4. Mechanics and Materials Flashcards
What is density?
The mass per unit volume of a material.
What does Hooke’s Law state?
That extension is directly proportional to the force applied, given environmental conditions (e.g. temperature) is kept the same.
Hooke’s Law is shown on the straight part of a force-extension graph.
What is the limit of proportionality?
The limit of proportionality (P) is the point after which Hooke’s law is no longer obeyed.
This, on a force extension graph, is where the gradient begins to change.
What is the elastic limit (E)?
The point after the limit of proportionality where if the force is increased beyond this, the material will deformed plastically.
How would you measure the effect of forces on springs?
Load a spring with weights and measure it’s length:
-carefully measure the starting length of the spring.
-use a set square or pointer to help reduce measurement uncertainties due to parallax.
-measure the same point on the spring each time.
-repeat the experiment several times and take an average.
Since there is no way to identify the elastic limit from a graph, the only way to find it is to remove each weight after adding it to see if it returns to it’s original length.
What is k?
The spring constant. This is a measure of the stiffness of the spring up to it’s limit of proportionality. It is measure in N/m.
(The gradient of an F-e graph)
What is an elastic and a plastic material?
An elastic material will return to its original shape once the deforming force is removed.
A plastic material will not return to its original shape once the deforming force is removed.
On a force extension graph, how is plastic deformation shown?
By one line representing the loading force, and another with the same gradient (as the stiffness will not have changed) representing the unloading which will intercept the x-axis at another point. The area between these graphs would be the work done. The energy is usually lost to the surroundings as heat.
What is the tensile stress?
The force applied per unit cross sectional area of the wire. It is measure in Pascals (Pa).
Stress = σ = F/A
What is tensile strain?
The extension per unit original length, it has no unit.
Strain = ε = ΔL/L
What is the elastic potential energy (or elastic strain energy)?
The energy stored in springs which is equivalent to the work done in stretching it.
It is the area under a force extension graph and can be given by Ep = 1/2FΔL or 1/2kΔ(L)^2
Springs in parallel:
F = (k1 + k2)ΔL
i.e. the spring constants add up.
Springs in series:
1/k = 1/k1 + 1/k2
So the effective spring constant is reduced.
What is the breaking stress?
Breaking stress is the value of stress at which the material will break apart, this value will depend on the conditions of the material e.g its temperature.
What is brittle behaviour?
Fracturing without showing any signs of plastic behaviour. The will follow Hooke’s Law for a short amount of time before fracturing.
What is ductile behaviour?
Plastic deformation. (Like a typical force extension graph.)
What is Young’s Modulus?
Tensile stress divided by tensile train (in question explain the terms). Measured in Nm^-2 or Pascals.
“The relation between tensile stress to tensile strain”
Stress strain graphs for different characteristics of materials
An experiment to find the Young’s modulus of a material?
Independent: force on the spring, determined by the mass hung from it.
Dependant: length measured with a ruler and diameter measured by vernier callipers.
Hang a long spring over a pulley at the edge of a horizontal surface. Make an initial measurement of the end of the spring to a marked point which is which is before the pulley. Make this distance at least 1 meter. Also, measure it’s diameter at three different points along the spring’s length. Add masses of 100N until a combined force of 1000N onto the end of the spring and repeat taking the measurements.
Safety: wear goggles in case the spring snaps and place a cushion below the masses on the floor.
Analysis: take an average of the diameter to find the cross-sectional area (πd^2/4). Use this to find the stress: F/A. Also calculate strain ΔL/L. Plot stress against strain and calculate the gradient.
What is a scalar/vector quantity?
Scalar: has only magnitude: speed, mass, weight, distance.
Vector: has direction and magnitude: velocity, force, acceleration, displacement.
What is a system of equilibrium?
A system where all the forces and moments are balanced meaning there is no resultant force or torque.
What is a couple?
A pair of coplanar forces where the two forces are equal in magnitude but act in opposite directions.
What does the principle of moments state?
For an object in equilibrium, the sum of anti-clockwise moments about a pivot is equal to the sum of clockwise moments.
What is the centre of mass?
The point at which an object’s mass acts.
For a uniform object, this is it’s centre.
What is an experiment to determine the value for g?
- Using a set square ensure a clear glass tube is clamped upright.
- Attach two light gates one at the top of the tube and another underneath it.
- Measure the distance between the two light gates as the height, h, with a metre ruler, initially set this to 10 cm.
- Place a cushion under the tube.
- Drop a ball bearing through the tube so that it passes through the first light gate, starting a timer which then stops when the ball passes through the second. Record the time, t.
- Increase h in 5 cm intervals and repeat the experiment 3 times for each value of h.
- Plot 2h/t on the y-axis, t on the x-axis. Gradient =a=g. y-intercept = 2u.
What’s a distance-time and velocity-time graph?
Distance-time graph: gradient = speed. If the line is flat then the object is stationary.
Velocity-time graph: If the line is flat then the object is moving at a constant velocity. gradient = acceleration. Area under the line = distance travelled.
What forces are acting in projectile motion?
Weight, as an unbalanced force this means there is acceleration in the vertical direction. There is no acceleration in the horizontal direction.
Mechanics skills:
-resolving vectors into their horizontal and vertical components
-use scales to actually draw vector quantities in diagrams
-find the resultant force using the closed triangle method
-resolve two perpendicular forces
What are Newton’s Laws?
I: A body will remain at rest or move with constant velocity unless acted on by a resultant force.
II: F=ma
III: Every action has an equal and opposite reaction.
How does an object reach it’s terminal velocity?
Initially the velocity increases due to the downward force of weight. As the object accelerates, they impact with particles in the air. Due to Newton’s third law this means that the particles will have an increasing upwards force on the object. This is air resistance. As air resistance increases as velocity increases, due to Newton’s Second Law, this means the resultant force and therefore acceleration decreases (F = ma). When weight is equal to drag, the resultant force is zero so the object has reached it’s maximum, constant, terminal velocity.
A velocity-time graph for a free falling object with and without a parachute:
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What is an elastic and inelsatic collision?
Elastic: where both momentum and kinetic energy are conserved
Inelastic: where only momentum is conserved, while some of the kinetic energy is converted into other forms (e.g heat, sound, gravitational potential)
What is the calculation for efficiency?
Useful / total x 100
How do you find the volume of an irregularly shaped object?
Displacement can or fill a beaker with water.
What is the conservation of linear momentum?
The total momentum before a collision = the total momentum after a collision provided no external force acts
