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A 30 cm wrench is used to loosen a bolt with a force applied 0.3 mm from the bolt. It takes 60 N to loosen the bolt when the force is applied perpendicular to the wrench. How much force would it take if the force was applied at a 30 degree angle from perpendicular?

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musiclover10045

The torque required to loosen the bolt when perpendicular was:

t = 60N x 0.3 = 18 Nm

To have the same torque applied at 30 degrees:

18 Nm = Force x 0.3cos(30 degrees)

Simplify:

18 Nm = Force x 0.2598

Force = 18Nm / 0.2598

Force = 69.28 N

Round the answer as needed.

onyebuchinnaji

The magnitude of force required when the force is applied to an angle is 69.28 N.

The given parameters;

  • length of the wrench, r = 30 cm = 0.3
  • force applied , F = 60 N
  • angle of inclination, = 30⁰

The torque applied in loosening the bolt is calculated as follows;

τ = Fr

τ = 60 x 0.3

τ = 18 Nm

The magnitude of force required when the force is applied to an angle is calculated as follows;

[tex]18 = F \times 0.3 \times cos30\\\\18 = F \times 0.3 \times 0.866\\\\F = \frac{18}{0.3 \times 0.866} \\\\F = 69.28 \ N[/tex]

Thus, the magnitude of force required when the force is applied to an angle is 69.28 N.

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