Mechanics Flashcards
Glover
Difference between buoyancy and upthrust
Buoyancy is the ability of an object to float in a fluid whereas upthrust is a force exerted on a submerged object by a fluid
This fluid can be a liquid or gas
inclined plane
slope
angle of elevation
An angle that is formed between the horizontal line and the line of sight (the ‘slope’ that you’re looking along)
An apple with a weight of 1.5 N is at rest on an inclined plane at 29° to the horizontal. Find the component
of its weight that acts along the slope.
- Draw a diagram - the angle between the slope and horizontal component = 29°
- Using the horizontal and vertical components to form a triangle, you can find that the angle between the length we are looking for (W1) = 90 - 29 = 61°, and therefore the angle between W1 and its perpendicular bisector is also 29°
- Use trigonometry to find the magnitude of W1 ->
sin(29) = W1 / 1.5
W1 = 0.7272… ~ 0.73N
couple
a pair of parallel equally-sized forces that act in opposite directions
coplanar
acting in the same place
Are couples coplanar or non-coplanar?
Coplanar
A couple doesn’t cause any ____ ____ ____,
but does produce a _____.
resultant linear force
turning force/moment
torque
The rotational force that causes an object to rotate about its axis
difference between a moment and a torque
A moment ‘bends’ (e.g. a force pushes down on a beam on a wall) whilst a torque ‘twists’ an object about its axis (i.e. it rotates, often fully)
Another way of distinguishing the pair:
A moment is a turning effect, whereas a torque is a turning effect of a force.
I think, don’t quote me
freefall
The motion of an object with an acceleration of g; constant acceleration without resistive forces; motion of an object where the force due to gravity is the only force acting on it
Why can you model throwing a rock with only weight acting downwards?
At relatively small distances, the effect of air resistance is negligible
Projectile motions assumptions (4)
- ONLY gravitational attraction acts on the object so the ONLY acceleration is downwards
- Acceleration in the vertical component of s is always g which is 9.8N on Earth
- Horizontal velocity of the object is constant (u = v) - massive assumption
- **The horizontal and vertical motions are completely independent of each other **
acceleration due to gravity
9.81m/s2
given in formula booklet
centripetal force
The force acting on a object in circular motion that is directed toward the centre of the circle
formula for velocity of an object in travelling in a circle
v = πd / T
where T is the time for a single rotation
derived from s = vt, where s is the cirumference
What is the centripetal force caused by?
A force which is causing an acceleration on a mass
instantaneous speed
The speed of an object over an infinitely small time period (at a particular moment in time)
How is instantaneous speed measured?
Using speed cameras
How can you find the instantaneous speed from a distance-time graph?
Find the gradient of a tangent at the point
What is the main difference between a speed-time graph and a velocity-time graph?
Velocity time graphs can have a negative quadrant to show something
travelling in the opposite direction
Decreasing velocity in the first quadrant on a velocity-time graph
Negative acceleration i.e. it’s slowing down, not coming back in the opposite direction
Negative velocity in the fourth quadrant on a velocity-time graph
Moving in the opposite direction (speed increasing if the velocity is getting more negative)
A ball of mass m kg falls with a speed of v. There is a resisitive force of kv. What is the ball’s terminal speed?
Weight downwards force = mg
Terminal speed -> 0 resultant force -> kv = mg
Rearrange to get v = mg/k
The horizontal and vertical components are ____.
independent of each other
What would the distance-time graphs look like for the horizontal and vertical components of a rock being thrown?
Horizontal - directly-proportional i.e. straight line through the origin (no acceleration)
Vertical - positive cubic graph (distance doesn’t decrease)
What would the displacement-time graphs look like for the horizontal and vertical components of a rock being thrown?
Horizontal - initially directly-proportional i.e. straight line through the origin (no acceleration) which peaks then immediately returns to s = 0 with the same gradient
Vertical - negative quadratic graph (displacement increases then decreases)
A rock is thrown towards a tree. Do the
a) horizontal component
and b) the vertical component
change? Explain why.
a) no - the horizontal component says constant as the system is modelled without air resistance.
b) yes - there is acceleration due to the force of gravity acting downwards.
You need to use the SUVAT formulae for vertical / horizontal / both components.
Vertical - you can just use speed = distance / time for the horizontal component as the accerelation is zero; the initial and final velocities are the same
How is the time taken for an object thrown horizontally to fall related to its initial velocity?
The time taken and the initial velocity are independent of each other.
How is the time taken for a thrown object to fall to the ground related to its horizontal and vertical components?
This is worded sort of weirdly, but I don’t know how to make it better.
The time taken to fall to the ground is the same for its horizontal and vertical components - both distances must be 0, obviously.
This is highly useful in mechanics free fall calculations.
The time taken for a thrown object to fall depends on its ____ ____.
vertical height
Forces on a block should meet at the ____.
centre of mass
Give four assumptions in order to do calculations for projectile motion.
- ONLY the gravitational attraction acts as a force on the object so the ONLY acceleration is downwards
- Acceleration in the vertical component is always g which is 9.81N on Earth
- The horizontal velocity of the object is constant (u = v) i.e. there is no air resistance [this is one massive assumption]
- The horizontal and vertical components are completely independent of each other
You know the initial horizontal component of a projectile motion. How can you calculate the magnitude of the velocity of an object just before it hits the ground?
Calculate the vertical component of the motion using SUVAT equations from the top of the parabola to the x-axis (where s = 0). You know u, a, and either s or t (you may have already calculated this in a previous part of the question)
Then use the magnitude formula i.e. √(h2) + (v2) where h and v represent the horizontal and vertical components respectively
A motocyclist passes a cyclist at t = 0s. The motorcyclist continues moving at 8.8m/s for 200s, after which it stops to wait for the cyclist. The cyclist moves at a constant speed of 2.2m/s. How long does the motorcyclist have to wait for the cyclist to catch up?
Motorcyclist: v = 8.8m/s, t = 200s, s = ?
distance travelled = 1760m
Cyclist: v = 2.2m/s, s = 1760m, t = ?
time taken overall for the whole process = 800s
Time taken motorcyclist has to wait =
800 – 200 = 600s (overall time includes the time during which the motorcyclist is travelling)
What does a force-extension graph look like?
Directly proportional initially, curves to a plateau after the limit of proportionality
What does an extension-froce graph look like?
Directly proportional initially, curves upwards after the limit of proportionality (sort of like a vertical plateau)
A girl is bouncing on a trampoline. Assuming that air resistance is negligible, her acceleration
A is zero when she reaches maximum height.
B is constant when she is in the air.
C changes direction as she rises and then falls.
D is maximum just before she lands on the trampoline.
B as she is still under the influence of gravity, so there is constantly the acceleration of 9.81m2 downwards.
All objects fall with an acceleration independent/dependent of mass (as long as ____ forces act).
indepdent, no other
Acceleration (SUVAT) formulae don’t take mass into account
Explain why air resistance increases with speed.
The rate of collisions between air molecules and the object increases.
As a falling object accelerates, the acceleration ____. Explain your answer.
decreases - the air resistance increases (due to the increase in the rate of collisions between the object and air particles)
Suggest a place where scientists could test the effect of no air resistance on the velocity of two falling objects.
On the Moon, because there is only a very thin atmosphere and so only a very, very small (i.e. negligible) air resistance
Explain why air resistance is negligible over very short distances.
The object starts off moving slowly so the rate of collisions between the object and the air particles is low. This means the object’s deceleration is very small.
A car driver has two hands on either side of a wheel. They turn the wheel clockwise with each hand exerting forces equal in magnitude. What is the moment?
M = force by exerted by one hand * perpendicular distance of the diameter of the wheel
This is because the moments are both clockwise and the distance to each hand from the pivot is half the diameter (you can find the moments of each hand separately then add them up to get the same formula)
When will an object fall over? Explain your answer.
When the weight acting directly downwards from the object’s centre of mass is no longer within the object’s base area (the pivot)
The more stable an object is, the ____ the base area and the ____ the centre of mass.
larger, lower
The closer the object’s centre of mass is to a support, the ____ the force on the support.
larger (distance decreases so force decreases to maintain equilibrium from no moment)
You can choose which point is the pivot for some moments questions. T/F and explain the benefit of this.
True - you can ignore any perpendicular forces (e.g. weight/normal contact force) that act at the pivot you choose.
A plank with a weight of 40 N rests on two supports 6m and 2m from the plank’s centre of mass. Find the upwards force provided by each support.
Take one support as the pivot, calculate the force using the principle of moments, then repeat for the other support.
Say the left support is the pivot (normal contact force on right pivot is being calculated):
Mc: 40 * 6 = 240Nm
Ma: 8F
240 = 8F
F = 30N
Say the right support is the pivot (normal contact force on left pivot is being calculated):
Mc: 8F
Ma: 40 * 2 = 80Nm
8F = 80
F = 10N
So the support furthest from the centre of mass provides 10 N of force,
while the support closest to the centre of mass provides 30 N of force.
line of action
An imaginary line that shows the direction that a force acts
If the ____ from the ____ is beyond ____ of an object, the object topples.
line of action, centre of mass, base
stable equilibrium (+ example)
The position in which an object returns to after being moved to one side (e.g. tilting a bookcase slightly, a swing)
unstable equilibrium (+ example)
Any slight offset will make an object move away from the equilibrium position e.g. a plank balanced perfectly on a ball
A uniform beam of weight 23.5 N is attached by a hinge to a vertical wall and supported by
a string.
The string makes an angle of 35° to the wall.
What is the tension in the string?
AS Paper 2 - June 2022, Q22 - struggled 21/2/25
Hidden moments question:
Vertical upwards force = T cos35 (where T = tension)
T cos35 * length = 23.5 * (length / 2)
T = 14.3N
The edge of a uniform plank touches a bank and balances on a rock 0.8m from the end of the plank. It doesn’t tip. Where are the forces involved?
Weight acting downwards from centre of plank
NCF acting upwards from the rock (it’s in equilibrium, so clockwise moments = anticlockwise moments about the rock pivot, and this anticlockwise moment abou the rock is caused by this NCF).
No NCF acts upwards from the bank on the plank because no force acts there! Remember, weight acts from the centre of mass.
Newton’s First Law = law of ____
inertia
State Newton’s First Law.
An object will continue moving at a certain velocity if no external resultant force acts on the object.
The resultant force is the ___ ___ of all the forces.
vector sum
State Newton’s Second Law in words.
The resultant force on an object is equal
State Newton’s Third Law.
If object A exerts a force (F) on object B, then object B exerts an equal but opposite force (-F) on object A.
Considering Newton’s Third Law, explain how objects actually move (wouldn’t there be a resultant force of 0?)
The forces act on the two different objects and represent the interaction from two different perspectives.
A pen rests on a table. Dinah says this demonstrates Newton’s Third Law. Discuss.
Dinah isn’t correct as the two forces are of different types i.e. weight acting downwards on the table and the normal contact force acting upwards on the pen
Although the forces are equal in magnitude and act in opposite directions, so there’s an acceleration of 0 and so this therefore demonstrates Newton’s First Law.
There is a resultant force of F N on an object. What could be changing?
either the acceleration is changing and isn’t 0, or there is a change in mass over time (consider F = ma; Newton’s Second Law).
The formula for acceleration can be substituted into Newton’s Second Law. What formula does this create?
F = m * (v / t)
F = change in momentum / time
What are the two formulae that represent Newton’s Second Law?
F = ma
F = change in momentum / time
Can mass, gravitational field strength and weight ever be 0?
g = theoretically yes, e.g. centre of Earth (although it’s never really zero, just very, very close to it)
weight = yes, if g = 0
m = no, because it’s an intrinsic property - the mass of an object can’t be 0 (at least for the purposes of mechanics)
average velocity formula
(final velocity + intial velocity) / 2
