I understand the derivation of gravitational potential energy when an object is moved away from Earth but when I try to derive the formula for gpe by considering a test mass moving from infinity to r then I end up with a positive gravitational potential energy. Because integrating F.dr from...
Why did you put the magnitude of force, shouldn't it contain minus sign as well? Because F is in opposite direction to r?
I read a post online that said if we state -dr we are already assuming the motion of the body is downwards so the limits should be switched and if we state dr then only we...
I am still not clear about the integration because the work done by a variable force is ∫F.dx where dx is a very small DISPLACEMENT.
Whereas while calculating the work done by the gravitational force we do ∫F.dr where dr is a radial displacement that is always outwards. So is dr equal to dx? I...
"dr" is used when potential energy is derived from integration. Here is dr a small displacement in the direction of r?
To calculate the work done by gravity using integration when a body if falling is dr positive or negative?
Here when you said "when we push it back with the same magnitude, you do F x D work again" I think we should also account the direction of the force because the force is constant both in magnitude and direction throughout the motion. So shouldn't the work done by the force on the crate when...
In a closed loop when we apply an applied force on an object the object starts at point A and stops at point A.
Since the displacement is 0, Work done by the applied force on the object is = F x s x cosθ...
What I meant was:
Consider a particle on the ground. This particle is raised by a force of magnitude mg to a height h above the ground. At this point, the work done on the particle by the force is mgh, which is equal to the potential energy of the particle. But, during this period, the force of...
This question may sound weird but when we lift an object with a force equal to the weight of the object up to a certain height the Earth is doing negative work on the object as well. So shouldn't the net work be zero?
Why is infinite kept as a lower limit in the derivation of gravitational potential energy? Shouldn't the lower limit be smaller than the upper limit?
Why can ratios be written as fractions?
if there are 5 men in 20 people the ratio of men to total people is 5:20 which is 1:4.
But when we write 1/4 it gives 0.25. And 0.25 means the magnitude of each part when 1 is divided into 4 equal parts.
So how does ratio and fraction give a...
If a positive charge A moves towards another stationary positive charge B then the A's electric potential energy increases. But shouldn't the electric potential energy of B also increase as it is also in a way moving towards the A inside the A's electric field?
So shouldn't the total...
V = ωr
ω = angular velocity
r = radius
How is the direction of ω perpendicular to the plane of rotation?
Is the formula ω = vsinθ χ 1/r which is the cross product of vsinθ and 1/r the reason why ω is perpendicular to the plane of rotation?
Cross product is used to find the perpendicular vector of two vectors. If there is any two vectors in a plane then there is always a perpendicular vector to both of them.
So in circular motion if the motion is horizontal then is there a perpendicular force to the object in circular motion?
When a positive charge leaves the positive part if the battery it has maximum electric potential energy then as it moves through a wire with a zero resistance the charge is closer to the negative side of the battery.
So, while traveling in a wire in a circuit does it lose electric potential...
If the potential difference between point A and point B is 10 Volts, then when a unit positive charge passes from A to B, the charge loses 10 J of energy.
But when an electron passes from A to B does it gain energy, because in W = Q . V , Q is negative.
I am really confused in potential...
"F in the definition of potential energy is the force exerted by the force field, e.g., gravity, spring force, etc. The potential energy U is equal to the work you must do against that force to move an object from the U=0 reference point to the position r. The force you must exert to move it...
when a magnet is falling through a solenoid, voltage is produced.
Once positive is produced and the when the magnet leaves the solenoid negative voltage is produced.
Voltage is the energy lost by a unit charge when traveling from one point to the other.
So if there is negative voltage...
If we want to push an electron towards another electron we give equal but opposite force which means we push the electron with the same amount of force that it is being pushed back.
Shouldn't both the forces cancel out the electron remain stationary?
" The potential energy U is equal to the work you must do against that force to move an object from the U=0 reference point to the position r. The force you must exert to move it must be equal but oppositely directed."
The above definition is from hyperphysics.
U = -GMm/R
If a positive charge is pushed towards another positive charge then the potential energy of the system increases.
When negative charge attracts positive charge why doesn't the system gain potential energy?
In both cases force is being applied?
So can the potential energy of the rocket can be calculated by the formula
(Thrust - Gravitational force) * distance
In my book the gain in GPE of the rocket is calculated by -GMm/r which basically came from integrating Gravitational force* distance
Is there any difference?
I am really...