Advertisements
Advertisements
Question
A person normally weighing 50 kg stands on a massless platform which oscillates up and down harmonically at a frequency of 2.0 s–1 and an amplitude 5.0 cm. A weighing machine on the platform gives the persons weight against time.
- Will there be any change in weight of the body, during the oscillation?
- If answer to part (a) is yes, what will be the maximum and minimum reading in the machine and at which position?
Advertisements
Solution
In this case, acceleration is variable. In accelerated motion, the weight of body depends on the magnitude and direction of acceleration for upward or downward motion.
a. Hence, the weight of the body changes during oscillations
b. Considering the situation in two extreme positions. as their acceleration is maximum in magnitude.
We have, mg – N = ma
∵ At the highest point, the platform is accelerating downward.
⇒ N = mg – ma
But a = ω2A .....[In magnitude]
∴ N = mg – mω2A
Where, A = amplitude of motion
Given, m = 50 kg, frequency v = 2 s–1
∴ ω = 2πv = 4π rad/s
A = 5 cm = 5 × 10–2 m
∴ N = 50 × 9.8 – 50 × (4π)2 × 5×10–2
= 50[9.8 – 16π2 × 5 × 10–2]
= 50[9.8 – 7.89]
= 50 × 1.91
= 95.5 N
When the platform is at the lowest position of its oscillation,
It is accelerating towards the mean position that is vertically upwards.
Writing the equation of motion
N – mg = ma = mω2A
or N = mg + mω2A
= m[g + ω2A]
Putting the data N = 50[9.8 + (4π)2 × 5 × 10–2]
= 50[9.8 + (12.56)2 × 5 × 10–2]
= 50[9.8 + 7.88]
= 50 × 17.68
= 884 N
Now, the machine reads the normal reaction. It is clear that
Maximum weight = 884 N ......(At lowest point)
Minimum weight = 955 N .....(At top point)
APPEARS IN
RELATED QUESTIONS
The periodic time of a linear harmonic oscillator is 2π second, with maximum displacement of 1 cm. If the particle starts from extreme position, find the displacement of the particle after π/3 seconds.
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.
Which of the following example represent periodic motion?
An arrow released from a bow.
Which of the following example represent (nearly) simple harmonic motion and which represent periodic but not simple harmonic motion?
General vibrations of a polyatomic molecule about its equilibrium position.
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?
Answer in brief:
Derive an expression for the period of motion of a simple pendulum. On which factors does it depend?
A particle executes simple harmonic motion with a frequency v. The frequency with which the kinetic energy oscillates 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
Consider a simple harmonic motion of time period T. Calculate the time taken for the displacement to change value from half the amplitude to the amplitude.
Find the time period of the motion of the particle shown in figure . Neglect the small effect of the bend near the bottom.
The period of oscillation of a body of mass m1 suspended from a light spring is T. When a body of mass m2 is tied to the first body and the system is made to oscillate, the period is 2T. Compare the masses m1 and m2
Find the number of oscillations performed per minute by a magnet is vibrating in the plane of a uniform field of 1.6 × 10-5 Wb/m2. The magnet has a moment of inertia 3 × 10-6 kg/m2 and magnetic moment 3 A m2.
When two displacements represented by y1 = a sin(ωt) and y2 = b cos(ωt) are superimposed the motion is ______.
The displacement time graph of a particle executing S.H.M. is shown in figure. Which of the following statement is/are true?
- The force is zero at `t = (T)/4`.
- The acceleration is maximum at `t = (4T)/4`.
- The velocity is maximum at `t = T/4`.
- The P.E. is equal to K.E. of oscillation at `t = T/2`.
Show that the motion of a particle represented by y = sin ωt – cos ωt is simple harmonic with a period of 2π/ω.
A person normally weighing 50 kg stands on a massless platform which oscillates up and down harmonically at a frequency of 2.0 s–1 and an amplitude 5.0 cm. A weighing machine on the platform gives the persons weight against time.
- Will there be any change in weight of the body, during the oscillation?
- If answer to part (a) is yes, what will be the maximum and minimum reading in the machine and at which position?
When a particle executes Simple Harmonic Motion, the nature of the graph of velocity as a function of displacement will be ______.
