13
votes
Pushing something on a theoretically frictionless surface
While you are applying the force the object will undergo acceleration
\begin{equation}
\boldsymbol a = \frac{\boldsymbol F}{m}.
\end{equation}
If the force stops acting on the object after time $t_{0}$...
- 856
5
votes
Accepted
How many equations of motion? The higher order derivatives are highly correlated
The plots indicate that higher order derivatives aren't providing any real additional information — and you probably cannot trust the 3rd and higher ones too much either, given the low granularity of ...
- 11.8k
3
votes
Accepted
Faster Small Tires vs Slower Large Tires
As per rolling resistance law, ratio of engine work done opposing rolling resistance force negative work ,in case big and small tires is :
$$ \frac {W_{_R}}{W_r} = \sqrt {\frac {r}{R}} ~~~~~~~~~~~~~~~~...
- 7,480
3
votes
Accepted
Is this $x$-$t$ graph possible? Is the distance decreasing over time in this graph?
The velocity should be displacement over time, while the speed is the distance over time. In contrast to displacement, which is a vector and could have a negative sign, the distance is the length ...
- 54
3
votes
Standing Wave Equation: Why does assuming a small slope $du/dx$ not make $d^2u/dx^2$ negligible as well?
Let's take an example signal: $y=\cos(x)$ about $x=0$.
$\frac{dy}{dx}=-\sin(0)=0$;
$\frac{d^2y}{dx^2}=-\cos(0)=-1$.
It is important to note that one is not simply the square of the other.
- 908
3
votes
Accepted
Simple difference between module of velocity and time derivative of module of position
The first describes the rate at which the distance between the object and the (often arbitrary) origin is changing, whereas the second is the actual speed of the object (the speed being the magnitude ...
- 4,302
3
votes
The value of $g$ in free fall motion on earth
It means the speed increases by $9.8$ m/s every second.
At the beginning (when you release the body) its speed is $0$.
After $1$ second the speed is $9.8$ m/s, after $2$ seconds the speed is $19.6$ m/...
- 26.9k
2
votes
When does a free body moving on a smooth circular path make a complete revolution?
From what I think you mean from
Like a ball in a closed circular tube
the radial or normal force from the tube, $N$ in the diagram above, can only be positive. If $N$ is negative, the ball will fall ...
- 497
2
votes
Accepted
Is this expert report wrong about basic kinematics?
You've misinterpreted the quote. The quote describes stopping distance, not stopping time. The distances are expressed as times at a certain starting speed. Context from the quote suggests that this ...
- 8,982
2
votes
Can we have motion in systems where inertia is neglected?
I'm not completely sure I fully understand your question, but I'll try to give you an answer...
It might help to think of this problem in a pseudo-relativistic context, wherein the physical motion of ...
- 184
2
votes
Accepted
What's the difference between using $a=(v2-v1)/t$ and $s=u\cdot t+1/2\cdot a\cdot t^2$?
The two kinematic equations for constant acceleration that you have quote are correct.
If they are combined the error that you have made is revealed.
Substituting for the acceleration $a= \dfrac {v-u}{...
- 78.1k
2
votes
Can something have momentum but not velocity?
Momentum does not require mass.
For example the electromagnetic field carries momentum, the momentum density of the EM field is:
$$\vec{p} = \epsilon_{0} \vec{E} × \vec{B}$$
For light:
$$p = \frac{E}{...
- 4,461
2
votes
The value of $g$ in free fall motion on earth
It means the speed of the falling body increases with 9.8 m/s each second.
- 1,379
1
vote
Acceleration on a body in free fall inside a elevator which is going up
It's simply Newton's second law. What are the forces acting on the stone after its release? Well, it's completely out of contact with the elevator, so there's only the force of gravity, meaning that $...
- 3,073
1
vote
What radius should you take while converting rpm to m/s?
As you want to use the speed for the Lift equation, you have to compute the integral over the local lift from r=0 to r=max.
Maybe you can assume the blade profile to be the same all over the blade ...
- 2,343
1
vote
What radius should you take while converting rpm to m/s?
It all depends what you are using the data for.
The linear speed depends linearly of the distance from the centre.
Half the maximum speed (at the tip) gives the average speed.
$0.7(07) , \,\frac {1}{\...
- 78.1k
1
vote
Faster Small Tires vs Slower Large Tires
Long distance trucks use large tires in part because of rolling resistance, as @AgniusVasiliauskas pointed out.
But also a large tire has a more gentle curvature. This means a larger contact patch. ...
- 27.2k
1
vote
Is this $x$-$t$ graph possible? Is the distance decreasing over time in this graph?
Your “impossible” graph shows distance, while your counterexample shows the vector displacement relative to some origin.
Think about a car with an odometer and a GPS. You can make your total vector ...
rob♦
- 71.8k
1
vote
What's the difference between using $a=(v2-v1)/t$ and $s=u\cdot t+1/2\cdot a\cdot t^2$?
this is because v is not equal to s/t. otherwise the equation of kinematic would be s=vt not s=ut+1/2 a t^2. you cant apply speed= distance/time unless you have constant acceleration
1
vote
Finding motorcycle turning radius based on lean angle
The explanation by @user121330 uses arguments in the non-inertial frame of the rider. That'll work but I feel it is an overly complicated way to do it. Here is how you work it out in a simpler, ...
- 1,049
1
vote
Accepted
Why is instantaneous velocity tangent to trajectory?
The answer is in the definition of instantaneous velocity. While moving along a path a small change in position ${\rm d}\vec{r}$ over a small time frame ${\rm d}t$ the instantaneous velocity is ...
- 2,667
1
vote
Accepted
What direction should i exactly put for negative displacements?
Displacement is a vector. A vector has a direction, not a sign.
It is frequently convenient to choose a coordinate system where vectors to the east are represented with positive numbers and vectors to ...
rob♦
- 71.8k
1
vote
Accepted
Finding the time period under variable acceleration
You know that the tangential acceleration $Rd\omega/dt=\omega ^2 R$. So now you can integrate twice and find $\theta(t)$.
- 154
1
vote
Can we have motion in systems where inertia is neglected?
We sometimes assume a body has negligible mass, such as a rope in a pulley system where the pulley and weights on the ends of the rope have much greater mass than the light rope. This simplifies the ...
- 6,551
1
vote
Can we have motion in systems where inertia is neglected?
It is not clear what is meant by inertia is neglected:
Small/huge inertia It could be that the inertia is so small, that particle experience huge acceleration. We do often use this kind of an ...
- 39.3k
1
vote
How to create the function of an arrow being shot?
$$x=u_{x}t$$
$$y= u_{y}t + \frac{1}{2}at^2$$
Rearranging:
$$\frac{x}{u_{x}} = t$$
Substituting into y:
$$y= u_{y}\left(\frac{x}{u_{x}}\right) + \frac{1}{2}a\left(\frac{x}{u_{x}}\right)^2$$
If we want ...
- 4,461
1
vote
Accepted
Initial velocity of a body when the distance travelled by it in the last second before reaching its maximum height is $5\ \textrm{m}$
The question has either an infinite number of answers, or no answer.
It's convenient to follow the motion for the one second AFTER the ball reaches the peak of its trajectory. (Or run time backwards ...
- 10.4k
1
vote
Initial velocity of a body when the distance travelled by it in the last second before reaching its maximum height is $5\ \textrm{m}$
Assume that the velocity of the body right before the last second starts is V. It decreases to zero in 1s with an acceleration of g, about $10m/s^2$. So, V must be 10 m/s. Alo, the time to drop from ...
- 6,568
1
vote
How he came from the term: $L^2 - X^2 + 2Xdx = Y^2 + 2Y dy$ to $X dx = Y dy$? furthermore, how does the term $(X/Y)dx/dt = dy/dt = v'$?
The eq relating the values is
$$x^2 + y^2 = L^2$$
Implicitly differentiating with respect to time.
$$2x \frac{dx}{dt} + 2y \frac{dy}{dt} = 0$$
Rearranging,
$$ \frac{dy}{dt} = -\frac{x}{y} \frac{dx}{dt}...
- 4,461
1
vote
Determine the meaning of a gradient of a graph
It really depends on the specific situation. The general meaning of gradient is the spatial rate of change in a quantity. For example in a temperature field $T(x,y)$, the gradient $\vec {\nabla T}$ ...
- 2,499
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