Question
A grinding wheel having a diameter of 200 mm rotates at 3 000 r/min with a tangential force of 40 N on the workpiece. The motor runs at 1 500 r/min and the efficiency of the machine is 72%.
Calculate the torque
Calculate the torque
Answers
GPT-4o mini
To calculate the torque, we can use the relationship between tangential force, torque, and the radius of the grinding wheel. The formula for torque (\( T \)) is given by:
\[
T = F \times r
\]
where:
- \( T \) is the torque in Newton-meters (Nm),
- \( F \) is the tangential force in Newtons (N),
- \( r \) is the radius in meters (m).
1. **Calculate the radius of the grinding wheel:**
Given the diameter of the grinding wheel is 200 mm, we can find the radius:
\[
r = \frac{diameter}{2} = \frac{200 \text{ mm}}{2 \times 1000 \text{ mm/m}} = 0.1 \text{ m}
\]
2. **Calculate the torque:**
We have the tangential force \( F = 40 \) N and the radius \( r = 0.1 \) m. Plugging in the values:
\[
T = 40 \, \text{N} \times 0.1 \, \text{m} = 4 \, \text{Nm}
\]
So, the torque applied to the grinding wheel is **4 Nm**.
\[
T = F \times r
\]
where:
- \( T \) is the torque in Newton-meters (Nm),
- \( F \) is the tangential force in Newtons (N),
- \( r \) is the radius in meters (m).
1. **Calculate the radius of the grinding wheel:**
Given the diameter of the grinding wheel is 200 mm, we can find the radius:
\[
r = \frac{diameter}{2} = \frac{200 \text{ mm}}{2 \times 1000 \text{ mm/m}} = 0.1 \text{ m}
\]
2. **Calculate the torque:**
We have the tangential force \( F = 40 \) N and the radius \( r = 0.1 \) m. Plugging in the values:
\[
T = 40 \, \text{N} \times 0.1 \, \text{m} = 4 \, \text{Nm}
\]
So, the torque applied to the grinding wheel is **4 Nm**.