Transcript Potential Energy - McMaster University

Energy, Work and Power
Physics 1D03 - Lecture 22
HOMEWORK QUESTION
Please do this question and hand it by Tuesday after
the reading week, in class:
A 50kg child slides down a 45o frictionless hill for 60m,
starting with an initial velocity of 2m/s. The child then
slides for 10m over a flat surface that has a
coefficient of kinetic friction of 0.15, and finally back
up another frictionless hill with a slope of 30o.
Draw a pictures of the problem and determine how far
on the 2nd hill the child ends up (not the height).
Physics 1D03 - Lecture 22
For every conservative force, we can define a potential energy
function U so that
WAB = -DU = UA -UB
Note the negative
Examples:
Gravity (uniform g) : Ug = mgy, where y is height
Gravity (exact, for two particles, a distance r apart):
Ug = - GMm/r, where M and m are the masses
Ideal spring: Us = ½ kx2, where x is the stretch
Electrostatic forces (F=kq1q2/r), where q are the charges
Physics 1D03 - Lecture 22
Conservation of mechanical energy
If only conservative forces do work,
potential energy is converted into kinetic
energy or vice versa, leaving the total
constant. Define the mechanical energy E
as the sum of kinetic and potential energy:
E  K + U = K + Ug + Us + ...
Conservative forces only: W = -DU
Work-energy theorem:
W = DK
So, DK+DU = 0; which means that E
does not change with time.
Physics 1D03 - Lecture 22
Example: Pendulum
L
The pendulum is released from
rest with the string horizontal.
a) Find the speed at the lowest
point (in terms of the length L
of the string).
vf
Physics 1D03 - Lecture 22
Example: Pendulum
The pendulum is released from
rest at an angle θ to the
vertical.
a) Find the speed at the lowest
point (in terms of the length L
of the string).
θ
vf
Physics 1D03 - Lecture 22
Example
You slide 20m down a frictionless hill with a slope of 30o
starting from rest. At the bottom you collide and stick
to another person (at rest) that has 90% of your
mass.
a) Determine the final velocity of the system.
b) How would the calculation and final velocity
change if the slope had a coefficient of kinetic friction
of 0.1 ?
Physics 1D03 - Lecture 22
Power
The time rate of doing work is called power.
If an external force is applied to an object, and if work
is done by this force in a time interval Δt, the average
power is defined as:
P=W/Δt
(unit: J/s = Watt, W)
For instantaneous power, we would use the
derivative:
P=dW/dt
And since W=F.s, dW/dt=Fds/dt=F.v, so sometimes it
is useful to write:
P=F . v
Physics 1D03 - Lecture 22
Example
An elevator motor delivers a constant force of 2x105N
over a period of 10s as the elevator moves 20m.
What is the power ?
P=W/t
=Fs/t
=(2x105N)(20m)/(10s)
=4x105 W
The same elevator is moving with an average velocity
of:
The power is:
Physics 1D03 - Lecture 22