Homework Statement
Two identical carts (of mass m) are free to move on a frictionless, straight horizontal track. The masses are connected by a spring of constant k and un-stretched length l_{0}. Initially the masses are a distance l_{0} apart with the mass on the left having a speed v_{0} to...
For prelim preparation. I've also included a figure of the problem.
Homework Statement
A stick of length l is suspended by one end at point P so that it hangs vertically and so that the top end of the stick does not move. A horizontal impulse J is applied perpendicular to the stick a...
Homework Statement
A large, spherically symmetric collection of point particles of mass m move in circular orbits about a common center each with the same kinetic energy. If the only force acting is the mutual gravitational attraction of the particles, find the particle density (in the...
Homework Statement
Two blocks A and B with respective masses m_{A} and m_{B} with respective masses m_{A} and m_{B} are connected via a string. Block B is on a frictionless table, and block A is hanging at a vertical distance h from a spring with spring constant k that is at its equilibrium...
Ok I think I've got something.
From the continuity equation for mass,
\dot{m}=\rho v A where \rho is the density and A is the area.
\dot{m}=\rho Av_{rel}ln\frac{m_{1}}{m_{2}}
Does this look ok?
Thanks!
Homework Statement
A rocket ejects pressurized air with constant relative velocity v_{rel} and moves horizontally. Starting from rest and an initial mass m_{1}, find the speed of the rocket when its mass is m_{2}(m_{2}<m_{1}). How does this result depend on the rate r=dm/dt at which the air...
Homework Statement
A photon with initial momentum p collides with a free electron having
a mass m that is initially at rest. If the electron and photon recoil in opposite
directions, what will be the change in the photon’ wavelength? (Hint: use
relativistic forms for energy and momentum.)...
Homework Statement
The picture shows a rotating platform that serves as a playground
merry go round. The platform rotates on low-friction bearings about its center
axis. It has a radius of 2.0 meters, and its moment of inertia about the center
axis is 200 kg m2.
Suppose that the...
Yes your integral (the action) does have units of Energy x Time. Remember though, in physics you may come across different types of actions, that have different units. For fields, there is an action that is integrated over spatial dimensions rather than time...
Homework Statement
A bullet with mass and speed v hits a wooden block of mass M that is situated at rest on a frictionless surface. It penetrates the block and gets trapped inside it as a result of a constant retardation force F_{ret} that opposes relative motion between the two objects...
Also to find any equilibrium positions I looked at what would make \ddot{z}=0.
I got only 1 equilibrium position of z=\frac{g}{tan^{2}\theta\omega^{2}}.
I also concluded that this is stable since \omega and \theta are constant.
Ooops I made a typo. I meant to say that I'm interested in knowing whether or not my moment of inertia is correct.
Oh cool TSny you read it how I meant it.
TSny,
Using your advice I get:
L=\frac{1}{2}m(\frac{\dot{z}^{2}}{cos^{2}\theta}+(z^{2}\omega^{2})/(cos^{2}\theta))-mgz
\ddot{z}=\frac{2z\omega^{2}}{m}-gcos^{2}\theta
Does this look ok?
Thanks.
Homework Statement
A system consists of a pulley and two masses m1, m2 haning from it as shown in the figure. The pulley is a disk of radius R with constant mass density that has two circular hole with radius R/2. Find the angular acceleration of the pulley.
Figure attached.
Homework...