Test: Potential Energy - JEE MCQ

Total mass=80+20=100
w=mgh(where m=100, g=9.8, h=40m)
w=100×9.8×40
w=39200J
work done by man weighing 80 kg raising a stone of 20kgf to the top of building of Height is 40m is 39,200J

From the law of conservation of mechanical energy, the potential energy of a body at height h is converted into kinetic energy when it falls down. So, the magnitude of kinetic energy just before hitting the ground is equal to the potential energy at height h which is mgh.

Potential energy of a spring is proportional to the square of the difference of the springs length and its original length, hence whether it is compressed or stretched the potential the potential energy will eventually increase only.

We know that for a spring with spring constant k, work done by the spring when a compression or expansion is done of some length say x is ½ kx²
Also as the work done is in the opposite direction to that of force applied, we get the sign of the force to be negative.

Force between two stationary mass is gravitational force which is conservative. between two charge is electrostatic. muscular force is non conservative because we did work it lost or appear in form of heat and we need to eat food to gain energy for work done.

The forces acting on the body are the force of gravity and the air friction. By work energy theorem, the total work done on the body is
W=1/2m(1.2√gH)2−0=0.72mgH
The work done by the force of gravity is mgH.
. Hence, the work done by the air friction is,
=0.72mgH-mgH
=00.28mgH.
 

According to Newton's third law of motion, the force exerted on the floor by the person is equal and opposite the force exerted on the person by the floor.
According to the second law of Newton's law of motion, the net force exerted on the person is equal to the person’s mass times the person’s acceleration.
The net force exerted on the person = Force exerted by the floor+ Force exerted by gravity.
If the elevator goes up with acceleration g, the same is the person inside the elevator.
The work done on the man by the floor is the sum of the change in potential energy and kinetic
energy.
i.e W = Δ P.E + Δ K.E
But the elevator moves at a constant speed, so K.E =0.
W = Δ P.E
The work performed on you by the elevator is force times displacement = -Mgh
Negative sign shows it is moving upwards, i.e., against g.
 

P.E. stored in a spring = 1/2Kx²
where x is the extension or compression. In both cases, work is done on the spring.
∴ For the same x, the same potential energy will be stored in the springs.
∴ The difference between the energies is zero.

F=k x (compression in string).
X=L.
a=LT^-2.
F=ma.
ma= k L.
LT^-2/L=k/m.
T^-2=k/m.

We know that the total work done by gravity is always equal to the gravitational force in magnitude as it is a conservative force and as because no other non conservative force acts upon the body we can say the mechanical energy remains conserved. Thus we get the potential energy at top is exactly equal to KE just before the ball hitting the ground.

Change in GPE (Gravitational Potential energy) = mass x gravity x change in height
500 = 10 x 10 x change in height 

500 / 100 = change in height 

So, height from where it begins its dive = 5 m

mass = 50 x 100 = 5000 kg, g = 10 m/s²,  h = 10 m
Potential energy gained = mgh = 5000 x 10 x 10 = 5 x 10⁵ J

In A stretched bow. Compressed gas, compressed or elongated spring there is elastic potential energy but the lifted weight there is gravitational force, so the odd one here is lifted weight.

As the final velocity after the action of all forces is 0, therefore the person has 0 net acceleration.

And, as we know that

F_net = m.a_net

_{Therefore, the net force is 0 and hence, the net work done is also 0.}

The graphs are parabolas as the potential and kinetic energy vary as x².

 

The law of conservation of energy states that: the total mechanical energy of a system remains unchanged (constant) in any isolated system of objects that interact only through conservative forces. In other words, it states that: the energy may neither be created nor destroyed, but transferred from a form of energy to another. The total mechanical energy, E, is defined as:[ E = K + U] Where K is the total kinetic energy and U is the total potential energy of the system.
 
The conservation law of energy is , therefore, [E_i = E_f ],Where Ei and Ef are the initial and final energies, respectively. That implies to K_i + U_i = K_f + U_f

Potential Energy is any type of stored energy. It can be chemical, nuclear, gravitational, or mechanical. Kinetic Energy is found in movement. Nuclear power plants change the nuclear potential energy of uranium or plutonium into electricity too.

For a variable force, the work done can be expressed as a definite integral of force over displacement for any system.In case of a variable force, the is calculated with the help of integration. For example, in the case of a spring, the force acting upon any object attached to a horizontal spring can be given as Fs = -kx, where k is the spring constant and x is the displacement of the object attached. We can see that this force is proportional to the displacement of the object from the equilibrium position, hence the force acting at each instant during the compression and extension of the spring will be different. Thus, the infinitesimally small contributions of work done during each instant are to be counted in order to calculate the total work done.