Advertisements
Advertisements
प्रश्न
Solve the following problem.
Derive the expression for power in terms of F, m, and t.
उत्तर
- A constant force F is applied to a body of mass (m) initially at rest (u = 0).
- We have, v = u + at
∴ v = 0 + at
∴ v = at ....(1) - Now, power is the rate of doing work,
∴ P = `"dW"/"dt"`
∴ P = `"F"*"ds"/"dt" ....[because "dW" = "F"*"ds"]` - But `"ds"/"dt" = "v"`, the instantaneous velocity of the particle.
∴ P = F·v ....(2) - According to Newton’s second law,
F = ma .....(3) - Substituting equations (1) and (3) in equation (2)
P = (ma)(at)
∴ P = ma2t
∴ P = `("m"^2"a"^2)/"m" xx "t"`
∴ P = `"F"^2/"m" "t"` - As F and m are constant, therefore, P ∝ t.
APPEARS IN
संबंधित प्रश्न
Among the four fundamental forces, only one force governs your daily life almost entirely. Justify the statement by stating that force.
Find the odd man out:
Answer the following question.
You are sitting next to your friend on ground. Is there any gravitational force of attraction between you two? If so, why are you not coming together naturally? Is any force other than the gravitational force of the earth coming in the picture?
Answer the following question.
Distinguish between real and pseudo force.
Answer the following question.
Distinguish between conservative and nonconservative forces.
Solve the following problem.
As I was standing on a weighing machine inside a lift it recorded 50 kg wt. Suddenly for a few seconds, it recorded 45 kg wt. What must have happened during that time? Explain with complete numerical analysis.
Variation of a force in a certain region is given by F = 6x2 – 4x – 8. It displaces an object from x = 1 m to x = 2 m in this region. Calculate the amount of work done.
Solve the following problem.
In the following table, every item on the left side can match with any number of items on the right-hand side. Select all those.
| Types of collision | Illustrations | ||
| a. | Elastic collision | i. | A ball hit by a bat. |
| b. | Inelastic collision | ii. | Molecular collisions responsible for pressure exerted by a gas. |
| c. | Perfectly inelastic collision | iii. | A stationary marble A is hit by marble B and the marble B comes to rest. |
| d. | Head-on collision | iv. | A blob of clay dropped on the ground sticks to the ground. |
| v. | Out of anger, giving a kick to a wall. | ||
| vi. | A striker hits the boundary of a carrom board in a direction perpendicular to the boundary and rebounds. | ||
Two spheres of masses m and M are situated in air and the gravitational force between them is F. The space around the masses is now filled with a liquid of specific gravity 3. The gravitational force will now be ______
Two bodies A and B of equal mass are suspended from two separate massles springs of force constant k1 and k2, respectively. The bodies oscillate vertically such that their maximum velocities are equal. The ratio of the amplitudes of body A to that of body B is ______.
In air, a charged soap bubble of radius 'R' breaks into 27 small soap bubbles of equal radius 'r '. Then the ratio of mechanical force acting per unit area of big soap bubble to that of a small soap bubble is ______.
Which of the following is the correct order of forces?
Two particles of mass m1 and m2, approach each other due to their mutual gravitational attraction only. Then ______.
A body of mass 'm' begins to move under the action of time-dependent force `vec"F" = ("t"hat"i" + 2"t"^2hat"j")`N where `hat"i" and hat"j"` are unit vectors along x and y axis respectively. The power developed by the force in watt at time 't' is ______.
What is the amount of work done by a person when
- he holds a mass of 2 kg for 5 second and
- he lifts the same mass through 1 meter to keep it on the top of a table? g = 9.8 m/s2
A force of F = `("x"/2 + 15) "N"` acts on a particle. If x 2 is in metre, calculate the work done by the force during the displacement of the particle from x = 0 to x = 4 m
Work done in sliding a 1 kg block up a rough inclined plane of height 5 m is 100 J. Work done against the friction is ______.
(g = 10 m/s2)
A Diwali cracker releases 25 gram gas per second, with a speed of 400 ms-1 after explosion. The force exerted by gas on the cracker is ______.
'n' number of balls each having mass 'm' and velocity 'u' hit a wall elastically and normally in 2 seconds. The force exerted by them on the wall is ______.
Out of the fundamental forces in nature, maximum and minimum range is respectively for ______.
A force F acting on an object varies with distance x as shown here. The force is in N and x in m. The work done by the force in moving the object from x = 0 to x = 6 m is ______.
A gardener pushes a lawn roller through a distance of 20 m. If he applies a force of 30 kg-wt in a direction inclined at 60° to the ground, the work done by the gardener in pushing the roller is ______.
`["g" = 9.8 "m""/""s"^2, sin30^circ = cos60^circ = 1/2, cos30^circ = sin60^circ = sqrt3/2]`
A uniform beam is balanced at its mid-point an object placed on the beam as shown.
Which force will rebalance the beam?
