Question
Show that a force that does no work must be a velocity dependent force.
✓
Answer
To show that a force that does no work must be a velocity dependent force, then we have to assume that work done by force is zero. As shown by the equation below:
$\text{dW}=\vec{\text{F}}.\vec{\text{dI}}=0$
We can write, $\vec{\text{dI}}=\vec{\text{v}}\text{dt But}\text{ dt}\neq0 $
$\Rightarrow\ \vec{\text{F}}.\vec{\text{v}}\text{dt}=0$
$\Rightarrow\ \vec{\text{F}}.\vec{\text{v}}=0$
So we can say that force F must be velocity dependent, this implies that angle between F and v is 90°. If the direction of velocity changes, then direction of force will also change.
$\text{dW}=\vec{\text{F}}.\vec{\text{dI}}=0$
We can write, $\vec{\text{dI}}=\vec{\text{v}}\text{dt But}\text{ dt}\neq0 $
$\Rightarrow\ \vec{\text{F}}.\vec{\text{v}}\text{dt}=0$
$\Rightarrow\ \vec{\text{F}}.\vec{\text{v}}=0$
So we can say that force F must be velocity dependent, this implies that angle between F and v is 90°. If the direction of velocity changes, then direction of force will also change.
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
A spy report about a suspected car reads as follows. "The car moved 2.00km towards east, made a perpendicular left turn, ran for 500m, made a perpendicular right turn, ran for 4.00km and stopped". Find the displacement of the car.
Two identically charged particles are fastened to the two ends of a spring of spring constant 100Nm-1 and natural length 10cm. The system rests on a smooth horizontal table. If the charge on each particle is 2.0 × 10-8C, find the extension in the length of the spring. Assume that the extension is small as compared to the natural length. Justify this assumption after you solve the problem.
- How are electromagnetic waves produced? Explain.
- A plane electromagnetic wave is travelling through a medium along the +ve z-direction. Depict the electromagnetic wave showing the directions of the oscillating electric and magnetic fields.
A concave mirror has a focal length of 20cm. Find the position or positions of an object for which the imagesize is double of the object-size.
The drift current in a reverse-biased p-n junction increases in magnitude if the temperatu,re of the junction is increased. Explain this on the basis of creation of hole-electron pairs.
The normal body-temperature of a person is 97°F. Calculate the rate at which heat is flowing out of his body through the clothes assuming the following values. Room temperature = 47°F, surface of the body under clothes= 1.6m2, conductivity of the cloth $= 0.04\text{Js}^{-1}\text{m}^{-1}{^{\circ}}\text{C}^{-1},$ thickness of the cloth = 0.5cm.
→A carrom board (4ft × 4ft square) has the queen at the centre. The queen, hit by the striker moves to the front edge, rebounds and goes in the hole behind the striking line. Find the magnitude of displacement of the queen:
- From the centre to the front edge.
- From the front edge to the hole.
- From the centre to the hole.
Two sources of sound, S1 and S2, emitting waves of equal wavelength 20.0cm, are placed with a separation of 20.0cm between them. A detector can be moved on a line parallel to S1S2, and at a distance of 20.0cm from it. Initially, the detector is equidistant from the two sources. Assuming that the waves emitted by the sources are in phase, find the minimum distance through which the detector should be shifted to detect a minimum of sound.
Describe the motion of a charged particle in a cyclotron if the frequency of the radio frequency (rf) field were doubled.
A light ray incident at grazing angle on the face AB of a prism ABC, follows the path shown in the figure. Obtain the relation between the angle of prism A and the refractive index $\mu$ of its material.
→