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).
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Calculate the radius of the grinding wheel: Given the diameter of the grinding wheel is 200 mm, we can find the radius:
\[ r = \frac{diameter}{2} = \frac{200 \text{ mm}}{2 \times 1000 \text{ mm/m}} = 0.1 \text{ m} \]
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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.