Knowee
Questions
Features
Study Tools

A person normally weighing 50 kg50 kg stands on a massless platform which oscillates up and down harmonically at a frequency of 3.0 s−13.0 s-1 and an amplitude 6.0 cm6.0 cm. A weighing machine on the platform gives the person's weight against time. The maximum reading in the machine is X𝑋units. Then the value of X10𝑋10 must have been _____ (Take π2=10𝜋2=10 )

Question

A person normally weighing 50 kg50 kg stands on a massless platform which oscillates up and down harmonically at a frequency of 3.0 s−13.0 s-1 and an amplitude 6.0 cm6.0 cm. A weighing machine on the platform gives the person's weight against time. The maximum reading in the machine is X𝑋units. Then the value of X10𝑋10 must have been _____ (Take π2=10𝜋2=10 )

🧐 Not the exact question you are looking for?Go ask a question

Solution

The weight of a person in an oscillating lift varies between mg(1 - (2πf)²) and mg(1 + (2πf)²), where m is the mass of the person, g is the acceleration due to gravity, and f is the frequency of oscillation.

Given that the mass m = 50 kg, g = 10 m/s² (approx), and f = 3.0 s⁻¹, we can substitute these values into the equation for the maximum weight:

W_max = mg(1 + (2πf)²) = 50 kg * 10 m/s² * (1 + (2π3.0 s⁻¹)²) = 500 kgm/s² * (1 + 36π²) = 500 kgm/s² * (1 + 360) (since π² is approximated as 10) = 500 kgm/s² * 361 = 180500 kgm/s² = 180500 N (since 1 kg*m/s² = 1 N)

Therefore, the maximum reading on the weighing machine is 180500 N. If the machine measures weight in units of 10 N, then the maximum reading is X = 180500 N / 10 N/unit = 18050 units.

This problem has been solved

Similar Questions

A boy whose mass is 50kg stands on a spring balance inside a lift. The lift starts to ascent with an acceleration of  2ms−2.2𝑚𝑠−2. The reading of the machine or balance is  (g=10 ms−2)(𝑔=10 ms−2)

A 57.6-kg person rides in elevator while standing on a scale.The elevator is traveling downward but slowing down at a rate of 1.9 m/s2.What is the reading on the scale?Express your answer in N, to at least one digit after the decimal point.

A 66.0 kg Scona student is standing on a scale in an elevator. If the elevator is acceleratingdownward at 2.50 m/s2, then determine the scale reading.

A metre scale has a weight of 10 grams at a distance of 20 cm from the pivot. To balance this a student places another weight at a distance of 35 cm. Calculate the mass of this weight.

A body of mass 1 kg is executing simple harmonic motion. Its displacement 𝑦 cm at 𝑡 seconds is given by, 𝑦=6sin100𝑡+𝜋4. Its maximum kinetic energy is

1/3

Upgrade your grade with Knowee

Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.