# Finding the Force on a bolt from a wrench

• pinkfishegg
In summary, the problem involves determining the force applied to a bolt when a force is applied to the end of a wrench perpendicular to the wrench's length. The solution involves using the equation ∑τ=LF+bF=(I_bolt+I_wrench)α and considering the torque at both the length of the wrench and the radius of the bolt. The correct answer is c) FL/b, which represents the ratio of forces at these two points.
pinkfishegg

## Homework Statement

In an Effort to tighten a bolt, a force F is applied to the end of a wrench that has a length L perpendicular to the wrench. If the bolt itself has a radius of b, how much force is applied to the bolt

## Homework Equations

∑τ=RFsinθ ΣF=ma ∑T=Iα

## The Attempt at a Solution

I tried summing the torques
∑τ=LF+bF=(I_bolt+I_wrench)α

a)F
b)Fb/L
c)FL/b
d)FL/(b+L)
e)bL/F

I'm not even sure how you would solve this to get anything like that or why there is an F in the answer when we're solving for F. My friend says this is a conceptual engineering problems and that c makes sense since the Force is multiplied by the length of the bolt (they are really looking for torque) but divided by the length of the wrench.

pinkfishegg said:
how much force is applied to the bolt
That's not the title of your thread. You sure they aren't out to trick you ?

And: make a drawing

Last edited:
here's a pic drawn in paint

#### Attachments

• wrench physics.png
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L is a bit vague, don't you think ?

And do you think people mean that when they mention the radius of a bolt ? In the civilized world the M10 bolt has a radius of 5 mm, but the head is a bit bigger !

pinkfishegg said:
2. Homework Equations
∑τ=RFsinθ
ΣF=ma
∑T=Iα

3. The Attempt at a Solution
I tried summing the torques
∑τ=LF+bF=(I_bolt+I_wrench)α

Note that there is only one F in your drawing !

You be the judge: answering the question literally is a). But the force the thread of the bolt exerts on the thread on the inside of the hole (or nut) is c) as your friend sort of indicated. This multiplication factor is the reason wrenches exist

(Note that the length of a bolt is in general not the same as the radius...)

You know the torque from L x F. (angle is 90 degrees). At the thread of the bolt the torque is the same !

None of the answers has the dimension of torque ( Newton x meter or better: Force x length). All of them have the dimension of a force.

So are we looking for a ratio of the torques to find the Force?

BvU said:
L is a bit vague, don't you think ?

And do you think people mean that when they mention the radius of a bolt ? In the civilized world the M10 bolt has a radius of 5 mm, but the head is a bit bigger !
Note that there is only one F in your drawing !

You be the judge: answering the question literally is a). But the force the thread of the bolt exerts on the thread on the inside of the hole (or nut) is c) as your friend sort of indicated. This multiplication factor is the reason wrenches exist

(Note that the length of a bolt is in general not the same as the radius...)

You know the torque from L x F. (angle is 90 degrees). At the thread of the bolt the torque is the same !

None of the answers has the dimension of torque ( Newton x meter or better: Force x length). All of them have the dimension of a force.

Oh a radius of a bolt is the round thing before the threat, is the force applied there?

#### Attachments

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No. That's a specific type of bolt and that radius has little to do with the exercise.

I meant the radius of the shaft: so D/2 in the drawing below

pinkfishegg said:
So are we looking for a ratio of the torques to find the Force?
I tried to explain that there is only one torque and that the ratio of the forces at L and at b is the ratio of b and L : ##\tau = L \times F_L ## and ##\tau = b \times F_b##

Last edited:
BvU said:
No. That's a specific type of bolt and that radius has little to do with the exercise.

I meant the radius of the shaft: so D/2 in the drawing below

I tried to explain that there is only one torque and that the ratio of the forces at L and at b is the ratio of L and b : ##\tau = L \times F_L ## and ##\tau = b \times F_b##

Ohhh that makes so much sense thanks

## 1. What is the force on a bolt from a wrench?

The force on a bolt from a wrench is the amount of energy or pressure exerted on the bolt when the wrench is used to tighten or loosen it. This force is measured in units of Newtons (N).

## 2. How is the force on a bolt from a wrench calculated?

The force on a bolt from a wrench can be calculated using the equation F = P x A, where F is the force, P is the pressure applied by the wrench, and A is the area of contact between the wrench and the bolt. This equation is known as the pressure formula.

## 3. What factors affect the force on a bolt from a wrench?

The force on a bolt from a wrench can be affected by various factors, such as the length of the wrench, the applied torque, the type of bolt or nut being tightened, and the condition of the wrench and bolt.

## 4. How does the direction of the wrench affect the force on a bolt?

The direction of the wrench affects the force on a bolt by changing the angle at which the force is applied. The force on the bolt will be greater when the wrench is perpendicular to the bolt compared to when it is at an angle.

## 5. Is it important to consider the force on a bolt from a wrench?

Yes, it is important to consider the force on a bolt from a wrench as it can impact the tightness and security of the bolt. Applying too much or too little force can result in a loose bolt or damage to the bolt and wrench. It is important to use the correct amount of force for the specific bolt and task at hand.

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