Final answer:
The diameter be in order to transmit 36 hp at 75 rpm is when the diameter is 2 inches.
Step-by-step explanation:
To find the diameter of the shaft, we can use the formula for joint variation. When the diameter is 2 inches, the shaft can transmit 36 hp at 75 rpm. Using this information, we can find the value of k and solve for the diameter when the shaft can transmit 134 hp at 35 rpm.
Step-by-step explanation:
To solve this problem, we can use the formula for joint variation:
hp = k × (rpm) × (diameter)³
where hp represents the horsepower, rpm represents the speed in revolutions per minute, diameter represents the diameter of the shaft, and k is a constant of variation.
To find the diameter, we can use the given information. When the diameter is 2 inches, the shaft can transmit 36 hp at 75 rpm. Let's substitute these values into the formula and find the value of k:
36 = k × 75 × 2³
Simplifying the equation, we get:
k = 36 / (75 × 8) = 0.06
Now we can use this value of k to solve for the diameter when the shaft can transmit 134 hp at 35 rpm:
134 = 0.06 × 35 × (diameter)³
Simplifying the equation, we get:
diameter³ = 134 / (0.06 × 35) = 8
Taking the cube root of both sides, we find:
diameter = 2 inches
Therefore, the diameter of the shaft must be 2 inches in order to transmit 134 hp at 35 rpm.
Your full question was
The horsepower (hp) that a shaft can safely transmit varies jointly with its speed (in revolutions per minute, rpm) and the cube of its diameter. If a shaft of a certain material 2 inches in diameter can transmit 36 hp at 75 rpm, what diameter must the shaft have in order to transmit 134 hp at 35 rpm.