Download Height height X10 Velocity Velocity2 V2/2 .09 .9 1.3 1.69 .85 .19 1.9

Ramp Velocity - Inquiry in motion
Velocity measured as
cart is at the end of
the track
height to
bottom of
track at front
of cart
5o
Height height X10
10o .09
15o .19
.27
.9
1.9
2.7
Velocity Velocity2
1.3
1.9
2.4
1.69
3.61
5.76
V2/2
.85
1.8
2.9
5o
10o .075
.75
1.1
1.21
.6
15o .17
1.7
1.8
3.24
1.6
.26
2.6
2.2
4.84
2.4
The relationship between height and velocity is 10 times height
equals velocity squared divided by 2
10 X height = Velocity2
2
10 X mass X Height = Mass X Velocity2
2
Gravitational Potential Kinetic Energy
Energy
More accurately gravitational potential energy is 9.8 m/s2 X
mass (kg) X height (m)
Mechanical Energy
Energy of moving or potentially moving macroscopic objects
Kinetic energy
energy of a moving object
Kinetic energy = mass X
2
velocity2
K.E. = (1/2)mv2
Gravitational potential Energy (GPE)
Potential energy due to a gravitational field
GPE = Mass X acceleration of gravity X height
GPE = mgh
g = 9.8m/s2
Spring Potential Energy or Elastic Potential Energy
Potential energy due to a compressed or extended
spring or elastic material
Problems from inquiry on 11/7
Angle Height(m)
5o
0.075
10o
0.17
o
15
0.26
Velocity(m/s)
1.1
1.8
2.2
What is the kinetic energy of the cart at 5o?
m= 0.5kg v = 1.1m/s
KE = (1/2)m v2
= (1/2) (0.5kg)(1.1m/s)2
= 0.30 kg m2/s2
Units for energy
kg m2/s2 known as a
joule (J)
What was the potential energy of the cart at the top of the
track at 15o?
m = 0.5kg
height = .26m g = 9.8m/s2
GPE = mgh
= (0.5kg)(9.8m/s2)(.26m)
= 1.3 kg m2/s2
Units for energy
kg m2/s2 known as a
joule (J)
Units for both kinetic and gravitational potential energy
are the same.
Conservation of Energy
A second important concept from the original data is concept of
conservation of mechanical energy in an isolated system
Isolated system - defined so that neither matter nor energy enter
or leave the system
10 X mass X Height =(1/2) Mass X Velocity2
Gravitational Potential
Kinetic Energy
Energy
This shows that for any given height, the potential energy
at the top equals the kinetic energy at the bottom.
Another Example:
A 0.2-kg ball thrown in the air at 5m/s, how high does the ball go?
Maximum height so maximum potential energy
Maximum velocity at bottom so maximum kinetic energy
KE =(1/2) mv2 =(1/2) (.2kg)(5m/s)2 = 2.5J
Potential energy at top = Kinetic energy at bottom
GPE = mgh
2.5J =(.2kg)(10m/s2)h
1.25m = h
If it is caught at the same height, what would its maximum speed
be?
5m/s if no energy is lost then kinetic energy is the same
Example 3:
A 5kg rock is on a cliff 40 m in the air.
The rock would have (5kg) (10m/s2)(40m) = 2000J of
potential energy.
Conservation of energy means it would have 2000J of kinetic
energy at the instant it hit the ground.
"At the instant" is just before the ground can slow the
object down
You could then determine the velocity of the rock.
KE = (1/2)mv2
2000J =(1/2) (5kg)v2
4000 = 5v2
800 = v2 take the square root of both sides
28.3m/s = v
Example 4:
A 0.05 kg toy rocket is launched using a spring with 2.5 J of
elastic potential energy.
What is the Kinetic Energy of the rocket at the instant it leaves
the spring?
EPE = KE = 2.5J
What is the Gravitational potential energy at the highest point in
the rockets flight?
KE = GPE = 2.5J
What is the maximum height of the rocket?
GPE = mgh
2.5J = (0.05kg)(10m/s2)h
5m=h
What was the velocity of the rocket at the instant it leaves the
spring?
KE = (1/2) mv2
2.5J = (1/2) (0.05kg)v2
100m2/s2 = v2
10m/s = v
Energy transfers
Cart springing up ramp
Against block - spring potential energy
After release - kinetic energy
On the way up - loses K.E. and gains
gravitational potential energy
At top - gravitational potential energy
Ball thrown into the air
As it is launched - Kinetic Energy
Traveling up - K.E. and G.P.E.
Top - G.P.E.
Falling down - G.P.E. and K.E.
Before caught - K.E.
Pendulum
A
At A - maximum GPE
A - B - both KE and GPE
B - maximum KE
B - C both kE and GPE
C - Maximum GPE
C
B
Spring
C
A
A
B
A is equilibrium point No energy to start
B - spring potential energy
A - Kinetic energy
C - gravitational potential energy