All Questions
Tagged with calculus newtonian-mechanics
122
questions
1
vote
1
answer
260
views
Tidal forces mathematics
Let's calculate the difference in force, $\Delta F$, experienced by
the rocks. Because $\Delta r$ is very small compared to $r$,
$$\Delta F = F_{\text{out}} - F_{\text{in}} \approx\frac{dF}{dr}\Delta ...
0
votes
0
answers
126
views
Work-Energy Principle Derivation
I am currently in Mechanics I and both my professor and my book have derived the work principle in this way and I even asked about its derivation during class, but it has me puzzled.
I don't ...
0
votes
2
answers
83
views
Kinematics confusion regarding sign of integration
I was solving some problems regarding non-inertial frames, and Newtonian mechanics in general, when I faced a major doubt regarding one of the seemingly simple topics, and I'd appreciate it if someone ...
- 1,791
0
votes
1
answer
81
views
Doubt in finding center of mass of extended bodies [closed]
While finding center of mass of extended bodies, we generally write the coordinate of the starting point of the infinitesimal mass element. Why not the ending or starting point? How does the error ...
0
votes
1
answer
39
views
Velocity while falling from table
Suppose there is a chain of mass $m$ in a semicircular tube of radius $r$. If it's pushed, then find the velocity of the chain while leaving the tube.
This is a simple problem which we can do using ...
- 1,179
2
votes
4
answers
643
views
Work done by a vector field (Force field) on a particle travelling along a curve
Assume a particle travelling along a curve, the work done by any Force field on the particle while moving along a curve is given by the line integral of $\vec{\bf{F}} \cdot \vec{\bf{dr}}$, but shouldn'...
- 367
1
vote
1
answer
130
views
Finding velocity $v$ and position $r$, given a time $t$ under the acceleration of a gravitational force [closed]
I was messing with the maths, when I tried to find the velocity as a function of time, $v(t)$, and the position, also, as a function of time, $r(t)$ under the gravity force.
$$ m \ddot{r} = -G \frac{...
- 1,525
2
votes
1
answer
67
views
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
167
views
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
views
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
vote
2
answers
73
views
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
views
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
views
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
166
views
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
views
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
views
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
views
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
0
votes
1
answer
33
views
Average torque on a Projectile of mass $m$ with initial speed $u$ and angle of projection $θ$ between initial ($P$) and final ($Q$) positions is [closed]
Question is as follows:
Average torque on a Projectile of mass $m$ with initial speed $u$ and angle of projection $θ$ between initial $(P)$ and final $(Q)$ positions is
I researched a lot but wherever ...
0
votes
0
answers
142
views
How to calculate the derivative of the angular momentum vector $ d\vec L = d(\hat I \vec \omega)?$
My last question, but also the most important one How to calculate the derivative of the angular momentum vector?
$$ d\vec L = d(\hat I \vec \omega)$$
I'm especially interested in derivative tensor to ...
0
votes
1
answer
120
views
Why can we multiply by $dt/dt$ to change variable of integration? Please look at equation 5-20 [closed]
I am struggling to understand why can we just multiply by $dt/dt$. I was thinking it was just a change of variables, but I cannot come up how that works. Can someone explain why we are allowed to do ...
- 37
0
votes
3
answers
147
views
The force of gravity between a shperical shell and a particle
I am trying to understand the proof of why the force acting on a spherical shell and a particle is
$$\frac{GMm}{r^2}$$
Where M is the mass of the sphere and m is the mass of the particle.
I am looking ...
- 5
1
vote
3
answers
65
views
Position Dependence in Equation of Motion
Our lecturer gives study material which contained that Newton's second law could be written as:
$$ \begin{aligned} F &= m \ddot{x} \\ &= m \frac{d \dot{x}}{dt} \\ &= m \frac{dx}{dx} \frac{...
- 13
0
votes
1
answer
141
views
Differential Equation & MacLaurin Series for Newton’s Second Law
I am currently working with a differential equation, where I think I need to take the derivative of $ma$ (corrected as per comment). I am trying to write $F = ma$ as a MacLaurin series and eventually ...
- 151
-1
votes
2
answers
563
views
What does $d$ stand for in this formula?
Context: I am building a tennis ball machine and am having trouble interpreting the following formula for the flight path of the ball. I know all of the other values in the formula but the source I am ...
1
vote
1
answer
80
views
Problem finding Centre of Mass [closed]
My Question: For finding the Center of Mass ($COM$) of a hollow cone, why do we use its area to define its elemental mass ($dm$) and not its volume, which we use to find the $COM$ of a solid cone.
The ...
- 111
1
vote
1
answer
77
views
Equation for stationary string
I have some doubts on the following derivation of the EOM of a stationary string.
Let $F_x, F_y$ be horizontal and vertical tension of the string
$\mu$ be the mass per unit length of the string [kg/m]
...
- 180
0
votes
4
answers
1k
views
Acceleration due to gravity during its journey up and down
When we throw an object up into the air, ignoring air resistance, etc, we define acceleration to be -9.8 m/s^2. When it goes down after its journey up, like a parabola, do we define the acceleration ...
- 23
2
votes
5
answers
333
views
Significance of $\frac{dv}{dx}=0$
Suppose an object is moving with varying acceleration in time.
What does it mean when it hits a point where $\frac{dv}{dx}=0$?
Does it mean the object has hit maximum velocity?
Assume the object ...
- 77
1
vote
2
answers
83
views
For regular moving objects around us, how many times can I differentiate their position with respect to time until I reach a constant? [duplicate]
When I practise problems, I come across ideal situations like constant velocities, constant accelerations, etc. But in real situations, objects usually don't magically gain momentum or acquire ...
- 385