Phys104 W15 Midterm exam solutions
1). (10 points) Prove that the shortest path connecting two points in the x-y plane is a straight line.
This is the Calculus of Variations example that we did repeatedly in class.
We want to nd the function (or path), y(
Homework 2 Solutions
Physics 104
Winter 2014
1 Taylor 7.50
A mass m1 rests on a frictionless horizontal table. Attached to it is a string which runs horizontally
to the edge of the table, where it passes over a frictionless, small pulley and down to where
Homework 4 Solutions
Physics 104
Winter 2015
1 Taylor 10.11
(a) Use the result of Problem 10.4 to nd the moment of inertia of a uniform solid sphere (mass
M , radius R) for rotation about a diameter. (b) Do the same for a uniform hollow sphere whose
inner
Homework 2 Solutions
Physics 104
Taylor 7.4
Consider a mass m moving in a frictionless plane that slopes at an angle with the horizontal.
Write down the Lagrangian in terms of coordinates x, measured horizontally across the slope, and
y, measured down the
Homework 2 Solutions
Physics 104
Winter 2015
1 Taylor 7.3
1
Consider a mass m moving in two dimensions with potential energy U (x, y) = 2 kr2 , where r2 = x2 +y 2 .
Write down the Lagrangian, using coordinates x and y, and nd the two Lagrange equations of
Homework 1 Solutions
Physics 104
Winter 2015
4 Taylor 6.1
The shortest path between two points on a curved surface, such as the surface of a sphere, is called a
geodesic. To nd a geodesic, one has rst to set up an integral that gives the length of a path
Homework 5 Solutions
Physics 104
Winter 2015
1 Taylor 11.4
(a) Find the normal frequencies for the system of two carts and three springs shown in Figure 11.1,
for the case that m1 = m2 and k1 = k3 , (but k2 may be dierent). Check that your answer is corre
Homework 6 Solutions
Physics 104
Winter 2015
1 Taylor 13.7
A roller coaster of mass m moves along a frictionless track that lies in the x-y plane (x horizontal
and y vertically up). The height of the track above the ground is given by y = h(x). (a) Using
Homework 7 Solutions
Physics 104
Winter 2015
1 Taylor 16.9
The motion of a nite string, xed at both ends, was determined by the wave equation (16.19) and
the boundary conditions (16.20). We solved these by looking for a solution that was sinusoidal in
tim
Phys104 W15 Final exam solutions
1). (15 points) (a) Explain how Lagranges equations are equivalent to Newtons 2nd law. (You only need
to explain with an illustration, not prove it rigorously.) (b) Derive Hamiltons equations from Lagranges
equations. For
Phys103 F14 Final exam
(Form A)
You must fully show your work and explain steps to get credit.
See back for a list of possibly useful mathematical relations.
1. (10 points) A sand-spraying locomative sprays sand horizontally into a freight car as shown
in
Homework 1 Solutions
Physics 104
Taylor 6.1
The shortest path between two points on a curved surface, such as the surface of a sphere, is called a
geodesic. To nd a geodesic, one has rst to set up an integral that gives the length of a path on the
surface
Phys103 F14 Final exam solutions
You must fully show your work and explain steps to get credit.
See back for a list of possibly useful mathematical relations.
1. (10 points) A sand-spraying locomative sprays sand horizontally into a freight car as shown
i
Phys104, W15, Homework 5
Due Friday, 2/20, by 4:00 PM in box in Broida lobby
Make sure to fully show your work and explain steps.
To facilitate ordering the graded homeworks and returning them to you, please write your lastname in block letters on the upp
Phys104, W15, Homework 3
Due Wednesday, 1/28, by 4:00 PM in box in Broida lobby
Make sure to fully show your work and explain steps.
To facilitate ordering the graded homeworks and returning them to you, please write your lastname in block letters on the
Phys104, W15, Homework 2
Due Wednesday, 1/21, by 4:00 PM in box in Broida lobby
Make sure to fully show your work and explain steps.
To facilitate ordering the graded homeworks and returning them to you, please write your lastname in block letters on the