All Questions
Tagged with calculus newtonian-mechanics
119
questions
0
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1
answer
81
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Doubt in finding center of mass of extended bodies [closed]
While finding center of mass of extended bodies, we generally write the coordinate of the starting point of the infinitesimal mass element. Why not the ending or starting point? How does the error ...
0
votes
1
answer
39
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Velocity while falling from table
Suppose there is a chain of mass $m$ in a semicircular tube of radius $r$. If it's pushed, then find the velocity of the chain while leaving the tube.
This is a simple problem which we can do using ...
- 1,179
2
votes
4
answers
633
views
Work done by a vector field (Force field) on a particle travelling along a curve
Assume a particle travelling along a curve, the work done by any Force field on the particle while moving along a curve is given by the line integral of $\vec{\bf{F}} \cdot \vec{\bf{dr}}$, but shouldn'...
- 367
1
vote
1
answer
129
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Finding velocity $v$ and position $r$, given a time $t$ under the acceleration of a gravitational force [closed]
I was messing with the maths, when I tried to find the velocity as a function of time, $v(t)$, and the position, also, as a function of time, $r(t)$ under the gravity force.
$$ m \ddot{r} = -G \frac{...
- 1,515
2
votes
1
answer
67
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Forces along and perpendicular to a curve
A uniform rope of length $l$ is suspended from two hinges, making an angle of $\theta$ with the horizontal at the hinges. Find the depth $d$ of the lowest point of the rope.
Similar questions include ...
- 23
0
votes
1
answer
166
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Maximum height of a projectile when $g$ is not constant [closed]
How can I calculate the maximum height of a projectile that is launched from the surface of the earth with a given initial velocity? (ignoring air resistance in the atmosphere)
I understand how to ...
26
votes
14
answers
4k
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Explaining how we cannot account for changing acceleration questions without calculus
For context, I am a high school physics teacher.
I am teaching students about the basics of electromagnetic force between two point charges. The equation we use is $F=\frac{kq_1q_2}{r^2}$.
This gives ...
1
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2
answers
73
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How do you differentiate this differential equation? [closed]
I have to differentiate this equation (Gravitational force between N-Bodies)
$\begin{align}
\frac{d^2}{dt^2}\vec{r_i}(t)=G
\sum_{k=1}^{n}
\frac
{m_k(\vec{r}_k(t)-\vec{r}_i(t))}
{\lvert\...
0
votes
1
answer
25
views
Issue with a derivation in Marion's Dynamics [closed]
I was solving problem 2-14 in Marion's "Classical dynamics of particles and systems" edition 5. In this problem we calculate the range of a trajectory to be $d=\frac{2{v_0}^2\cos{\alpha}\sin{...
- 93
0
votes
3
answers
181
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Trouble understanding the center of mass equation
I'm learning about center of mass, but I have trouble understanding the definition. How is $x_{com}=\frac{1}{M}\sum_{i=1}^{n}m_ix_i$ equal to $x_{com}=\frac{1}{M}\int xdm$?
At first I thought it ...
- 535
1
vote
2
answers
81
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Is it possible to lift an object from rest with constant power?
This is inspired by the following question.
Consider some object which I want to lift from rest with a constant power throughout the whole process; the power I apply when lifting the object from rest ...
- 6,621
0
votes
3
answers
165
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Power and work contradiction
A body is starting from rest. A force is acting on it for a short period of time. In that given time, power delivered to it at any instance $t$ is given
$$P = F \cdot v_1 = ma \cdot v_1 = mv_1^2/t,$$
...
1
vote
2
answers
369
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Area Swept by particle under central forces is an approximation
From Kepler's second law, we infer, the conservation of angular momentum is equivalent to saying the areal velocity is constant,
And the proof goes like this
$$ mr^2{\dot\theta=L}
$$
where $L$ is ...
- 784
-2
votes
2
answers
1k
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Why distance equals initial velocity times time Plus acceleration over two times time Squared? [duplicate]
i am a beginner in physics and I do not understand why is the d=vi(t)+(1/2)a(t^2).
- 1
-1
votes
2
answers
92
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Infinitesimals meaning in this context
I was solving this rocket propulsion's classic mechanics exercise: M is the instantaneous rocket's mass, and v its velocity. The exhaust gases are ejected with speed 𝑢 relative to the speed 𝑣 of the ...
- 169