Question

If luis pulls straight down on the end of a wrench that is tilted θ = 30∘ above the horizontal and is r = 35 cm long, what force must he apply to exert a torque of -13 n⋅m ?

Answer 1

To exert a torque of -13 N·m with a wrench tilted at 30° and 35 cm long, Luis must apply a force of 74.29 N downward on the wrench.

Step-by-step explanation:

The student is asking how to calculate the force required to apply a specific torque when pulling down on a wrench. Given that the torque (τ) is -13 N·m, the wrench length (r) is 35 cm (which is 0.35 m), and the angle (θ) above the horizontal is 30°, we can use the formula for torque, τ = rFsinθ, where F is the force applied.

We can rearrange the formula to solve for F: F = τ / (rsinθ). Plugging in the given values, F = -13 N·m / (0.35 m × sin(30°)) = -13 N·m / (0.35 m × 0.5) = -13 N·m / 0.175 m = -74.29 N. Since a negative force doesn't make physical sense in this context, we take the absolute value and conclude that Luis must apply a force of 74.29 N.

In summary, to exert a torque of -13 N·m by pulling straight down on the tilted wrench, Luis must apply a force of 74.29 N.

Answer 2

42.89 N

Step-by-step explanation:

For this particular problem, the equation to use is Force = Torque / ( Length * cos( Angle ) ).

35 cm = 0.35 m

F = -13/(0.35*cos(30))

F = -42.89

Force = 42.89 N with a negative direction.