Mechanics

Question 1

Difference between buoyancy and upthrust

Answer 1

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

Question 2

inclined plane

Answer 2

slope

Question 3

angle of elevation

Answer 3

An angle that is formed between the horizontal line and the line of sight (the ‘slope’ that you’re looking along)

Question 4

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.

Answer 4

• 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

Question 5

couple

Answer 5

a pair of parallel equally-sized forces,
but they act in opposite directions

Question 6

coplanar

Answer 6

acting in the same place

Question 7

Are couples coplanar or non-coplanar?

Answer 7

Coplanar

Question 8

A couple doesn’t cause any ____ ____ ____,
but does produce a _____.

Answer 8

resultant linear force
turning force/moment

Question 9

freefall

Answer 9

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

Question 10

Why can you model throwing a rock with only weight acting downwards?

Answer 10

At relatively small distances, the effect of air resistance is negligible

Question 11

Projectile motions assumptions (4)

Answer 11

• 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 **

Question 12

acceleration due to gravity

Answer 12

9.81m/s²

given in formula booklet

Question 13

centripetal force

Answer 13

The force acting on a object in circular motion that is directed toward the centre of the circle

Question 14

formula for velocity of an object in travelling in a circle

Answer 14

v = πd / T
where T is the time for a single rotation

derived from s = vt, where s is the cirumference

Question 15

What is the centripetal force caused by?

Answer 15

A force which is causing an acceleration on a mass

Question 16

instantaneous speed

Answer 16

The speed of an object over an infinitely small time period (at a particular moment in time)

Question 17

How is instantaneous speed measured?

Answer 17

Using speed cameras

Question 18

How can you find the instantaneous speed from a distance-time graph?

Answer 18

Find the gradient of a tangent at the point

Question 19

What is the main difference between a speed-time graph and a velocity-time graph?

Answer 19

Velocity time graphs can have a negative quadrant to show something
travelling in the opposite direction

Question 20

Decreasing velocity in the first quadrant on a velocity-time graph

Answer 20

Negative acceleration i.e. it’s slowing down, not coming back in the opposite direction

Question 21

Negative velocity in the fourth quadrant on a velocity-time graph

Answer 21

Moving in the opposite direction (speed increasing if the velocity is getting more negative)

Question 22

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?

Answer 22

Weight downwards force = mg
Terminal speed -> 0 resultant force -> kv = mg
Rearrange to get v = mg/k

Question 23

The horizontal and vertical components are ____.

Answer 23

independent of each other

Question 24

What would the distance-time graphs look like for the horizontal and vertical components of a rock being thrown?

Answer 24

Horizontal - directly-proportional i.e. straight line through the origin (no acceleration)
Vertical - positive cubic graph (distance doesn’t decrease)

Question 25

What would the displacement-time graphs look like for the horizontal and vertical components of a rock being thrown?

Answer 25

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)

Question 26

A rock is thrown towards a tree. Do the
a) horizontal component
and b) the vertical component
change? Explain why.

Answer 26

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.

Question 27

You need to use the SUVAT formulae for vertical / horizontal / both components.

Answer 27

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

Question 28

How is the time taken for an object thrown horizontally to fall related to its initial velocity?

Answer 28

The time taken and the initial velocity are independent of each other.

Question 29

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.

Answer 29

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.

Question 30

The time taken for a thrown object to fall depends on its ____ ____.

Answer 30

vertical height

Question 31

Forces on a block should meet at the ____.

Answer 31

centre of mass

Question 32

Give four assumptions in order to do calculations for projectile motion.

Answer 32

• 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

Question 33

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?

Answer 33

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

Question 34

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?

Answer 34

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)

Question 35

What does a force-extension graph look like?

Answer 35

Directly proportional initially, curves to a plateau after the limit of proportionality

Question 36

What does an extension-froce graph look like?

Answer 36

Directly proportional initially, curves upwards after the limit of proportionality (sort of like a vertical plateau)