Solving Non-Inertial Frame Homework: Spring Force, Mass, Acceleration

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In summary, the conversation discusses an exercise involving a block attached to a light spring hanging from the ceiling of an accelerating lift. The equation of motion for the block is derived and the approach to solving it is discussed.
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1. Homework Statement

A light spring force const. k hands from ceiling of an accelerating lift with a block of mass m attached to its bottom end. Block is held stationary (in lift frame) with the string at its equilibrium length while the lift is accelerating at a rate Ag where A is between -1 and 1 (const.) At t=0 the block is released from rest allowing it to execute SHM. Denote X by distance of block from origin of intertial FoR and Xo its distance when the spring is at equil. length..

write down eqn of motion of block in interial FoR..

then more qs

2. Homework Equations



3. The Attempt at a Solution

I think (Xo-X)'' + k/m(Xo-X) = g

I know Xo'' = Ag

but how do i solve this eqn of motion?

help? Thanks
 
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  • #2
Your equation seems right (although I haven't checked for sign issues), but I'd approach the problem in a different way. You can easily find the equation of motion of the block in the accelerating frame; just consider the acceleration of gravity to be Ag+g. You can also find the equation of motion for Xo; it's accelerating constantly. Add them together and you get the equation of motion for the block.
 

FAQ: Solving Non-Inertial Frame Homework: Spring Force, Mass, Acceleration

How do you determine the spring force in a non-inertial frame?

To determine the spring force in a non-inertial frame, you need to first identify the acceleration of the frame. Then, use the formula F = -kx - ma, where k is the spring constant, x is the displacement of the spring, and m is the mass of the object attached to the spring. Finally, subtract the product of ma from the calculated spring force to account for the acceleration of the frame.

Can mass affect the acceleration of a non-inertial frame?

Yes, the mass of an object can affect the acceleration of a non-inertial frame. This is because according to Newton's second law, F = ma, where F is the net force acting on an object, m is the mass of the object, and a is the acceleration. Therefore, the greater the mass of the object, the greater the force needed to accelerate it, which in turn affects the acceleration of the frame.

How does the spring constant affect the spring force in a non-inertial frame?

The spring constant, k, is a measure of the stiffness of a spring. In a non-inertial frame, the spring force can be calculated using the formula F = -kx - ma. This means that the spring constant directly affects the magnitude of the spring force, as a higher k value will result in a greater force being exerted on the object attached to the spring.

Can the spring force change in a non-inertial frame?

Yes, the spring force can change in a non-inertial frame. This is because the spring force depends on the displacement of the spring, the mass of the object, and the acceleration of the frame. If any of these variables change, the spring force will also change accordingly.

How does the displacement of the spring affect the spring force in a non-inertial frame?

The displacement of the spring directly affects the spring force in a non-inertial frame. This is because the spring force is calculated using the formula F = -kx - ma, where x is the displacement of the spring. As the displacement increases, the spring force will also increase, and vice versa.

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