Homework Statement
Some of the details in this question are based off the use of matlab. If it's needed I can show the matrices that MATLAB creates.
Let A = magic(8); A = A(:,1:3) and let S be the Column Space of A. For b = [1:8]' compute the projection of b onto the Column Space of A...
So, the solution to this problem was posted on my course website, but I'm still having issues. Basically, the answer is the same as mine until:
a_{0} = \frac{c^{4}}{4(1+\epsilon)^{2}GM}
The (1+ε)2 is simplified as (1+2ε)... ok, if ε is really small, I suppose assuming ε2 = 0 is alright.
But...
Homework Statement
The radius Rh and mass M of a black hole are related by Rh = \frac{2GM}{c2}, where c is the speed of light. Assume that the gravitational acceleration ag of an object at a distance ro = (1 + ε)Rh from the center of a black hole is given by ag = \frac{GM}{r2}, where ε is a...
Right, rotated about it's end the moment of inertia is I = (m L2) /3
I was assuming that the rotational axis is in the center of the blade though, leading to my equation.
Using I = (m L2) /3 actually leads to correct answers. Thanks ^^
Solving for T, I got 76.97 N
I'm willing to bet the discrepancy is rounding.
To be sure, I used
mg-Tsin(θ) = N
friction = (mg-Tsin(θ))μ
Tcos(θ)=friction = (mg-Tsin(θ))μ
T(cos(θ) + sin(θ)μ) = mgμ
so, T =mgμ/(cos(θ) + sin(θ)μ)
The first thing to do is to make a picture. You'll notice that there are only 2 forces acting on the plane. Namely, tension and gravity.
You know that the horizontal motion is circular, so that leads to Fnet = mv^2/r
You know Fnet in the x direction, and velocity. Find a relationship to...
Homework Statement
A uniform helicopter rotor blade is 8.82 m long, has a mass of 108 kg, and is attached to the rotor axle by a single bolt. (a) What is the magnitude of the force on the bolt from the axle when the rotor is turning at 302 rev/min? (Hint: For this calculation the blade can...
The idea of time dilation is that light moves at the same constant rate seen from any perspective and that other moving objects don't. As you move faster you're perception of reality has a decreased rate. Everything else appears slower to you. To find the time distortion you would use Einstein's...
The problem is that you're angle is wrong. Try drawing a small graph with the angle starting from the positive y-axis (north) and going towards the x-axis (east). You see that the 55° angle is made with the y-axis, and not the x-axis.
The question is asking you to find the angle between the velocity and the line of sight. If you solve both triangles you'll find the angle is the same:
tan ^-1 (distance y/ distance x) = tan ^-1 (Vy/Vx)
so, the angle between the two is:
tan ^-1 (distance y/ distance x) - tan ^-1 (Vy/Vx) = 0