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The scalar product of two vectors A and B is
Explanation:Scalar product means dot product and dot product of 2 vectors gives a scalar , example dot product of force and displacement gives work which is scalar
Mass and energy are equivalent and are related by
Explanation:Mass–Energy equivalence states that anything having mass has an equivalent amount of energy and vice versa, with these fundamental quantities directly relating to one another by Einstein's theory of special relativity. It shows that matter (as mass) and energy can be converted into each other according to the famous equation E=mc2
A railway porter is holding a weight of 100 kgs on his head and is standing still. What is the work done by him?
Explanation:W = Force x displacement in the direction of forceWork done will be zero because porter is stationary (i.e. displacement is zero)
A person trying to lose weight (dieter) lifts a 10 kg mass, one thousand times, to a height of 0.5 m each time. Assume that the potential energy lost each time she lowers the mass is dissipated. How much work does she do against the gravitational force?
Explanation:Work done by force applied against gravity for one lift will be
W = Fs = mgh = 10 x 9.8 x 0.5 = 49J
So work done for 1000 lifts = 49 x 1000 = 49000 J
A12-pack of Omni-Cola (mass 4.30 kg) is initially at rest on a horizontal floor. It is then pushed in a straight line for 1.20 m by a trained dog that exerts a horizontal force with magnitude 36.0 N. Use the work–energy theorem to find the final speed of the 12-pack if there is no friction between the 12-pack and the floor
from work–energy theorem
change in kinetic energy = work done
ΔK = W
Kf - Ki = Fs
1/2mv2 - 0 = Fs
m = 4.30 kg, s = 1.2m, F = 36N
vf = vm/s , vi = 0
The work done by the force is defined to be
Explanation:Work done is given by
W = (Fcosθ)d
here Fcosθ is the component of applied force in direction of displacement and d is magnitude of displacement.
Power is defined as
Explanation:Power is the rate of doing work. It is the amount of energy consumed per unit time. Having no direction, it is a scalar quantity. In the SI system, the unit of power is the joule per second (J/s), known as the watt.The integral of power over time defines the work performed.
A weight of 20kg falls from a height of 10 m. The work done by the gravitational force is (Take g = 10 mms-2)
S.I unit of power is
Explanation:The SI unit of power, equivalent to one joule per second, corresponding to the rate of consumption of energy (Work done).
In which case is the work done zero?
Explanation:Work done is given as
W = Fdcosθ
Here θ is the angle between F and d if both are perpendicular then θ = 90 degree so cosθ = 0 and thus work done is 0 .
Which of the following laws used to solve problems in collisions?
Explanation:If external force is absent then linear momentum of system remains conserved. In collision force of impact due to collision is internal and very large.
A pump on the ground floor of a building can pump up water to fill a tank of volume 30 m3 in 15 min. If the tank is 40 m above the ground, and the efficiency of the pump is 30%, how much electric power is consumed by the pump?
The S.I unit of force is
Explanation:In International System of Units (SI) the newton is the unit for force. It is equal to the amount of net force required to accelerate a mass of one kilogram at a rate of 1 m/sec2 in direction of the applied force. It is named after Isaac Newton in recognition of his work on classical mechanics, specifically Newton's second law of motion.
Dyne is a cgs unit of force. One dyne is equal to 10−5 N
In an elastic collision
Explanation:kinetic energy is transferred to other forms of energy—such as thermal energy, potential energy, and sound—during the collision process. After collision if recovery of kinetic energy is 100% then it is called elastic collision.So that in an elastic collision the total kinetic energy of the system is the same after the collision as before.
Work-energy theorem does not give information on
Explanation:According to work energy theorem :Net work done on a body equals change in its kinetic energySo it does not give any information about time dependence.
In an inelastic collision
Explanation:kinetic energy is transferred to other forms of energy—such as thermal energy, potential energy, and sound—during the collision process. After collision if recovery of kinetic energy is less than % then it is called inelastic collision i.e.. some part of kinetic energy is not recover. So that in an inelastic collision the total kinetic energy after the collision is less than before the collision
Physically, the notion of potential energy is applicable only to
Explanation:Potential energy is the stored energy of an object. It is the energy by virtue of an object's position relative to other objects. Potential energy is often associated with restoring forces such as a spring or the force of gravity. It is applicable only for conservative forces.
If a machine is lubricated with oil
When a machine is lubricated with oil friction decreases. Hence the mechanical efficiency of the machine increases.
A bolt of mass 0.3 kg falls from the ceiling of an elevator moving down with an uniform speed of 7 m/s. It hits the floor of the elevator (length of the elevator = 3 m) and does not rebound. What is the heat produced by the impact?
Whole of the potential energy of bolt converted in to heat energy
heat produced by the impact = mgh =0.3×9.8×3=8.82J
The work done by a conservative force
Explanation:A force is said to be conservative if work done by this force is independent of path and is dependent only on end points .
In which of the following cases is the work done positive?
Explanation:Work done is positive when force applied and displacement are in same direction.
W=F .s =Fscosθ
in this case angle between force and displacement is zero (i.e. cosθ=1) so that work done is positive.
The total mechanical energy of a system is conserved if the
Explanation:Mechanical energy is the sum of kinetic and potential energy in an object that is used to do work. In other words, it is energy in an object due to its motion or position, or both. In case of conservative forces total mechanical energy remains conserved because potential energy applicable only for conservative forces.
The casing of a rocket in flight burns up due to friction. At whose expense is the heat energy required for burning obtained?
Explanation:Heat energy required for burning of casing of rocket comes from the rocket itself. As a result of work done against friction the kinetic energy of rocket continuously deceases and this work against friction reappears as heat energy. This results in reduction of the mass of the rocket.
A tandem (two-person) bicycle team must overcome a force of 165 N to maintain a speed of 9.00 m/s. Find the power required per rider, assuming that each contributes equally.
Total power required to overcome a force of 165 N and to maintain a speed of 9.00 m/s
F = 165N
v = 9m/s
P = Fv = 165 x 9 = 1485 W
if each rider contribute equal power, then power required per rider will be P/2 = 1485/2 = 742.5W
For a ball dropped from a tower of height h the total mechanical energy is
Explanation:mechanical energy = sum of potential and kinetic energiesa falling ball will have both these energies in between topmost and bottomost points of its motion so mechanical energy is the sum of potential and kinetic energies.
A trolley of mass 200 kg moves with a uniform speed of 36 km/h on a frictionless track. A child of mass 20 kg runs on the trolley from one end to the other (10 m away) with a speed of 4 ms−1 relative to the trolley in a direction opposite to the its motion, and jumps out of the trolley. How much has the trolley moved from the time the child begins to run?
Mass of troly M = 200Kg
mass of child m = 20Kg
speed of trolley v = 36Km/hr=36 x 5/18 = 10m/s
Let v' be the final velocity of the trolley with respect to the ground.
Final velocity of the boy with respect to the ground = v,−4
from conservation of linear momentum
Time taken by the boy to run t = 10/4 = 2.5 sec
Distance moved by the trolley = vt = 10.36 x 2.5 = 25.9 m
A 50.0-kg marathon runner runs up the stairs to the top of a 443-m-tall Tower. To lift herself to the top in 15.0 minutes, what must be her average power output?
In which of the following cases is the work done positive?
Explanation:When a body is moving on a rough horizontal surface then their will be 2 forces acting on the body 1. Applied force ( in the direction of motion) 2. friction ( opposite to direction of motion)As applied force is in same direction as displacement so work done will be positive.
The launching mechanism of a toy gun consists of a spring of unknown spring constant. When the spring is compressed 0.120 m, the gun, when fired vertically, is able to launch a 35.0-g projectile to a maximum height of 20.0 m above the position of the projectile before firing. Neglecting all resistive forces, determine the spring constant.
Potential energy of spring converted in to potential energy
If F is a force and d is the displacement in the direction of force then the work done by the force is given by
Explanation:Work done = force in the direction of displacement multiplied by displacement