Mechanics Flashcards
Mechanics practice
Is momentum a vector or a scalar?
Momentum is a vector quantity, as it includes both mass and velocity of an object. Because velocity is already a vector, by multiplying it by a scalar quantity (mass), the result will still be a vector.
What is momentum useful for?
Momentum is used for explaining collisions and sometimes explosions.
What is the formula for momentum and what does each letter stand for
P = mv
P = momentum in kgms-1 m = mass in kg v = velocity in ms-1
What’s the deal with change in momentum?
What’s the deal with impulse?
When an external force is applied, the momentum will have changed.
This momentum is calculated by ∆p = Pf - Pi.
Pf is the final momentum
Pi is the initial momentum
The change in momentum is always constant (linked to impulse equation F∆t)
The change of any value can be generalised using the formula ∆ = Final - Initial
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Impulse (of a force) is another way to look at change in momentum of an object.
The formula is ∆P = F x ∆t
F x ∆t is impulse (Ns)
∆P is change in momentum (kgms-1)
Impulse is important as it relates time and force to the change in momentum.
Therefore, the two ways to calculate ∆P (change in momentum is:
∆P = Pf - Pi
∆P = F x ∆t
What’s the deal with conservation of momentum?
If no external force (like friction) is applied, the total momentum will always be conserved (i.e. same before and after collision).
Notes:
- No external force can be a reason for justifications and explanations for excellence
- This concept is useful for explaining and justifying problems involving collision and explosions
Pi = Pf
Total initial momentum = Total final momentum
e.g.
For 2 objects colliding with one another
P(initial)1 + P(initial)2 = P(final)1 + P(final)2
Explain how vectors relate to momentum
When calculating momentum, we have to consider vectors
If the vectors are opposing each other in direction, like if two objects are colliding with each other, then make one vector positive and the other negative for calculations.
→ ←
For example, make final momentum positive and initial momentum negative.
That way, to find out the change in momentum, if you were to use Pf - Pi = ∆P, it would really just be Pf - (-Pi) = ∆P. Hence → Pf + Pi = ∆P
When we say what the (change in/total) momentum is (∆p), we say for example: 10kgms-1 to the left.
This is because vectors have both size and direction.
Using vectors to add or subtract momentum is an important concept to know. Especially for change in/total momentum.
Rules (must understand these):
- —-> +
- —-> -
What would happen if two objects were to stick together after they collide?
(momentum)
Both their velocity and mass would be combined together to form a total velocity and total mass.
Some questions might ask how to reduce the chances of injury in a car crash. How might you explain this?
(momentum)
Less force means less chance of injury.
We can rearrange the impulse equation to get:
F = ∆P/∆t
Therefore, the decrease force (F) we can increase the time (t) or decrease the momentum (p).
What are the requirements for equilibrium to be achieved?
Torque
The upwards and downwards forces must be equal and balanced and the torques (clockwise and anticlockwise) must be equal to each other and therefore cancel out
What is the formula for torque? Include units
T = Fd
T = Torque F = Force - the mass is often given, so make sure to multiply with gravity (F = mg) to get the force in Newtons (N) d = Distance
The unit of torque is Nm (based off the formula)
Define torque
Torque is a force acting at a distance from the pivot point.
What are some important things to note about torque?
- All forces causes torque around a pivot point unless the force acts exactly on the pivot point (as there is no distance)
- Torque is either clockwise or anticlockwise
- Any point can be the pivot point - the place to choose the pivot point is often where you want to ignore a value or a place that features the unknown value (i.e. distance = 0)
- If the clockwise and anticlockwise torques balance/cancel each other out, the system is in equilibrium. This means that it is still, but could also mean that it is rotating at a constant speed.
- A question will often require you to make an equation stating that the anticlockwise torque equals to the clockwise torque, Then, you would solve for an unknown force or direction.
What can be considered upward force?
Torque
Support forces (i.e. from the objects supporting the plank/bridge etc)
How does gravity affect objects travellings upwards compared to objects travelling downwards?
If an object is travelling upwards, it is opposing gravity (-9.8 m/s^2). It will decelerate. If the object is travelling downwards, it is going along gravity (+9.8 m/s^2). It will accelerate.
What do vector components form?
Triangles
