Advertisements
Advertisements
प्रश्न
A block of mass 30 kg is being brought down by a chain. If the block acquires a speed of 40 cm/s in dropping down 2 m, find the work done by the chain during the process.
Advertisements
उत्तर
\[\text{ Given }, \]
\[\text{ Mass of the block, m = 30 kg} \]
\[\text{ Speed acquired by the block,} \nu = 40 \text{ cm/s } \]
\[ = 0 . 4 \text{ m/s } \]
\[\text{ Distance covered by the block, s = 2 m } \]
Let a be the acceleration of the block in the downward direction.
From the diagram, the force applied by the chain on the block,
\[\text{ F } = \left( \text{ ma - mg }\right)\]
\[ = \text{ m } \left( \text{ a - g } \right)\]
\[\text{ a } = \frac{\nu^2 - \text{ u }^2}{2\text{s}}\]
\[ = \frac{16}{- 4} = 0 . 04 \text{ m/ s}^2 \]
\[\text{ Work done by the chain, } \]
\[\text{ W = Fs } \cos \theta\]
\[= \text{ m } \left(\text{ a - g} \right) \times \text{s} \cos 0^\circ\]
\[ = 30 \left( 0 . 04 - 9 . 8 \right) \times 2\]
\[ = - 30 \times \left( 9 . 76 \right) \times 2\]
\[ = - 585 . 6 = - 586 \text{ J }\]
\[\Rightarrow \text{ W = - 586 J }\]
APPEARS IN
संबंधित प्रश्न
Is work-energy theorem valid in non-inertial frames?
Consider the situation of the previous question from a frame moving with a speed v0 parallel to the initial velocity of the block. (a) What are the initial and final kinetic energies? (b) What is the work done by the kinetic friction?
The US athlete Florence Griffith-Joyner won the 100 m sprint gold medal at Seoul Olympics in 1988, setting a new Olympic record of 10⋅54 s. Assume that she achieved her maximum speed in a very short time and then ran the race with that speed till she crossed the line. Take her mass to be 50 kg. Calculate the kinetic energy of Griffith-Joyner at her full speed.
An unruly demonstrator lifts a stone of mass 200 g from the ground and throws it at his opponent. At the time of projection, the stone is 150 cm above the ground and has a speed of 3 m/s. Calculate the work done by the demonstrator during the process. If it takes one second for the demonstrator to lift the stone and throw it, what horsepower does he use?
In a factory, 2000 kg of metal needs to be lifted by an engine through a distance of 12 m in 1 minute. Find the minimum horsepower of the engine to be used.
Consider the situation shown in the following figure. The system is released from rest and the block of mass 1 kg is found to have a speed 0⋅3 m/s after it has descended a distance of 1 m. Find the coefficient of kinetic friction between the block and the table.
A small block of mass 200 g is kept at the top of a frictionless incline which is 10 m long and 3⋅2 m high. How much work was required (a) to lift the block from the ground and put it an the top, (b) to slide the block up the incline? What will be the speed of the block when it reaches the ground if (c) it falls off the incline and drops vertically to the ground (d) it slides down the incline? Take g = 10 m/s2.
A block of mass 5 kg is suspended from the end of a vertical spring which is stretched by 10 cm under the load of the block. The block is given a sharp impulse from below, so that it acquires an upward speed of 2 m/s. How high will it rise? Take g = 10 m/s2.
Following figure following shows a smooth track, a part of which is a circle of radius R. A block of mass m is pushed against a spring of spring constant k fixed at the left end and is then released. Find the initial compression of the spring so that the block presses the track with a force mg when it reaches the point P, where the radius of the track is horizontal.
The bob of a stationary pendulum is given a sharp hit to impart it a horizontal speed of \[\sqrt{3 gl}\] . Find the angle rotated by the string before it becomes slack.
A heavy particle is suspended by a 1⋅5 m long string. It is given a horizontal velocity of \[\sqrt{57} \text{m/s}\] (a) Find the angle made by the string with the upward vertical when it becomes slack. (b) Find the speed of the particle at this instant. (c) Find the maximum height reached by the particle over the point of suspension. Take g = 10 m/s2.
A particle slides on the surface of a fixed smooth sphere starting from the topmost point. Find the angle rotated by the radius through the particle, when it leaves contact with the sphere.
Figure ( following ) shows a smooth track which consists of a straight inclined part of length l joining smoothly with the circular part. A particle of mass m is projected up the incline from its bottom. Find the minimum projection-speed \[\nu_0\] for which the particle reaches the top of the track.
A chain of length l and mass m lies on the surface of a smooth sphere of radius R > l with one end tied to the top of the sphere. Find the tangential acceleration \[\frac{d\nu}{dt}\] of the chain when the chain starts sliding down.
An electron and a proton are moving under the influence of mutual forces. In calculating the change in the kinetic energy of the system during motion, one ignores the magnetic force of one on another. This is because ______.
A rocket accelerates straight up by ejecting gas downwards. In a small time interval ∆t, it ejects a gas of mass ∆m at a relative speed u. Calculate KE of the entire system at t + ∆t and t and show that the device that ejects gas does work = `(1/2)∆m u^2` in this time interval (neglect gravity).
A particle moves in one dimension from rest under the influence of a force that varies with the distance travelled by the particle as shown in the figure. The kinetic energy of the particle after it has travelled 3 m is ______.
