21
votes
Accepted
Intuition behind the differential equation for forced oscillations
It's better to write the differential equation for forced oscillations in a different way that makes it more relatable to Newton's second law:
$$m\ddot{x}=F_0\sin{(\omega''t)}-b\dot{x}-kx$$
Now we can ...
- 346
5
votes
Would it be possible to ride a bicycle on the surface of Mars?
Could you ride a standard bicycle on the surface of mars?
Yes, you could. You would balance a little differently, because the force of gravity is a little different, but the force is similar because ...
- 7,021
4
votes
Accepted
Dependence (or lack thereof) of forces on frames of reference
When you say "blocks A and B move with a relative acceleration of -3 m/s2" you are considering the motion of one block in the reference frame attached to the other block (block C). But the ...
- 6,300
4
votes
Would it be possible to ride a bicycle on the surface of Mars?
Because your question refers to a "standard bicycle" therefore assuming the bikes' tires where inflated on Earth with normal air, whatever pressure concerns:
At an altitude of 130 km Mars $...
- 3,001
4
votes
About Contact, Normal and Friction force
We know that the basic expression for the friction is
$$f_a = \mu N$$
That's the basic equation for kinetic friction where $f_{k}=\mu_kN$ and $\mu_k$ is the coefficient of kinetic friction.
In the ...
- 55.5k
2
votes
Shouldn't length contraction cause friction under certain circumstances?
I don't think it's all that complicated.
Let’s assume that in your train problem there is a rack and pinion action between the train wheels and the track instead of friction.
Assume that the speeding ...
- 41
2
votes
Is work done by torque due to friction in pure rolling?
Which answer is correct?
The second answer is correct*.
For some reason, friction tends to mentally twist people in knots. It is just an ordinary mechanical force and obeys all of the usual rules ...
- 64.3k
2
votes
Friction when a car is moving in a circle
First of all, there are problems with the figures.
The centripetal force always acts towards the center of the circular motion. The centripetal force and the static friction force shown in the ...
- 55.5k
1
vote
Why power of engine must be equal to power of friction?
If the engine produces more power, that has to go somewhere, and in the situation you describe, it will go into kinetic energy, meaning to accelerate the car.
If it produces less power, the friction ...
- 2,048
1
vote
Problem with possibly infinite possible solutions
I don't see any obvious problems with your analysis.
This problem appears to be statically indeterminate. If so, the "real" value of the tension would be determined by knowing the material ...
- 37.1k
1
vote
Friction when a car is moving in a circle
There is a static friction force from the road acting on the bottom of each tire. One component of this provides the centripetal force (and centripetal acceleration) toward the center of a circular ...
- 11.4k
1
vote
Is work done by torque due to friction in pure rolling?
Setting the second Newton's law of the situation, and using the definition of work:
The net force for rolling without slip in an incline is $mgsin(\theta) - f_f$, where $\theta$ is the angle of the ...
- 11.8k
1
vote
Is work done by torque due to friction in pure rolling?
Work is clearly done. The body speeds up and spins faster.
First torque is the result of two parallel forces displaced sideways from each other. See Toppling of a cylinder on a block for more.
One ...
- 25.5k
1
vote
Is work done by torque due to friction in pure rolling?
Work depends on frame of reference. The reason is that, displacement also depends on frame of reference.
We have three ways of analyzing work done by friction.
If reference is ground, work done by ...
- 415
1
vote
Accepted
Would it be possible to ride a bicycle on the surface of Mars?
…Would you go faster or slower? How much faster or slower?
In general, the limiting speed is defined primarily by wind resistance. A steady speed will be reached when wind resistance equals the ...
1
vote
Shouldn't length contraction cause friction under certain circumstances?
This question is complicated by using accelerated frames (not just one but two differently accelerated frames, one for the front and one for the back of the train) plus the unintuitive weirdness that ...
- 8,488
1
vote
Accepted
Is change of angular momentum of two rotating disks colliding w.r.t. time $L(t) = \omega_0 I(1-e^{-t/C})$?
with
$$ \underbrace{I\,\frac{d\omega}{dt}}_{\dot L}=\tau\quad \Rightarrow\\
I\,\int_{\omega_i}^{\omega_f}\,d\omega=I\,(\omega_f-\omega_i)=\int \tau\,dt$$
where $\omega_f~$ is the final angular ...
- 8,379
1
vote
Is change of angular momentum of two rotating disks colliding w.r.t. time $L(t) = \omega_0 I(1-e^{-t/C})$?
I think you mean they have a coefficient of friction $\mu$ between their surfaces. If that's the case, for instance let us consider the lower disc, the upper disc applies a torque on it trying to slow ...
1
vote
Accepted
How to describe a series of damped harmonic oscilators?
I don’t have a particular reference to propose. However, in general, you won’t be able to fond an effective $k$ and $c$. The simplest way to see this is going to frequency space. I’ll choose the ...
- 1,145
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