a wrench is rotated with torque of magnitude 175 N (M). the force is applied 45 cm from the pivot point at an angle of 48 degrees. what is the magnitude of the force, to one decimal place?
Angle to what? Not knowing do not know sin or cos
F (cos 48 or sin 48)(0.45) = 175
Well, it seems like you're trying to have some wrenching fun with torque! Let's do some math with a twist, shall we?
To find the magnitude of the force, we can use the equation for torque:
Torque = Force × Distance × sin(θ),
where Torque is given as 175 N·m, Distance is 45 cm (or 0.45 m), and θ is the angle of 48°.
Now, we need to solve for the Force. Rearranging the equation, we have:
Force = Torque / (Distance × sin(θ)).
Substituting in the given values, we get:
Force = 175 N·m / (0.45 m × sin(48°)).
Calculating this, the magnitude of the force will be approximately 202.0 Newtons.
So, it looks like the magnitude of the force required is 202.0 Newtons to get the wrench rotating. Keep it tight, my friend!
To find the magnitude of the force, we can use the equation τ = r * F * sinθ, where τ is the torque, r is the distance from the pivot point to the point where the force is applied, F is the magnitude of the force, and θ is the angle between the force and the lever arm.
Given:
τ = 175 N·m
r = 45 cm = 0.45 m
θ = 48 degrees
Now we can rearrange the formula to solve for F:
F = τ / (r * sinθ)
F = 175 / (0.45 * sin 48°)
Using a calculator, we can evaluate sin 48°:
F ≈ 175 / (0.45 * 0.7431)
F ≈ 522.22 N (rounded to one decimal place)
So, the magnitude of the force is approximately 522.2 N.
To find the magnitude of the force, we can use the formula for torque:
Torque = Force × Distance × sin(θ)
Where:
- Torque is the product of force and distance from the pivot point,
- Force is the magnitude of the force,
- Distance is the distance from the pivot point (given as 45 cm),
- θ (theta) is the angle between the force and the lever arm (given as 48 degrees).
Rearranging the formula, we have:
Force = Torque / (Distance × sin(θ))
Now let's plug in the given values and calculate the magnitude of the force:
Force = 175 N·m / (0.45 m × sin(48 degrees))
≈ 175 N·m / (0.45 m × 0.743)
≈ 175 N·m / 0.334
≈ 523.5 N
Therefore, the magnitude of the force is approximately 523.5 N to one decimal place.