a) Estimate the internal energy E in the high temperature (equipartition) limit for CO.
b) Estimate the heat capacity Cv in the high temperature (equipartition) limit for NH3.
Do not use partition functions in your calculations.
<E> = KbT
Cv = (7/2)R...
In textbooks, I often see the sum of the first two normal modes given in the equation attached (on the right). I'm wondering how they arrive at that equation based on the general formula (on the left).
I tried subbing in n= 1 and 2 in the general formula, but I'm not sure...
Prove that there are n-1 nodes on a string fixed at both ends for the nth harmonic.
It is simple to show this using a diagram.
However, is there a way to show this mathematically?
A 66.0-cm-diameter cyclotron uses a 530 V oscillating potential difference between the dees.
How many revolutions does the proton make before leaving the cyclotron?
f = (q*B)/(2*pi*m)
The Attempt at a Solution
I find the cyclotron frequency:
I checked, and that was the correct answer!
As for problem B, I'm not sure what they're asking. I found the average kinetic energy to be: 3.11x10^-16 J at 15 million K. Do I divide this by a certain number?
kq^2/r = (1/2)mv^2 + (1/2)mv^2 = mv^2
Solving for v:
v = sqrt(kq^2/mr) = sqrt(((9x10^9)(1.6x10^-19)^2)/((1.6x10^-27)(2.4x10^-15))) = 7.6 x 10^6 m/s
Now plugging that into this equation:
T = (mv^2)/(3kb)
I obtain a value of 2.3 x 10^9 K.
The sun is powered by fusion, with four protons fusing together to form a helium nucleus (two of the protons turn into neutrons) and, in the process, releasing a large amount of thermal energy. The process happens in several steps, not all at once. In one step, two protons...
Your lab assignment is to use positive charge Q to launch a proton, starting from rest, so that it acquires the maximum possible speed. You can launch the proton from the surface of a sphere of positive charge Q and radius R, or from the center of a ring of charge Q and...
If you take snapshots of a standing wave on a string, there are certain instants when the string is totally flat.
What has happened to the energy of the wave at those instants?
The Attempt at a Solution
I'm assuming that nothing has happened to the energy. At...
A sound wave is described by D(y,t) = (0.02mm)sin[(8.96 rad/m)y + (3140 rad/s)t + pi/4 rad)], where y is in metres, and t is in seconds.
Draw a displacement-versus-time graph D(y=1.00m,t) at y= 1.00 m from t= 0 s and t= 4 ms.
D(y,t) = (0.02mm)sin[(8.96...
Ships measure the distance to the ocean bottom with sonar. A pulse of sound waves is aimed at the ocean bottom, then sensitive microphones listen for the echo. The graph shows the delay time as a function of the ship's position as it crosses 60 km of ocean.
The 20 cm-long wrench in the figure swings on its hook with a period of 0.92s. When the wrench hangs from a spring of spring constant 350 N/m, it stretches the spring 3.5 cm.
What is the wrench's moment of inertia about the hook...
The compressive force per area necessary to break the tibia in the lower leg, is about F/A =1.6 ×10 N m^2. The smallest cross sectional area of the tibia, about 3.2 cm^2, is slightly above the ankle. Suppose a person of mass m =6.0 ×10 kg jumps to the ground from a height h0...
A block of mass M is attached to a light string. The string passes over a massless, frictionless pulley and is attached to a solid uniform ball of mass 3M. The ball is at rest and completely submerged in a fluid as shown. What is the ratio of the density of the fluid to...
Two objects of equal mass m are whirling around a shaft with a constant angular velocity ω. The first object is a distance d from the central axis, and the second object is a distance 2d from the axis. You may assume the strings are massless and inextensible. You may ignore...
A small block of mass m is held at the top of a rough quarter-circle ramp of radius R as shown in the figure, and then released from rest. When it reaches the bottom of the ramp, it is moving with speed V. How much work did friction do on the block from the top to the...
You lift a ball at constant velocity from a height hi to a greater height hf . Considering the ball and the earth together as the system, which of the following statements is true?
1. The potential energy of the system increases.
2. The kinetic energy of the system decreases.
3. The earth does...