Question

a shaft of 50 mm diameter transmits a torque of 800 n-m. the width of the rectangular key used is 10 mm. the allowable shear stress of the material of the key being 40 mpa, the required length of the key would be

Answer 1

To calculate the required length of the key, we can use the formula:

Length of key = (Torque * Width of key) / (Allowable shear stress * Diameter)

Plugging in the given values:

Length of key = (800 N-m * 10 mm) / (40 MPa * 50 mm)

Simplifying the units:

Length of key = (800 * 0.01 m * 10 * 0.001 m) / (40 * 10^6 N/m^2 * 0.05 m)

Calculating further:

Length of key = (8 * 10^-2 N-m * 10^-3 m) / (40 * 10^6 N/m^2 * 5 * 10^-2 m)

Length of key = 8 * 10^-5 N-m-m / (2000 * 10^4 N/m^2)

Length of key = 4 * 10^-9 m^2 / (2000 * 10^4 N/m^2)

Length of key = 2 * 10^-13 m

So, the required length of the key would be 2 * 10^-13 meters.