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15 votes

How can forces be added?

It is self-evident that successive displacements add by the tail-to-head arrow method. Velocities, being rates of change of displacement, add in the same way, as must momenta, and therefore forces, ...
  • 29.2k
8 votes

How can forces be added?

Here is one way of looking at it that might help you. To add vector A to vector B in the diagrams you provided, take each vector and draw its horizontal and vertical component like in this image. It ...
3 votes

Gravitational potential energy for more than two object

For an arbitrary number of particles, just sum that expression, $-Gm_im_j/|\vec r_i-\vec r_j|$, over all pairs $i$, $j$ of particles. This is easy to see if you imagine bringing each particle ...
  • 401
3 votes

How can forces be added?

Let's rearrange this last situation as you are regarding force instead of displacement. The above diagram actually more likely represent displacement. The forces seems to be on seperate points. This ...
3 votes

How can forces be added?

The idea of vectors addition, subtraction, resolution, etc. is found everywhere in life. Using basic trigonometry, one could show that some force $F$ that makes an angle $\theta$ with the horizontal ...
3 votes

Insecurity about introductory classical mechanics

You're right, you can evaluate force taking the gradient of the potential. Just evaluate the center of mass $\mathbf{x}_G = \dfrac{\sum_i M_i \mathbf{x}_i}{\sum_i M_i} = \dfrac{\sum_i M_i \mathbf{x}...
  • 2,318
2 votes

Rod in zero gravity pushed

The equations are easy enough. First, $momentum = impact$. $m\ v=p$ where the velocity $v$ is in the direction of the impact. The orientation of the rod makes no difference. Next, $angular\ momentum =...
  • 1,353
2 votes
Accepted

A basic question on friction

Your mistake is assuming that the frictional force that acts on B, which is $f$, is equal to the force $F$ exerted on A. Since A exerts a force $f$ on B, then by Newton's 3rd Law, B exerts an equal ...
  • 36.9k
2 votes

Why does small work done mean $dw=f.ds$ and why not $dw=df.ds$ and why not $dw=s.df$?

I think that it is better to start with power than with work. Recall that momentum, $\vec p$, is conserved and that force, $\vec F$, is the rate of change of momentum. Also, recall that impulse, $\vec ...
  • 71.3k
1 vote

Tension in moving chain

The tension will not remain the same. We can simplify as follows: take a catenary curve that is very narrow. (For instance, we can take a catenary curve such that the height is several times the ...
  • 16.1k
1 vote

Relationship between net torque and net force in constrained systems

Yes, since you do can have loading combinations that produce no motion. Specifically for the ladder problem, consider the kinematics. Points A and B are only allowed to slide, which means the center ...
  • 34.1k
1 vote
Accepted

How to calculate the Coriolis Force/Effect of an object moving West or East ALONG the Equator

You are supposed to calculate the Coriolis force using the vector equation you provided, not the latitude dependent resolution tangential to the Earth's surface. See https://en.wikipedia.org/wiki/...
  • 24.7k
1 vote

Justification of assumption of constancy of Spring Constant

First of all, the spring constant $k$ measures the stiffness of the spring. It depends on the material from which the spring is made, the thickness of the spring, and other factors. Therefore, it has ...

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