Calculating Force and Torque for Linear motion (image provided)

In summary, in order to calculate the torque (T1) created at the axis of rotation due to the spring, you would need to multiply the distance (2 in.) by the force from the spring (20 lbs/In). This results in a torque of 40 lbs/In. Similarly, to calculate the force (F1) needed at the end of the handle to compress the spring with a torque of 40 lbs/In, you would divide the torque by the combined distance (6 in.) between the point of connection and the end of the handle. This results in a force of 6.67 lbs. If the spring already has a compression of 1 inch, the torque needed would be 80 lbs/In
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Cadormare
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Homework Statement
This isn't a homework problem. This is for a project I am working on. I am trying to understand how to calculate the force needed to compress the spring in the mechanism shown in the image.
Relevant Equations
A = the distance from the axis of rotation to the pivot joint that connects the handle (shown in black) to the rod (show in blue) and spring (shown in gray) assembly.

B = the distance from the location force will be applied to the handle (shown in black) to the pivot joint that connects the handle (shown in black) to the rod (shown in blue) and spring (shown in gray) assembly.

C = the distance the spring (shown in gray) needs to be compressed.

As the handle (shown in black) has force applied to it the spring (show in gray) will be compressed.
This is how I understand the torque (T1) created at the axis of rotation due to the spring would be calculated.
This is considering the spring is starting from a fully extended state and is not already compressed.
This is considering that (A) has a distance of 2 in. and the force from the spring is 20 lbs/In.
T1 = (2 in.) x (20 lbs/In)
T1 = 40 lbs/In

If the torque (T2) needed to compress the spring is 40 lbs/In then this is how I understand to calculate how much force (F1) is needed at the end of the handle (show in black).
This is considering that (A) has a distance of 2 in. and (B) has a distance of 4 in.
T2 = (A + B) x F1
T2 = 6 in. x F1
F1 = T2 / 6in.
F1 = (40 lbs/In) / 6 In
F1 = 6.67 lbs.

So to compress the spring an inch I would need 6.67 lbs of force for every inch I wanted to compress the spring?
If I wanted to compress the spring half an inch would it be ( 6.67 lbs. ) x (0.5) = 3.33 lbs. ?If the spring has a rate of 20 lbs./In and is already compressed an inch, would T1 then be (40 lbs/In) x 2 = 80 lbs/In ?
 

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Welcome!
The force with which the spring pushes back on the point of connection with the handle depends on how much distance or deflection it is compressed.
The rate or constant of this spring has a magnitude of 20 lbf/in.
If the handle deforms it 0.5 inch, it will push back with 10 lbf.

If you can actually apply the center of your hand's force at 6 inches from the pivot (A+B distances), then you have a mechanical advantage of 2.
That means that the rod-handle joint will "feel" twice the force that you hand applies (on a perpendicular direction) on the end of the handle.

Please, see:
https://en.wikipedia.org/wiki/Mechanical_advantage

If we consider the angles, the spring is "feeling" magnitudes of force that differ from the above for significant deviations from vertical of the handle.
In practical terms, there should be some way to decouple the angular movement of the lever and the rectilinear movement of the rod.
 
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1. What is force and torque in linear motion?

Force is a physical quantity that causes an object to accelerate or change its motion. It is measured in Newtons (N) and is represented by the symbol F. Torque, on the other hand, is the rotational equivalent of force. It is the measure of the force that causes an object to rotate around an axis and is measured in Newton-meters (N·m).

2. How do you calculate force in linear motion?

To calculate force in linear motion, you need to know the mass of the object (m) and its acceleration (a). The formula for force is F = m x a, where F is force, m is mass, and a is acceleration. This means that the force acting on an object is directly proportional to its mass and acceleration.

3. How do you calculate torque in linear motion?

To calculate torque in linear motion, you need to know the force (F) acting on the object and its distance from the axis of rotation (r). The formula for torque is T = F x r, where T is torque, F is force, and r is distance. This means that the torque acting on an object is directly proportional to the force and the distance from the axis of rotation.

4. How is force and torque related in linear motion?

Force and torque are related in linear motion because they both involve the application of a force on an object. Force causes an object to accelerate in a linear direction, while torque causes an object to rotate around an axis. They are both measured in Newtons, but torque also takes into account the distance from the axis of rotation.

5. Can you provide an example of calculating force and torque in linear motion?

Let's say we have a mass of 5 kg accelerating at a rate of 2 m/s^2. To calculate the force, we would use the formula F = m x a, so F = 5 kg x 2 m/s^2 = 10 N. Now, let's say this object is attached to a lever arm that is 0.5 meters long, and a force of 20 N is applied at the end of the lever arm. To calculate torque, we would use the formula T = F x r, so T = 20 N x 0.5 m = 10 N·m. This means that the force and torque acting on the object are equal in this scenario.

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