Explanation
As the area above the time axis is numerically equal to area below the time axis therefore net momentum gained by body will be zero because momentum is a vector quantity.
As particle is projected with some velocity therefore its initial kinetic energy will not be zero.As it moves downward under gravity then its velocity increases with time K.E. ∝ v2 ∝ t2 [As v ∝ t]. So, the graph between kinetic energy and time will be parabolic in nature.
Potential energy increases and kinetic energy decreases when the height of the particle increases it is clear from the graph (a).
Work done = area under curve and displacement axis = 1 × 10 – 1 × 10 + 1 × 10 = 10J
When the distance between atoms is large then interatomic force is very weak. When they come closer, force of attraction increases and at a particular distance force becomes zero. When they are further brought closer becomes repulsive in nature. This can be explained slope of U – x curve shown in graph (a).
Work = Area under (F– d) graph = 8 + 5 = 13J
Friction is a non-conservative force. Work done by a non-conservative force over a closed path is not zero.Here, option (c) is a false statement.
By definition
If two protons are brought near one another, work has to be done against electrostatic force because same charge repel each other. This work done is stored as potential energy in the system.
From Einstein equation E = mc2
Since the gaseous pressure and the displacement (of piston) are in the same direction. Therefore θ = 0o . Therefore, Work done = Fs cos θ = Fs = Positive.Thus during expansion work done by gas in positive.
If roads of the mountain were to go straight up, the slope θ would have been large, the frictional force μmg cos θ would be small. Due to small friction, wheels of vehicle would slip. Also for going up a large slope, a greater power shall be required.
The work done on the spring against the restoring force is stored as potential energy in both conditions when it is compressed or stretched.
The gravitational force on the comet due to the sun is a conservative force. Since the work done by a conservative force over a closed path is always zero (irrespective of the nature of path), the work done by the gravitational forces over every complete orbit of the comet is zero.
Rate of change of momentum is proportional to external forces acting on the system. The total momentum of whole system remain constant when no external force is acted upon it. Internal forces can change the kinetic energy of the system.
Work done in the motion of a body over a closed loop is zero only when the body is moving under the action of conservative forces (like gravitational or electrostatic forces), i.e., work done depends upon the nature of force.
K.E of one bullet = k . Therefore, K.E of n bullet = nk.
According to law of conservation of energy, the kinetic energy of bullets be equal to the work done by machine gun per sec.
For conservative forces the sum of kinetic and potential energies at any point remains constant throughout the motion. This is known as law of conservation of mechanical energy. According to this law.
kinetic energy + Potential energy = constant
or, ΔK + ΔU = 0 or , ΔK = – ΔU
When the force retards the motion, the work done is negative. Work done depends on the angle between force and displacement W = Fs cos θ
In an elastic collision both the momentum and kinetic energy remains conserved. But this rule is not for individual bodies, but for the system of bodies before and after the collision. While collision in which there occurs some loss of kinetic energy is called inelastic collision. Collision in daily life are generally inelastic. The collision is said to be perfectly inelastic, if two bodies stick to each other.
Work done and power developed is zero in uniform circular motion only.
In a quick collision, time t is small, As F × t = constant, therefore, force involved is large , i.e., collision is more violent in comparison to slow collision.
From,definition, work done in moving a body against a conservative force a independent of the path followed .
When we supply current through the cell, chemical reactions takes place, so chemical energy of cell is converted into electrical energy.
When two bodies of same mass undergo an elastic collision, their velocities get interchanged after collision. Water and heavy water are hydrogenic materials containing protons having approximately the same mass as that of a neutron. When fast moving neutrons collide with protons. the neutrons come to rest and protons move with the velocity of that of neutrons.
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