The oil drain plug on a car's engine has just been tighten to a torque of 25m*N.
a) if a 0.15m long wrench is used to change the oil, what is the minimum force needed to loosen the plug?
b) due to limited workspace, it will be necessary to crawl under the car. the force cannot be applied perpendicularly to the length of the wrench. if the applied force makes a 30-degree angle with the length of the wreach, what force is required to loosen the drain plug?
how do I do this???
Well, in theory
a) F * 0.15 = 25
b)F * .15 sin 30 = 25
but we know sin 30 = 1/2
so
F * .075 = 25
To solve this problem, we can use the principles of torque and trigonometry.
a) To find the minimum force needed to loosen the plug when using a 0.15m long wrench, we can use the formula for torque:
Torque = Force * Distance
Given that the torque is 25 m*N, and the distance (length of the wrench) is 0.15m, we can rearrange the formula to solve for the force:
Force = Torque / Distance
Substituting the given values:
Force = 25 m*N / 0.15m
b) To find the force required to loosen the drain plug when the applied force makes a 30-degree angle with the length of the wrench, we need to consider the component of the force that is perpendicular to the length of the wrench.
The torque is calculated as the product of the force and the lever arm (distance from the point of application to the pivot point). In this case, the lever arm is the distance between the center of the drain plug and where the force is applied on the wrench.
To calculate the component of the force perpendicular to the wrench, we can use trigonometry. The formula for the perpendicular component of a force is:
Perpendicular Force = Force * sin(angle)
Given that the angle is 30 degrees, and the force is the same as in part a (which we calculated above), we can solve for the perpendicular force using this formula.
I hope this helps! Let me know if you have any further questions.
To calculate the minimum force needed to loosen the oil drain plug, we can use the concepts of torque and moment of force. Torque is calculated by multiplying the applied force by the lever arm length.
a) To find the minimum force needed to loosen the plug, we need to calculate the torque required to overcome the tightening torque applied. We can use the following formula:
Torque = Force × Lever Arm Length
Given:
Tightening Torque = 25 m*N
Lever Arm Length = 0.15 m
To calculate the minimum force required to loosen the plug, we rearrange the equation as follows:
Force = Torque ÷ Lever Arm Length
Substituting the given values, we get:
Force = 25 m*N ÷ 0.15 m = 166.67 N
Therefore, the minimum force required to loosen the plug is approximately 166.67 N.
b) When the force is applied at an angle to the length of the wrench, we need to consider the component of force perpendicular to the lever arm length. This force component is responsible for loosening the plug.
In this case, the force makes a 30-degree angle with the length of the wrench. To find the force required to loosen the plug, we need to calculate the perpendicular component of the force. The formula for the perpendicular component of force is:
Perpendicular Force Component = Force × sin(θ)
Given:
Angle (θ) = 30 degrees
To calculate the force required to loosen the plug, we divide the torque by the perpendicular component of force:
Force = Torque ÷ Perpendicular Force Component
Substituting the given values, we have:
Force = 25 m*N ÷ (166.67 N × sin(30 degrees))
Calculating the sin(30 degrees), we have:
Force = 25 m*N ÷ (166.67 N × 0.5) = 300 N
Therefore, the force required to loosen the drain plug, when the applied force makes a 30-degree angle with the length of the wrench, is 300 N.
To summarize, in order to calculate the minimum force needed to loosen the oil drain plug:
a) Force = 166.67 N
b) Force = 300 N