Advertisements
Advertisements
प्रश्न
The piston in the cylinder head of a locomotive has a stroke (twice the amplitude) of 1.0 m. If the piston moves with simple harmonic motion with an angular frequency of 200 rad/min, what is its maximum speed?
Advertisements
उत्तर १
Stroke of piston = 2 times the amplitude
Let A = amplitude,stroke = 1 m
`:. => A = 1/2 m`
Angular frequency, ` omega = 200 "rad/min"`
`V_"max" = ?`
We know that the maximum speed of the block when the amplitude is A
`V_"max" = omegaA = 200 xx 1/2 = 100 "m.min"`
`= 100/60 = 5/3 ms6(-1)= 1.67 ms^(-1)`
उत्तर २
Angular frequency of the piston, ω = 200 rad/ min.
Stroke = 1.0 m
Amplitude, `A = 1.0/ 2= 0.5 m`
The maximum speed (vmax) of the piston is give by the relation:
`V_"max" = Aomega`
`= 200 xx 0.5 = 100 "m/min"`
संबंधित प्रश्न
A seconds pendulum is suspended in an elevator moving with constant speed in downward direction. The periodic time (T) of that pendulum is _______.
A copper metal cube has each side of length 1 m. The bottom edge of the cube is fixed and tangential force 4.2x108 N is applied to a top surface. Calculate the lateral displacement of the top surface if modulus of rigidity of copper is 14x1010 N/m2.
The length of the second’s pendulum in a clock is increased to 4 times its initial length. Calculate the number of oscillations completed by the new pendulum in one minute.
The total mechanical energy of a spring-mass system in simple harmonic motion is \[E = \frac{1}{2}m \omega^2 A^2 .\] Suppose the oscillating particle is replaced by another particle of double the mass while the amplitude A remains the same. The new mechanical energy will
Two bodies A and B of equal mass are suspended from two separate massless springs of spring constant k1 and k2 respectively. If the bodies oscillate vertically such that their maximum velocities are equal, the ratio of the amplitude of A to that of B is
A particle moves in a circular path with a uniform speed. Its motion is
A particle is fastened at the end of a string and is whirled in a vertical circle with the other end of the string being fixed. The motion of the particle is
A spring stores 5 J of energy when stretched by 25 cm. It is kept vertical with the lower end fixed. A block fastened to its other end is made to undergo small oscillations. If the block makes 5 oscillations each second what is the mass of the block?
A small block of mass m is kept on a bigger block of mass M which is attached to a vertical spring of spring constant k as shown in the figure. The system oscillates vertically. (a) Find the resultant force on the smaller block when it is displaced through a distance x above its equilibrium position. (b) Find the normal force on the smaller block at this position. When is this force smallest in magnitude? (c) What can be the maximum amplitude with which the two blocks may oscillate together?
Find the time period of the motion of the particle shown in figure . Neglect the small effect of the bend near the bottom.
Find the time period of small oscillations of the following systems. (a) A metre stick suspended through the 20 cm mark. (b) A ring of mass m and radius r suspended through a point on its periphery. (c) A uniform square plate of edge a suspended through a corner. (d) A uniform disc of mass m and radius r suspended through a point r/2 away from the centre.
A uniform disc of radius r is to be suspended through a small hole made in the disc. Find the minimum possible time period of the disc for small oscillations. What should be the distance of the hole from the centre for it to have minimum time period?
A simple pendulum is inside a spacecraft. What will be its periodic time?
What are the two basic characteristics of a simple harmonic motion?
Show that the motion of a particle represented by y = sin ωt – cos ωt is simple harmonic with a period of 2π/ω.
The time period of a simple pendulum is T inside a lift when the lift is stationary. If the lift moves upwards with an acceleration `g/2`, the time period of the pendulum will be ______.
A particle performs simple harmonic motion with a period of 2 seconds. The time taken by the particle to cover a displacement equal to half of its amplitude from the mean position is `1/a` s. The value of 'a' to the nearest integer is ______.
