If a torque of 25 Nm is applied and the lever arm is 5 m, what is the angle at w

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Question: If a torque of 25 Nm is applied and the lever arm is 5 m, what is the angle at which the force is applied if the force is 10 N?

Options:

Correct Answer: 60 degrees

Solution:

Torque = Force × Distance × sin(θ) => 25 Nm = 10 N × 5 m × sin(θ) => sin(θ) = 0.5 => θ = 30 degrees.

If a torque of 25 Nm is applied and the lever arm is 5 m, what is the angle at which the force is applied if the force is 10 N?

If a torque of 25 Nm is applied and the lever arm is 5 m, what is the angle at which the force is applied if the force is 10 N?

Step 1: Understand the formula for torque, which is Torque = Force × Distance × sin(θ).
Step 2: Identify the values given in the question: Torque = 25 Nm, Force = 10 N, Distance (lever arm) = 5 m.
Step 3: Substitute the known values into the torque formula: 25 Nm = 10 N × 5 m × sin(θ).
Step 4: Simplify the equation: 25 Nm = 50 N·m × sin(θ).
Step 5: Divide both sides by 50 N·m to isolate sin(θ): sin(θ) = 25 Nm / 50 N·m.
Step 6: Calculate sin(θ): sin(θ) = 0.5.
Step 7: Find the angle θ by using the inverse sine function: θ = sin⁻¹(0.5).
Step 8: Determine the angle: θ = 30 degrees.

Torque Calculation – Understanding how torque is calculated using the formula Torque = Force × Distance × sin(θ).
Trigonometric Functions – Applying the sine function to find the angle when given the sine value.
Units of Measurement – Recognizing and correctly using units such as Newton meters (Nm) for torque.