Newton's Second Law - Machine Problem

[JeYo]

A machine has an 760g steel shuttle that is pulled along a square steel rail by an elastic cord . The shuttle is released when the elastic cord has 16.0N tension at a 45º angle. What is the initial acceleration of the shuttle?

Here is the only photo associated with this problem:knight_Figure_05_59.jpg


Now I think the only equations necessary are $$\Sigma$$F_x = n_x + T_x + F_Gx + f_kx = ma_x and $$\Sigma$$F_y = n_y + T_y +F_Gy + f_ky = ma_y.



I thought that I could use those two equations in tandem and use the values for a_x and a_y as the a and b sides of a the right triangle whose hypotanuse of which is the answer to the problem and lies along the cord that pulls the shuttle.

 

[Kurdt]

I think all you'll need to do for this problem is resolve the force and use the component acting along the steel rail to find the acceleration after the cord is released.

 

[ogb p]

I would approach this problem by first identifying the relevant variables and principles involved. In this case, the relevant variables include the mass of the shuttle (760g) and the tension in the elastic cord (16.0N), while the relevant principle is Newton's Second Law of Motion.

Using the equations provided, we can determine the acceleration of the shuttle by breaking it down into its x and y components. In the x-direction, the only force acting on the shuttle is the tension in the elastic cord, while in the y-direction, there are multiple forces including the normal force from the rail, the weight of the shuttle, and any kinetic friction present.

By setting up the equations and solving for the acceleration in each direction, we can then use the Pythagorean theorem to determine the magnitude of the overall acceleration of the shuttle. This will give us the initial acceleration of the shuttle as it is released from the elastic cord.

It is important to note that this calculation assumes ideal conditions and does not take into account any external factors such as air resistance or variations in the material properties. However, it provides a good starting point for understanding the motion of the shuttle in this scenario. Further experimentation and calculations may be needed to account for these factors and accurately predict the motion of the shuttle.