# Calculating Torque on a Wrench

• tennisgirl92
In summary, the conversation discusses the calculation of torque in various scenarios involving a wrench and a bolt. It includes equations and diagrams to explain the concepts. The main focus is on determining the magnitude and direction of torque in different situations, and the use of trigonometry to calculate these values. Through a discussion of a specific problem, the concept of checking corner cases and using the appropriate trigonometric function is also highlighted.
tennisgirl92

## Homework Statement

(a) Suppose you have just barely loosened a rusty bolt. Your mass is 80 kg and you have a wrench of length L = 50 cm placed as shown in the diagram below, and hung off the end so all your weight was applied, in the downward direction, to the end of the wrench. What is the magnitude and direction of the torque?
magnitude 392 N m
direction counterclockwise

(b) Now suppose you had a bolt that needed to be tightened to 250 N · m. You place the wrench as shown in the diagram below, and hung off the end so all your weight was applied, in the downward direction, to the end of the wrench. What length wrench would you need to tighten the bolt completely?
L = .3189 m

(c) Suppose you had the same wrench as in part (a), but you placed the wrench at an angle θ = 54° with the vertical, as shown below. How much torque is applied to the bolt?
magnitude
direction clockwise

## Homework Equations

Torque=radius x force (in this case, weight) x sin(theta)

## The Attempt at a Solution

I am having difficulty with the 3rd part. If the torque is as the above equation,
T=.5 m x 80kg x 9.8 m/s2 x sin(54)
=-219.0
which magnitude is 219 N m with a clockwise direction
However, this is incorrect. Perhaps this is my angle-do I need to subtract 54 from 90? How do you know what angle to look at? Where do you form the right triangle for the correct trig?

tennisgirl92 said:
T=.5 m x 80kg x 9.8 m/s2 x sin(54)
=-219.0
The algebra is right, but you should have noticed it ought to give a positive answer. (To get the expected negative sign for the torque you would need to put in the appropriate sign on the angle, i.e. -54 degrees.)
What did you forget to do when you entered the angle into the sine function on your calculator?

haruspex said:
The algebra is right, but you should have noticed it ought to give a positive answer. (To get the expected negative sign for the torque you would need to put in the appropriate sign on the angle, i.e. -54 degrees.)
What did you forget to do when you entered the angle into the sine function on your calculator?
hmm...my calculator was in radian mode. I need degree mode, don't I? ha

tennisgirl92 said:
hmm...my calculator was in radian mode. I need degree mode, don't I? ha
Right.

With regard to deciding when to take sine and when cosine, I always check by considering a corner case, i.e. the angle being 0 or 90. Would the value of the trig function make sense in context? In the present case, when the angle is a right angle you would get maximum torque, so sine is right.

haruspex said:
Right.

With regard to deciding when to take sine and when cosine, I always check by considering a corner case, i.e. the angle being 0 or 90. Would the value of the trig function make sense in context? In the present case, when the angle is a right angle you would get maximum torque, so sine is right.

Thank you! That was most helpful.

## 1. What is torque and why is it important to calculate on a wrench?

Torque is a measure of the twisting force applied to an object. In the case of a wrench, it is the force applied to turn a bolt or nut. It is important to calculate torque on a wrench because it determines the amount of force needed to properly tighten a bolt or nut, which is crucial for safety and functionality.

## 2. How do you calculate torque on a wrench?

To calculate torque on a wrench, you need to know the length of the wrench (from the center of the handle to the center of the head), the amount of force applied to the handle, and the angle at which the force is applied. The formula for torque is torque = force x distance x sin(angle).

## 3. What units is torque typically measured in?

Torque is typically measured in newton-meters (Nm) or foot-pounds (ft-lb). These units represent the amount of force needed to produce one unit of torque on an object.

## 4. Why is it important to use the correct units when calculating torque on a wrench?

Using the correct units is important because it ensures that the torque measurement is accurate and consistent. Using the wrong units can lead to incorrect torque calculations, which can result in improperly tightened bolts or nuts.

## 5. Are there any other factors that can affect the torque on a wrench?

Yes, there are several other factors that can affect the torque on a wrench, such as the type and size of the bolt or nut, the condition of the threads, the lubrication used, and the accuracy of the torque wrench being used. It is important to consider all of these factors when calculating torque on a wrench to ensure proper tightening and safety.

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