Linear motion Flashcards
What is a particle? What conditions are required for an object to be treated as a particle?
A particle: an object with with mass but negligible size and shape.
Finite sized objects (parhaps like a plane) can be treated as particles if:
* The motion is characterized by the motion of the bodies centre of mass.
* Any rotation is negligible
Which of the two graphs is showing position, and which is showing displacement? How do we define position and displacement (i.e. in equation or def)?
What is the definition of velocity? How do we derive it from postion?
- Velocity is the rate of change in the position.
- It is a vector and can be written in scalar or vector form.
- v = ds/dt
What is the definition of acceleration? How do we derive it from velocity?
- Acceleration is the rate of change in velocity.
- It is a vector and can be written in scalar or vector form.
- a = dv/dt
What is the equation for acceleration, a, using position, s?
a = v dv/ds
What are all the ways we can write the three equations (2 acceleration equations and one velocity equation) to cover all types of variables?
When do we use SUVAT equations?
When acceleration is constant (like in free fall, when acceleration is g)
State Newtons three laws of motion.
What is the equation for Newtons Second Law?
F = ma
What is a free-body diagram, and kinetic diagram? Why are they useful?
- Free-body diagram: shows all the forces acting on the particle
- Shows the vector, ma, acting on the particle.
- From the two we can apply Newtons second law, to see how the forces make ma.
What is the condition for Newtons second law to hold true?
Only valid if acceleration is measured in a Newtonian or inertial frame of reference. I.e. when acceleration is constant or not accelerating.
- We assume the motion near the earth’s surface has a fixed inertial frame to the earth.
- For satellite analysis, or rockets that inertial frame is fixed to the stars.
What is the equation for gravitational force between two bodies, and for acceleration experienced by a body of mass, m, close to another body?
- Gravitational force, Fg = G (Mm / r^2)
- Acceleration, g(r) = Fg/m = GM/r^2)
What is the equation for Weight? How does it differ from Mass?
What is the equation of motion (simple) for an object falling near earths surface.
-mg = ma
What is the equation that relates acceleration at an altitude (y) relative to the acceleration at the earths surface?
What is the equation that satisfies static friction force, Fs?
Coulomb’s theory for dry friction. Try to draw a simple FBD for an obj.
Note:
* This isn’t an equation. It’s an inequality. It just helps us describe the way static friction builds up with a force applied.
* Static friction only exists when there is no motion
* At the limit, Fs_max, the bodies are still at rest. Any increase of Fs, will cause sliding.
What is the equation for Dynamic / kinetic friction force, Fk?
Try draw a simple FBD and kinetic diagram for an object with it.
Note:
* The coefficient of kinetic friction is generally lower than coefficient of static friction.
* Fk is always opposes sliding.
* The equation can be used to calculate Fk.
What does a simple Friction vs Applied force diagram look like for an object?
Think static and kinetic friction.
- The Fs_max value is the maximum force that can exist under static conditions.
- Notice how the friction is proportional to the Applied force in the static region up until Fs_max.
- Then the object slides and undergoes kinetic friction, which is often lower force. Remember coefficient K < coefficient s.
- The kinetic friction is constant as long as the coefficient of kinetic friction is constant and Normal force is constant.
What is the equation for elastic/spring force, Fe? Try give a simple equation of motion?
Can you think what acceleration is a function of?
Note:
* Acceleration is no a function of position, due to the change in length variable.
What is the assumptions we make about ropes/cords?
- Ropes are usually assumed to be massless and inextensible.
- The tension in the ropes, T, can only be positive, i.e. ropes cannot resist to compression.
What is a simple equation for tension, and equation of motion for a rope/cord?
What are the two equations for drag force, FD? Give a simple equation of motion for a body in free fall with drag using that equation.
what is acceleration a function of in this equation of motion
Note:
* In dynamics it’s easiest to consider FD = Cv^2.
* See that acceleration is a function of speed, V, as V^2 is in the equation and changing.
What is the equation for Buoyancy force, FB? Give a simple equation of motion for an object in a fluid, thinkg about a FBD.
what is acceleration a function of in this equation of motion
Note:
* The rho and Vs, volume of displaced fluid, in the equation is essentially the mass of the fluid displaced.
* Acceleration is now a function of position again, due to the Volume, Vs, in the equation of motion.
Describe the steps to work out the equations of motion (i.e. velocity and acceleration) of two objects that are connected by pulleys, so that one objects motion depends on the other.
What are the assumptions with this method.
- Define the position coordinates from fixed datum lines, along the path of each particle (or object). Different datum lines can be used for each particle.
- Relate the position coordinates to the cord length. Segments of the cord that do not change in length during the motion can be left out.
- If a system contains more than one cord, relate the position of a point on one cord to the point on another cord. Seperate equations are written for each cord. Then the two can be equated
- Differentiate the position coordinate equation(s) to relate velocities and accelerations. Keep track of signs!
- Assumption: this is used to relate the dependent motion of particles moving along rectilineaar paths (only the magnitude and velodity and acceleration change, not their line of direction).
Example shown below. More examples can be found on 45-58 here: Footnote
https://blackboard.soton.ac.uk/ultra/courses/_220084_1/cl/outline
Work out the equation of motion for each block , A and B, in this example.
Why are pullies used to hoist heavy objects? Refer to FBD’s, equations of motions and mention mechanical advantage. Are there any drawbacks of using pulleys?
How do we simply identify mechanical advantage in a pulley system?
We can understand tension is the same in each part of the cord. Then we can look at each pully and block individually. See example of a compound pulley system, first analysed one way, then another (simpler way).
