What power (in horsepower) is developed by a grinding machine whose wheel has a radius of 8.10 in and runs at 2.50 rev/s, when the tool to be sharpened is held against the wheel with a force of 43.0 lb? The coefficient of friction between the tool and the wheel is 0.340 .
Help!! I have no idea how to even start this!!
Velocity radius over time taken = v=2.50+8.10=10.60 v2=43.0+0.340=0.770 10.60/20.370=0.5203731
Don't worry! I'll guide you through the steps to solve this problem.
To find the power developed by the grinding machine, we can use the formula for power:
Power = Force x Velocity
Here's what you need to do:
Step 1: Calculate the linear velocity of the wheel
The linear velocity of the wheel can be found using the formula:
Velocity = 2πr x rev/s
Given:
Radius of the wheel (r) = 8.10 in
Number of revolutions per second (rev/s) = 2.50
Substituting the values into the equation, we have:
Velocity = 2 x π x 8.10 in x 2.50 rev/s
Step 2: Convert the linear velocity to feet per second
To convert inches to feet, divide by 12:
Velocity(ft/s) = Velocity(in/s) / 12
Step 3: Calculate the force of friction
The force of friction can be determined using the formula:
Force of friction = coefficient of friction x normal force
Given:
Force of friction = 43.0 lb (tool held against the wheel)
Coefficient of friction = 0.340
Step 4: Convert the mass of the tool from pounds to slugs
To convert pounds to slugs, divide by the acceleration due to gravity:
Mass (in slugs) = Mass (in lb) / g
The acceleration due to gravity (g) is approximately 32.17 ft/s^2.
Step 5: Calculate the normal force
The normal force can be calculated using the equation:
Normal force = mass x acceleration due to gravity
Step 6: Calculate the power
Finally, substitute the values obtained into the formula for power:
Power = Force of friction x Velocity
Now that you know the steps to solve the problem, go ahead and use the given values to find the power developed by the grinding machine!