1 Flashcards
(24 cards)
What is work equal to (3 dimensions scenario)?
Work is equal to the dot product of the vectors for force and displacement.
What is work equal to (3 dimensions, variable force scenario)?
The sum of the integrals of the force in the x, y and z directions with respect to displacement in the x, y and z directions.
What is power equal to?
The rate of doing work.
Dot product of force vector and velocity vector.
What is the work-energy theorem?
The work done by the resultant force on a particle is equal to the change in the kinetic energy of the particle.
What are the key properties of a conservative force?
The work done is reversible.
The work done by the conservative force is independent of the force, and only depends on the starting and finishing points. (work done moving an object round a closed path is zero)
The work done can be expressed as the difference between the initial and final values of the potential energy function.
What is are two examples of conservative forces?
Gravitational, elastic
What is an example of a non-conservative force?
Friction
What does the mechanical energy of a system refer to?
The sum of the total potential energy and the total kinetic energy.
How is the potential energy function defined?
The potential energy function is (negative) the integral of the force function with respect to position.
How is the force function defined in terms of potential energy?
The force function is (negative) the differential of the potential energy function, with respect to position.
How must integrals and differentials be calculated in 3D vector space?
The x, y and z components must be calculated separately, and then summed.
Where is gravitational potential energy at a minimum?
At an infinite distance away from the mass ( potential = 0).
How can the centre of mass be calculated?
The sum of (product of mass and position) divided by the sum of (mass). [orthogonal components calculated separately]
[for a rigid body] The integral of (position with respect to mass) divided by the integral of (1 with respect to mass).
What is the key property of the centre of mass of a system of particles?
The product of the total mass and the average acceleration is equal to the sum of the forces acting on the particles.
What is the impulse?
The change in momentum, equal to the integral of force with respect to time.
What are the key properties of an elastic collision?
Kinetic energy and momentum are both conserved.
What is a property of an elastic collision between two bodies?
The relative velocity of the two bodies before the collision equals the negative relative velocity after the collision.
What is a property of an elastic collision between two bodies that have the same mass?
The bodies exchange velocities before and after the collision.
What is it important to remember when dealing with a situation involving an oblique impact?
Momentum is conserved, but must be resolved in perpendicular directions.
How can a situation be transformed so that it is in the COM frame?
Why is this useful?
Subtract the average velocity from every velocity vector.
In the COM frame, the total momentum is equal to zero.
How can the total KE of a system of particles be expressed in relation to the centre of mass?
The KE of the system = the KE associated with the COM motion + the sum of the KE’s of particles relative to the COM.
How can the velocity of the centre of mass be calculated?
The sum of (the product of the velocity and mass of each particle) divided by (the sum of the mass of each particle).
How can the KE of a system of two masses be expressed in relation to the centre of mass?
KE of system = (KE associated with the COM motion) + (1/2 * the reduced mass * the relative velocity of the masses)
What is reduced mass?
The reduced mass of a system of two interacting particles is (the product of the masses) divided by (the sum of the masses).
