Calculating Force Required to Loosen a Nut on a Car Wheel
What force must be exerted at the end of a 0.25 m lug wrench to loosen the nut when the angle between the force and the wrench is 52◦?
If the torque required to loosen a nut holding a wheel on a car is 89 n · m, answer in units of n.
Answer:
The force required to loosen the nut can be calculated using the formula:
τ = Fd sin θ
Where:
F is the force applied
d is the distance of the arm (the lug wrench)
θ is the angle between the direction of the force and the arm
In this problem, the torque required is 89 Nm, the length of the arm (the lug wrench) is 0.25 m, and the angle between the force and the wrench is 52◦. By rearranging the formula and plugging in the given data, we can find the magnitude of the force:
F = τ / (d sin θ) = 89 Nm / (0.25 m * sin 52◦) = 451.8 N
When working on a car, it is important to understand the physics involved in tasks such as loosening nuts holding wheels in place. In this scenario, we were given the torque required to loosen the nut (89 Nm), the length of the lug wrench (0.25 m), and the angle between the force and the wrench (52◦).
Using the formula for torque, τ = Fd sin θ, we rearranged the equation to solve for the force, F. By plugging in the values for torque, arm length, and angle, we calculated that a force of 451.8 N must be exerted at the end of the lug wrench to loosen the nut.
Understanding how forces, distances, and angles interact is crucial when working with tools and machinery. By applying the principles of torque, we can determine the amount of force needed to accomplish various tasks, such as loosening a nut on a car wheel. This calculation ensures that the appropriate force is applied to complete the job effectively and safely.