Section 4 - Mechanics Flashcards
What is a scalar quantity?
A quantity that only has a magnitude, without direction.
What is a vector quantity?
A quantity that has both magnitude and direction.
Sort these into scalar and vector: • Mass • Displacement • Velocity • Time • Force • Acceleration • Distance • Speed • Energy • Momentum
SCALAR • Mass • Temperature • Time • Distance • Speed • Energy VECTOR • Displacement • Velocity • Force • Acceleration • Momentum
Is mass vector or scalar?
Scalar
Is temperature vector or scalar?
Scalar
Is displacement vector or scalar?
Vector
Is velocity vector or scalar?
Vector
Is time vector or scalar?
Scalar
Is distance vector or scalar?
Scalar
Is force vector or scalar?
Vector
Is speed vector or scalar?
Scalar
Is weight vector or scalar?
Vector
Is energy vector or scalar?
Scalar
Is acceleration vector or scalar?
Vector
Is momentum vector or scalar?
Vector
What is the term for adding two forces together?
Finding the resultant of them.
What are the two methods for finding the resultant of two forces?
1 - Scale drawings
2 - Pythagoras + Trigonometry
How can the resultant of two forces be found using scale diagrams?
- Draw the two forces tip to tail
- Draw the resultant force
- Measure the length of the resultant force and the angle from the horizontal
How can the resultant of two forces be found using Pythagoras and trigonometry?
- Only works if the forces are at right angles
- Draw a right angled triangle out of the forces
- Use Pythagoras to find the magnitude of the resultant
- Use trig to find the direction of the resultant
When finding the resultant of two forces, when can Pythagoras + trigonometry be used?
When the forces are at right angles to each other.
What is splitting a force into horizontal and vertical components called?
Resolving the force.
When resolving a force (F) to the top right, what is the horizontal component equal to?
F x cosθ
Where θ is the angle from the horizontal.
When resolving a force (F) to the top right, what is the vertical component equal to?
F x sinθ
Where θ is the angle from the horizontal.
Why is vertical and horizontal components easy to find when resolving forces?
The two components don’t affect each other, so the two directions can be dealt with separately.
On a free-body diagram, do the sizes of the arrows matter?
Yes, because they represent the size of the force.
What is a free-body diagram?
A diagram that shows all the forces acting on a single body (and NOT the forces that the body exerts).
What are coplanar forces?
- Forces that are all in the same plane
* You’ll only have to deal with these types of forces
What are the conditions for an object to be in equilibrium?
- Forces acting on the object in each direction must be balanced.
- No resultant moment acting on the object.
Describe the motion of a body in equilibrium.
Either:
• At rest
• Moving at constant velocity
How can you demonstrate that three coplanar forces give no resultant force?
When you draw them out as a triangle, they form a closed loop.
When there are three forces acting on a body in equilibrium and one is unknown, how can it be calculated?
- Resolve each force horizontally and vertically
- The horizontal forces must add up to 0.
- The vertical forces must add up to 0.
- Find the missing force.
When resolving a force acting in an unusual direction, what is it important to do?
Choose axis that are sensible for the problem.
What axis should you choose when resolving a force acting on an object on a slope?
• Choose axis at right angles to the slope.
• Turning the page to be parallel with the slope will help.
(See diagram pg 41)
What is a moment?
- The turning effect of a force around a point.
* Equal to the force multiplied by the perpendicular distance from the line of action to the pivot.
What is the equation for the moment of a force?
Moment (Nm) = Force (N) x Perpendicular distance from the point to the line of action of the force (m)
M = F x d
What is d in the moments equation?
Perpendicular distance from the turning point to the line of action of the force (m).
What is the unit for moments?
Newtonmeter (Nm)
State the principle of moments.
For an object in equilibrium, the sum of the clockwise moments about any point equals the sum of the anticlockwise moments.
In a lever, what forces act against each other?
The effort force acts against the load force.
What is a couple?
- A pair of coplanar forces of equal size that act parallel to each other but in opposite directions.
- Produce a turning effect.
What is the equation for the moment of a couple?
Moment (Nm) = Size of one of the forces (N) x Perpendicular distance between the lines of action of the forces (m)
M = F x d
What is mass?
The amount of matter in an object.
What is the unit for mass?
Kilograms (kg)
What is inertia?
An object’s resistance to change in velocity.
What affects an object’s inertia?
- Its mass.
* The greater the mass, the greater the inertia.
Is an object’s mass affected by the gravitational field strength?
No
What is weight?
The force exerted on an object due to the Earth’s gravitational field.
What is the unit for weight?
Newton (N)
What is the equation for weight?
Weight = Mass x Gravitational Field Strength
W = m x g
What is the value of g?
9.81 N/kg
What is an object’s centre of mass?
- The point through which the whole weight can be said to act through.
- Object will balance around this point.
Is the centre of mass always on an object?
No, sometimes it is outside the object.
Where is the centre of mass of a uniform, regular solid (e.g. a sphere)?
At its centre.
How can the centre of mass of a regular object be found?
- Look at the lines of symmetry
* The centre of mass is where the lines cross
How can the centre of mass of an irregular object be found?
- Hang object from a point
- Draw vertical line downwards from point (using a plumb bob as guidance)
- Repeat with different point
- Centre of mass is where the lines cross
When will an object topple and why?
- When the vertical line from its centre of mass falls outside of the base area.
- Because the centre of mass causes a resultant moment around the pivot.
What makes an object stable?
• Low centre of mass
• Wide base
E.g racing cars won’t topple over on fast corners
For supports:
The closer the object’s centre of mass …..
….the stronger the force on the support …
What is speed?
How fast an object is moving, regardless of direction.
What is displacement?
How far an object has travelled from its starting point in a given direction.
What is the symbol for displacement?
s
What is velocity (in terms of displacement)?
The rate of change of an object’s displacement.
What is the symbol for velocity?
v
What is acceleration?
The rate of change of an object’s velocity.
What is the symbol for acceleration?
a
What is the equation for velocity?
v = Δs/Δt
What is the equation for acceleration?
a = Δv/Δt
What is instantaneous speed?
The speed at a given moment (as oppose to average speed).
Describe the displacement-time graph for an accelerating object.
- Curved graph
* If acceleration is constant, the rate of change of the gradient is constant.
Remember to practice predicting different displacement-time graphs.
Pg 46 of revision guide.
What does the gradient and area under the curve represent in a displacement-time graph?
- Gradient = Velocity
* Area = Nothing
How do you find the velocity from a displacement-time graph?
- Find the gradient.
* You may need to draw a tangent if the graph is a curve.
On a curved displacement-time graph, how do you find the AVERAGE velocity?
- Divide the overall displacement by the overall time.
* No need for tangents.
What is the difference between a speed-time and velocity-time graph?
A velocity-time graph can have a negative part to show motion in the opposite direction.
How is uniform acceleration shown on a velocity-time graph?
Straight line
How is a changing acceleration shown on a velocity-time graph?
Curved line
What does the gradient and area under the graph represent on a velocity-time graph?
- Gradient = Acceleration
* Area = Displacement
How do you find the acceleration from a velocity-time graph?
Gradient of the line
How did you find the displacement from velocity-time graph?
Area under the graph
On an acceleration-time graph, what does the area under the line represent?
The change in velocity.
What piece of equipment can be used in motion experiments?
Ultrasound position detector