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 repeat
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
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 co
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 pas
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.
Homework 4 Solutions
Physics 104
Winter 2016
1). Taylor 10.14
A stationary space station can be approximated as a hollow spherical shell of mass 6 tonnes (6000
kg) and inner and outer radii of 5 m and
Homework 7 Solutions
Physics 104
Winter 2016
1. Taylor 16.9
The motion of a finite string, fixed at both ends, was determined by the wave equation
(16.19) and the boundary conditions (16.20). We solve
Homework 6 Solutions
Physics 104
Winter 2016
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
Phys104, W17, Homework 2
Due Wednesday, 1/25, by 5:00 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 y
Homework 3 Solutions
Physics 104
Winter 2016
Taylor 9.1
Be sure you understand why a pendulum in equilibrium hanging in a car that is accelerating forward
tilts backward, and then consider the followi
Homework 5 Solutions
Physics 104
Winter 2016
1). Taylor 11.5
(a) Find the normal frequencies, 1 and 2 , for the two carts shown in Figure 11.15, assuming that
m1 = m2 and k1 = k2 . (b) Find and descri
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
Phys104, W17, Homework 5
Due Monday, 2/27, by 5:00 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,
Phys104, W17, Homework 4
Due Tuesday, 2/14, by 5:00 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
Phys104, W17, Homework 6
Due Wednesday, 3/8, by 5:00 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 yo
Phys104, W17, Homework 7
Due Friday, 3/17, by 5:00 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,
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
Phys 104 Section 6 Evan Losh
Last week, we solved a problem using the Euler equations in the body frame of an object.
We worked in the body frame so that I would be diagonal and not a function of time
Phys 104 Section 6
Gabriel
February 15th, 2017
Euler's Equations
The angular momentum is given by the tensorial equation
(1)
~ = I~
L
where I is the tensor of inertia. We can express
~ in the basis o
Homework 4 Solutions
Physics 104
Winter 2017
1). Taylor 10.22
A rigid body comprises 8 equal masses m at the corners of a cube of side a, held together by
massless struts. (a) Use the definitions (10.
Phys 104 Section 5 Evan Losh
When an object rotates about a principle axis (often an axis of symmetry) its moment of
inertia can be treated eectively as a scalar quantity. However, moment of inertia i
Homework 5 Solutions
Physics 104
Winter 2016
1). Taylor 11.5
(a) Find the normal frequencies, 1 and 2 , for the two carts shown in Figure 11.15, assuming that
m1 = m2 and k1 = k2 . (b) Find and descri
Phys 104 Section 5 Evan Losh
When an object rotates about a principle axis (often an axis of symmetry) its moment of
inertia can be treated eectively as a scalar quantity. However, moment of inertia i