Question

In: Physics

A 6.0 kilogram mass is to be suspended from a cylindrical cord made of rubber with...

A 6.0 kilogram mass is to be suspended from a cylindrical cord made of rubber with equilibrium length 1.5 meters. If an oscillation frequency of 5 Hertz is desired when the mass is pulled so the cord stretches, what diameter should the cord have? Assume the Young’s modulus of the rubber is 2*10^6 N/m^2 , the yield stress is 3*10^6 N/m^2, and the shear modulus is 0.5*10^6 N/m^2.

Expert Solution

Hi,

Hope you are doing well.

We know that,

Frequency of a SHM (Simple harmonic motion),

Where,

'' is the Force constant of rubber.(N/m)

'' is the Mass suspended.(kg)

Given that,

Frequency of a SHM,

Mass suspended,

Also we know that,Force constant of rubber, '' is given by

Where,

'' is the Young's modulus of rubber.(N/m²)

'' is the Area of cylindrical cord.(m²)

'' is the Length of cylindrical cord.(m)

From equation (1),

Given that,

Force constant of rubber,

Length of cylindrical cord,

Young's modulus of rubber,

Area of cylindrical cord,

Hope this helped for your studies. Keep learning. Have a good day.

Feel free to clear any doubts at the comment section.

Please don't forget to give a thumps up.

Thank you. :)

genius_generous answered 3 years ago

A 10 10 kilogram object suspended from the end of a vertically hanging spring stretches the...

A 10 10 kilogram object suspended from the end of a vertically hanging spring stretches the spring 9.8 9.8 centimeters. At time ?=0 t = 0 , the resulting mass-spring system is disturbed from its rest state by the force ?(?)=70cos(8?) F ( t ) = 70 cos ( 8 t ) . The force ?(?) F ( t ) is expressed in Newtons and is positive in the downward direction, and time is measured in seconds. a) Determine the...

A ball of mass M is suspended by a thin string (of negligible mass) from the...

A ball of mass M is suspended by a thin string (of negligible mass) from the ceiling of an elevator. The vertical motion of the elevator as it travels up and down is described in the statements below. Indicate for each of the situations described the relation between value of the tension in the cable, T, and the weight of the ball, Mg, or whether one Cannot tell. (Assume that there is no air, i.e., neglect the buoyancy effect of...

**A crate with a mass of 45 kg is suspended from a massless rope that runs...

**A crate with a mass of 45 kg is suspended from a massless rope that runs vertically upward over a light pulley. The other end of the rope is connected to a 35 kg crate, which lies on a tabletop. The coefficients of the kinetic friction and the static friction between the crate and the surface are 0.3 and 0.5 respectively. An applied force, F, pulls the 35 kg crate to the right. In the first case, the applied force...

When a rubber strip with a 3 by 1.5 mm cross section is suspended vertically and...

When a rubber strip with a 3 by 1.5 mm cross section is suspended vertically and various masses are attached to it, a student obtains the following data for length versus load. Load (g): 0 100 200 300 400 500 Length (cm): 5.0 5.6 6.2 6.9 7.8 10.0 Find Young’s modulus for the rubber strip for small loads. Find the energy stored in the strip when the load is 150 g. (Hint the energy can be given by U...

Suspended Mass (kg) Weight of Suspended Mass (mass x 9.8 m/s2), Newtons Time (sec) Average Time...

Suspended Mass (kg) Weight of Suspended Mass (mass x 9.8 m/s2), Newtons Time (sec) Average Time Average Time2 d (m) 2d (m) Acceleration = 2d/t2 3 Washers 0.0143 0.14N Trial 1: 1.76 1.84 s 0.34 m/s2 0.6m 1.2m 0.35 m/s2 Trial 2: 1.86 Trial 3: 1.90 4 Washers 0.0191 0.19N Trial 1: 1.50 1.1 s 1.21 s2 0.6m 1.2m 0.99 m/s2 Trial 2: 1.50 Trial 3: 1.45 5 Washers 0.025 0.25N Trial 1: 1.23 1.23 s 1.51 s2 0.6m 1.2m...

A mass m = 1 kg is suspended from a spring that is stretched 1 cm...

A mass m = 1 kg is suspended from a spring that is stretched 1 cm under the influence of the weight of this mass. Now a periodic force is applied external of F (t) = 200 cos (vt) on the mass, which was initially in static balance. Disregarding all friction, get a relationship for position of the mass as a function of time, x (t). Also determine the value of ω which will cause resonance to occur

1. A mass weighing 10 lbs. is attached to a spring suspended from the ceiling. The...

1. A mass weighing 10 lbs. is attached to a spring suspended from the ceiling. The mass will stretch the spring 6 inches. If the mass is pulled 5 inches below its equilibrium point and given an initial upward velocity of 0.3 ft./sec. and if damping forces are neglected, then what is the equation of motion of the mass? What is the amplitude of the motion? 2. A 980-newton force stretches a spring 0.4 meters. If a 200 kg mass...

A square plastic chunk with mass 0.750 kg is suspended from the lower end of a...

A square plastic chunk with mass 0.750 kg is suspended from the lower end of a light cord that is 1.66 mm long. The plastic chunk is stay still in the beginning without any motion. A bullet with mass 0.0132 kg is on the way to the plastic chunk with a horizontal velocity v0. The bullet hits the plastic chunk and then embedded in it. After collision, combined bullet and plastic chunk swings on the end of the cord. When...

A 25 kilogram mass is uniformly accelerated on a horizontal smooth frictionless surface from 2 meters...

A 25 kilogram mass is uniformly accelerated on a horizontal smooth frictionless surface from 2 meters per second to 10 meters per second in 4 seconds. A. So how much work is done? (energy based) B. How much power did this require? C. What was the momentum change? D. If the frictionless surface is tilted to become a ramp and the mass's elevation changes by 2 meters while it was being accelerated the same amount, how much additional work was...

Rubber sidewalks made from ground up tires are said to be environmentally friendly and easier on...

Rubber sidewalks made from ground up tires are said to be environmentally friendly and easier on people’s knees. RUBBERSIDEWALKS, Inc. of Gardena, California, manufactures the small rubberized squares that are being installed where tree roots, freezing weather, and snow removal have required sidewalk replacement or major repairs every 3 years. The District of Columbia spent $60,000 for a rubber sidewalk to replace broken concrete in a residential neighbourhood lined with towering willow oaks. If a concrete sidewalk costs $28,000 and...