Final answer:
To find the maximum speed of the saw blade moving left and right, the circumferential speed of the motor's rotating shaft, which rotates at 60 Hz with a radius of 3.0 cm, is calculated, yielding an approximate speed of 11.31 m/s.
Step-by-step explanation:
The student's question appears to relate to rotational motion and mechanical linkages, specifically the Scotch Yoke mechanism, which converts the rotational motion of a motor into linear motion.
To estimate the maximum speed of the saw blade moving left and right, we'll consider the motor's rotation rate and the radius of the rotation.
Given that the motor rotates at 60 Hz (which is equal to 3600 revolutions per minute (rpm)) and has a radius of 3.0 cm, we can calculate the linear speed at the edge of the rotating shaft (where the radius is maximal).
First, we convert the radius to meters:
We find the circumference of the circle described by the motor shaft during rotation as:
- Circumference = 2 × π × radius
This gives us:
- Circumference = 2 × π × 0.030 m ≈ 0.1885 m
Since every rotation moves the point at the edge of the shaft one circumference forward, the linear speed V is:
Substituting the values we have:
To convert rpm to revolutions per second (rps), we divide by 60:
So, the linear speed of the blade is:
which gives:
Therefore, the maximum speed of the saw blade as it moves left and right is approximately 11.31 m/s.