Fr = m(v-u)/t
Elastic vs inelastic
Inelastic loss of Ek
When energy is conserved in explosion
Usually Ek conserved, but in an explosion heat, light and sound all carry away energy
Deriving kinetic energy eq
Constant force on object from v=0 to v=v , s = 1/2(u+v) = v/2
a = v-u/t = v/t
W = fs = 1/2mv^2
Doesn’t hold for speeds close to c as mass changes w velocity so
When a powered object gains speed
Output force exceeds resistive force
Motive power = power wasted due to resistive + gain in Ek/s
P=fv
For constant velocity and force
Pulleys mechanical advantage
Force multipliers, consider single puller holding 1kg weight, tension required for rope is 0.5N so 0.5N for 1N weight
However in order to pull weight a distance of 1m, person has to pull total distance of 2m for each section of rope
Can verify using W=fs, pulley changes force required to move over a distance
Mechanical adv = number of ropes holding up weight
Also note the speed of the person pulling will be nx speed of n ropes, as greater distance travelled in same time
Differences in energy/s due to friction in bearings + energy must be supplied to raise weight
Deriving eq for effective k in series
Assume springs are massless, not a bad assumption since usually weight»>weight of springs
To stretch/compress a material
A pair of forces is required
Stable vs unstable equilibrium
A body is said to be in unstable equilibrium if it does not regains its original position after being slightly disturbed by an external force
I beg you don’t use suvat
When acceleration isn’t constant
Explaining unloading curve that doesn’t return to its original shape
Plastic deformation has produced permanent extension/re-alignment
of bonds in material hence intercept non-zero
Gradient is same because after extension identical forces between
bonds
