Advertisements
Advertisements
प्रश्न
A uniform chain of length L and mass M overhangs a horizontal table with its two third part on the table. The friction coefficient between the table and the chain is μ . Find the work done by friction during the period the chain slips off the table.
Advertisements
उत्तर
Let x length of the chain be on the table at a particular instant.
Consider a small element of length 'dx' and mass 'dm' on the table.
dm = \[\frac{M}{L}\text{ dx}\] Work done by the friction on this element is \[\text{ dW }= \mu \text{ Rx } = \mu \left( \frac{M}{L} \times \text{ gx } \right) \text{ dx }\]
Total work done by friction on two third part of the chain,
\[W = \int_{2L/3}^0 \mu\frac{M}{L} \text{ gx dx }\]
\[ \therefore W = \mu\frac{M}{L}\text{ g } \left[ \frac{\text{x}^2}{2} \right]_0^{2\text{L}/3} \]
\[ = - \mu\frac{M}{L}\text{g} \left[ \frac{4 L^2}{18} \right]\]
\[ = - \frac{2\mu \text{ MgL} }{9}\]
The total work done by friction during the period the chain slips off the table is \[- \frac{2\mu \text{ MgL }}{9}\]
APPEARS IN
संबंधित प्रश्न
A body of mass m is placed on a table. The earth is pulling the body with a force mg. Taking this force to be the action what is the reaction?
Let E, G and N represent the magnitudes of electromagnetic gravitational and nuclear forces between two electrons at a given separation. Then
The sum of all electromagnetic forces between different particles of a system of charged particles is zero
A 60 kg man pushes a 40 kg man by a force of 60 N. The 40 kg man has pushed the other man with a force of
At what distance should two charges, each equal to 1 C, be placed so that the force between them equals your weight ?
A block of mass 250 g slides down an incline of inclination 37° with uniform speed. Find the work done against friction as the block slides through 1m.
Find the average force needed to accelerate a car weighing 500 kg from rest to 72 km/h through a distance of 25 m.
A particle of mass m moves on a straight line with its velocity varying with the distance travelled, according to the equation \[\nu = a\sqrt{x}\] , where a is a constant. Find the total work done by all the forces during a displacement from \[x = 0 \text{ to } x - d\] .
A block of mass 2 kg kept at rest on an inclined plane of inclination 37° is pulled up the plane by applying a constant force of 20 N parallel to the incline. The force acts for one second. Find the kinetic energy of the block at the instant the force ceases to act. Take g = 10 m/s2.
Water falling from a 50-m high fall is to be used for generating electric energy. If \[1 \cdot 8 \times {10}^5 \text{ kg } \] of water falls per hour and half the gravitational potential energy can be converted into electrical energy, how many 100 W lamps can be lit with the generated energy?
The 200 m free-style women's swimming gold medal at Seoul Olympics in 1988 was won by Heike Friendrich of East Germany when she set a new Olympic record of 1 minute and 57⋅56 seconds. Assume that she covered most of the distance with a uniform speed and had to exert 460 W to maintain her speed. Calculate the average force of resistance offered by the water during the swim.
A uniform chain of mass m and length l overhangs a table with its two third part on the table. Find the work to be done by a person to put the hanging part back on the table.
A block of mass 1 kg is placed at point A of a rough track shown in figure following. If slightly pushed towards right, it stops at point B of the track. Calculate the work done by the frictional force on the block during its transit from A to B.
A bicyclist comes to a skidding stop in 10 m. During this process, the force on the bicycle due to the road is 200 N and is directly opposed to the motion. The work done by the cycle on the road is ______.
A body of mass 0.5 kg travels in a straight line with velocity v = a x3/2 where a = 5 m–1/2s–1. The work done by the net force during its displacement from x = 0 to x = 2 m is ______.
A body is being raised to a height h from the surface of earth. What is the sign of work done by gravitational force?
A block of mass 1 kg is pushed up a surface inclined to horizontal at an angle of 30° by a force of 10 N parallel to the inclined surface (Figure). The coefficient of friction between block and the incline is 0.1. If the block is pushed up by 10 m along the incline, calulate
- work done against gravity
- work done against force of friction
- increase in potential energy
- increase in kinetic energy
- work done by applied force.
A body is displaced from (0, 0) to (1 m, 1 m) along the path x = y by a force F = (x2`hat"J"` + y`hat"i"`)N. The work done by this force will be:
If a force varies linearly with displacement, the area under the F-s graph forms:
