What is work done?
Constant force for a motion in a straight line
-Constant in magnitude + direction
-Work=Joule
< 1 J =1 Nm
In a graph that is split up into smaller rectangles what do different properties represent?
- A = Work
- Width = 𐤃s
What happens when we break down the circular path into straight lines?
The forces and segments are always in a right angle.
- For the circular force the work done by the centripetal force =0
How do you get to the work-kinetic energy relation?
1) a= F/m
2) v^2 = u^2 + 2as
-Replace a with the one in 1
-v^2 = u^2 + F/m x s
3) Rewritten as:
- Fs = 1/2 mx v^2 -1/ m x u^2
What happens to the work when a body is displaced horizontally
The work done by mg = 0
-Because w = mg x cos (90) = 0
What happens to the work when a body falls?
When a body falls vertically by a distance h, the force of gravity acts in the same direction as the displacement.
- Force and displacement are parallel
< Angle =0
w= mgh x cos (0) = mgh
What happens when theres work done by an external force?
-Opposite to the force of gravity
-Opposite to displacement
Wf= -mgh (lowering)
Wf= mgh (raising)
What is gravitational potential energy (Ep)
Work done by the moving force in placing a body a height of h above the surface of the earth.
In a graph of tension in a string what do different characteristics show?
- The area is the work done
- Y axis= F
- F=kx
- X axis = x (extension)
Formula for work in a string (using the graph)
- Area = 1/2 kx x x
- Area = 1/2 kx^2
- W = 1/2 kx^2
How do we get to Ek + Ep = Et?
v^2 = v^2 + 2 g (h-h)
- Rewritten as : 1/2 v^2 +gh =1/2 v^2 +gh
- Multiply through by the mass m
1/2 mv^2 + mgh= 1/2 mv^2 + mgh
-Each side of the equation is the sum of the kinetic energy and the gravitational potential energy
-Total mechanical energy
- Law of conservation of total mechanical energy
Mechanical energy formula
Et = Ek + Ep
1/2 mv^2 + mgh
Under which conditions is Et conserved?
This happens when friction and resistance forces are absent and no other forces act on the system from outside the system
When a car slows down why does it stop?
It stops due to friction and air resistance.
- Negative work on the car: takes energy out of the system
<Mechanical energy decreases
Potential energy
Energy accumulated over a height.
Power
Rate at which work is done
-1W = 1 Js^-1
Aircraft example for power
- Power P produced by the engines is related to the Force pushing it and the velocity
- Constant speed= no acceleration
- Net force = 0
< F from the engines is balanced by the air resistance that opposes the motion
Sankey diagrams
Represent energy transfers
-Width is proportional to the energy transferred.
