A machine part has the shape of a solid uniform sphere of mass 205 g and diameter 4.10 cm. It is spinning about a frictionless a
xle through its center, but at one point on its equator, it is scraping against metal, resulting in a friction force of 0.0200 N at that point.
(a) Find its angular acceleration. Let the direction the sphere is spinning be the positive sense of rotation.
(b) How long will it take to decrease its rotational speed by 22.0 rad/s?
(a) Find its angular acceleration. Let the direction the sphere is spinning be the positive sense of rotation.
(b) How long will it take to decrease its rotational speed by 22.0 rad/s?
1 answer:
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Answer:
15.07 ksi
Explanation:
Given that:
Pitch (P) = 5 teeth/in
Pressure angle () = 20°
Pinion speed ( ) = 2000 rev/min
Power (H) = 30 hp
Teeth on gear () = 50
Teeth on pinion () = 20
Face width (F) = 1 in
Let us first determine the diameter (d) of the pinion.
Diameter (d) =
=
= 4 in
From the values of Lewis Form Factor Y for ( ) = 20 ; at 20°
Y = 0.321
To find the velocity (V); we use the formula:
V = 2094.40 ft/min
For cut or milled profile; the velocity factor can be determined as follows:
= 2.0472
However, there is need to get the value of the tangential load, in order to achieve that, we have the following expression
Finally, the bending stress is calculated via the formula:
15.07 ksi
∴ The estimate of the bending stress = 15.07 ksi