Assignment 5
Reading
: Energy 1
Key Concepts
: Scalar products, work, kinetic energy, workenergy theorem.
1.
Questions about the scalar product of two vectors.
a.
Use vectors to prove the law of cosines for a triangle. [Consider the
product
C
⋅
C
, where
C
=
A
+
B
, and draw the arrows.]
b.
In 1D kinematics with constant acceleration we had the formula
v
2
=
v
0
2
+
2
a
(
x
−
x
0
)
. Take the equations for constant acceleration in 3D
(page 2 of Kinematics 2) and show that this formula becomes
v
2
=
v
0
2
+
2
a
⋅
(
r
−
r
0
)
.
2.
With modern technology one can measure the acceleration of gravity
g
directly
by dropping an object and taking a photo of its fall with a rapidly flashing strobe
light. But in Galileo’s time the fall was too rapid to make accurate measurements,
so he used an incline to reduce the acceleration to a more measurable level.
Shown are the modern experiment (a) and Galileo’s (b). In both the object starts
from rest. Assume that in case (b) the object slides down a frictionless incline. (In
fact it was a small ball rolling without slipping.) Neglect air resistance.
Comment on the validity of each statement and explain your reasoning.
a.
The work done by gravity is the same in both cases.
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 Spring '07
 Mueller
 Physics, Energy, Force, Kinetic Energy, Mass, Work, WorkEnergy Theorem

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