Engineering College

A turbine disk of mass 50 lb rotates at a constant rate of 9040 rpm. Knowing that the mass center of the disk coincides with the center of rotation O, determine the reaction at O immediately after a single blade at A, of mass 2.1 oz., becomes loose and is thrown off. -12 in. The reaction at O is lb +

Answers

Answer 1

To determine the reaction at point O immediately after the blade becomes loose and is thrown off, we need to consider the conservation of angular momentum.

The angular momentum before and after the blade is thrown off should be equal, as there are no external torques acting on the system.

The angular momentum of the turbine disk before the blade is thrown off can be calculated as follows:

L_initial = I_initial * ω_initial

Where:

L_initial is the initial angular momentum

I_initial is the moment of inertia of the turbine disk

ω_initial is the initial angular velocity

Since the mass center of the disk coincides with the center of rotation, the moment of inertia of the disk can be calculated using the formula:

I_initial = m * r^2

Where:

m is the mass of the disk (converted to slugs)

r is the radius of the disk (converted to feet)

The angular velocity ω_initial can be calculated from the given rotational speed:

ω_initial = (2π * N_initial) / 60

Where:

N_initial is the initial rotational speed (converted to radians per second)

Once we have the initial angular momentum, we can calculate the final angular momentum after the blade is thrown off. Since the blade is thrown off at a distance of 12 inches from the center of rotation, the moment of inertia of the blade can be neglected compared to the disk.

L_final = I_final * ω_final

Since the mass of the blade is given in ounces, we need to convert it to slugs. The angular velocity ω_final remains the same as the initial angular velocity, as there are no external torques acting on the system.

Finally, the reaction at point O can be determined by subtracting the final angular momentum from the initial angular momentum:

Reaction at O = L_initial - L_final

Note: To perform the actual calculations, we need specific values for the mass of the disk, radius, and the rotational speed. Please provide those values to obtain a numerical result.

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Related Questions

When installing a spin-on oil filter, failure to lube the O-ring will: Select one: a. lead to double gasketing. b. damage the threads on the adapter. C. cause it to bind and roll out of the oil filter groove. d. damage the threads on the adapter.

Answers

The correct answer is c. cause it to bind and roll out of the oil filter groove.

Failure to lubricate the O-ring before installing a spin-on oil filter can cause it to bind and roll out of the oil filter groove. Lubricating the O-ring helps ensure a proper seal and prevents it from sticking or binding during installation. Without proper lubrication, the O-ring may not seat correctly, leading to oil leaks and potential engine damage.

When an oil filter gasket is too large for the application, it can prevent the oil filter from seating properly in the mounting plate and cause the gasket to bind against the engine block surface. This can create a gap between the gasket and the mounting plate, which can cause oil to leak from the filter.

Additionally, an oversized gasket can also cause the filter to roll out of the groove or become misaligned, which can cause oil to bypass the filter media and circulate unfiltered oil through the engine. This can lead to accelerated wear and damage to the engine components.

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