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Insights Subtleties Overlooked in Friction Questions: Object Slides Down Ramp
AI Thread Summary
An object sliding down a ramp at angle θ encounters kinetic friction on both the ramp and the level ground. The problem involves calculating the object's speed as it transitions from the ramp to the level surface, where it reaches speed u. The coefficients of friction, μ' on the ramp and μ on the level, play a crucial role in determining the final speed. The discussion emphasizes the need for a clear understanding of the forces acting on the object during its descent and upon reaching the level ground. The solution requires applying principles of physics, including energy conservation and frictional forces.
This is (ostensibly) not a trick shot or video*.
The scale was balanced before any blue water was added.
550mL of blue water was added to the left side.
only 60mL of water needed to be added to the right side to re-balance the scale.
Apparently, the scale will balance when the height of the two columns is equal.
The left side of the scale only feels the weight of the column above the lower "tail" of the funnel (i.e. 60mL).
So where does the weight of the remaining (550-60=) 490mL go...
Consider an extremely long and perfectly calibrated scale. A car with a mass of 1000 kg is placed on it, and the scale registers this weight accurately. Now, suppose the car begins to move, reaching very high speeds. Neglecting air resistance and rolling friction, if the car attains, for example, a velocity of 500 km/h, will the scale still indicate a weight corresponding to 1000 kg, or will the measured value decrease as a result of the motion?
In a second scenario, imagine a person with a...
Scalar and vector potentials in Coulomb gauge
Assume Coulomb gauge so that
$$\nabla \cdot \mathbf{A}=0.\tag{1}$$
The scalar potential ##\phi## is described by Poisson's equation
$$\nabla^2 \phi = -\frac{\rho}{\varepsilon_0}\tag{2}$$
which has the instantaneous general solution given by
$$\phi(\mathbf{r},t)=\frac{1}{4\pi\varepsilon_0}\int \frac{\rho(\mathbf{r}',t)}{|\mathbf{r}-\mathbf{r}'|}d^3r'.\tag{3}$$
In Coulomb gauge the vector potential ##\mathbf{A}## is given by...
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