A 155 N force is applied to the end of a 40 cm wrench at a angle of 45 degrees to the handle. What is the torque?

155N cos45 *0.40 m = ___ N-m

43.84 N m

To find the torque in this scenario, we need to use the formula:

Torque (τ) = Force (F) × Distance perpendicular to the force (r) × Sin(θ)

Where:
- Force (F) is the magnitude of the force applied.
- Distance perpendicular to the force (r) is the shortest perpendicular distance from the axis of rotation to the line of action of the force.
- θ is the angle between the force vector and the line from the axis of rotation to the point of application of the force.

In this case, the force is 155 N, and the distance perpendicular to the force is 40 cm. However, we need to convert the distance to meters before we can proceed with the calculation.

To convert cm to m, we divide the distance by 100:
40 cm ÷ 100 = 0.4 m

Now we can find the torque by plugging in the values into the formula:

τ = 155 N × 0.4 m × Sin(45 degrees)

To calculate Sin(45 degrees), we can use a scientific calculator, or you can use the known value of √2/2.

τ = 155 N × 0.4 m × √2/2
τ ≈ 55.08 N·m (rounded to two decimal places)

Therefore, the torque applied to the wrench is approximately 55.08 N·m.