Calculating Tangential Forces on Carbide Tips of Circular Saw

[Heat]

Homework Statement

The carbide tips of the cutting teeth of a circular saw are 8.6cm from the axis of rotation.

The no-load speed of the saw, when it is not cutting anything, is 4800 rev/min. Why is its no-load power output negligible?

While the saw is cutting lumber, its angular speed slows to 2400rev/min and the power output is 1.9hp. What is the tangential force that the wood exerts on the carbide tips?

The Attempt at a Solution

Would part a be that it's like that because it's not producing any work, there is no friction or any force acting/slowing down the rev/min.?

How do I start part b?

Before: 4800 rev/min 0hp
After 2400 rev/min 1.9hp

How would I calculate the tangential forces.?

Please and thank you.

 

[Astronuc]

The no-load speed of the saw, when it is not cutting anything, is 4800 rev/min. Why is its no-load power output negligible?

Well, at constant speed, it is accelerating, i.e. there is not angular acceleration.

See - http://hyperphysics.phy-astr.gsu.edu/hbase/mi.html - for equations of rotational motion.

See the relationship between torque, angular velocity and power. For relationship between applied force on moment arm and torque, see -

http://hyperphysics.phy-astr.gsu.edu/hbase/torq2.html#tc

 

[ogb p]

I would approach this problem by first understanding the concept of tangential force and its relation to circular motion. Tangential force is the force acting on an object in a circular path, directed tangentially to the circle. In this case, the carbide tips of the circular saw are experiencing tangential forces as they rotate around the axis of rotation.

To calculate the tangential force on the carbide tips, we can use the equation F = m * a, where F is the tangential force, m is the mass of the object, and a is the tangential acceleration. In this case, the mass of the carbide tips can be considered negligible, so we can focus on calculating the tangential acceleration.

To calculate the tangential acceleration, we can use the equation a = ω^2 * r, where ω is the angular velocity and r is the radius of rotation. In part a, the no-load speed of the saw is 4800 rev/min, which can be converted to radians per second by multiplying by 2π/60, giving us an angular velocity of 502.65 rad/s. The radius of rotation is given as 8.6cm, which can be converted to meters by dividing by 100, giving us a radius of 0.086m. Plugging these values into the equation, we get a tangential acceleration of 216.47 m/s^2.

To calculate the tangential force, we can now use the equation F = m * a. As mentioned earlier, the mass of the carbide tips can be considered negligible, so we can assume a value of 0 for m. This gives us a tangential force of 0 N.

In part b, the angular speed slows to 2400 rev/min and the power output is 1.9hp. We can follow the same steps as in part a to calculate the tangential acceleration, which comes out to be 60.66 m/s^2. To calculate the tangential force exerted by the wood on the carbide tips, we can again use the equation F = m * a. Since the mass of the wood is not given, we can use the power output as a substitute. Power is the rate of doing work, which is given by the equation P = F * v, where P is power, F is force, and v is velocity. In this case, we know the power output