Displacement of spring of a block going down an incline

AI Thread Summary
The discussion revolves around a physics problem involving a block sliding down an incline and compressing a spring. The inclined plane has an angle of 20 degrees, and the spring has a force constant of 455 N/m. The block, with a mass of 2.71 kg, is projected downward towards the spring with an initial speed of 0.750 m/s from a distance of 0.330 m. The user attempts to apply energy conservation principles but arrives at an incorrect compression value of 0.226 m. The thread seeks clarification on the error in the calculations leading to this incorrect result.
joedango
Messages
9
Reaction score
0

Homework Statement


An inclined plane of angle θ = 20.0° has a spring of force constant k = 455 N/m fastened securely at the bottom so that the spring is parallel to the surface as shown in the figure below. A block of mass m = 2.71 kg is placed on the plane at a distance d = 0.330 m from the spring. From this position, the block is projected downward toward the spring with speed v = 0.750 m/s. By what distance is the spring compressed when the block momentarily comes to rest?

Homework Equations


dE=dk+du=0

Kf-Ki+Dfsp-Disp+Dfg-Dig=0
Ki=1/2mv^2
Dfsp=1/2kx^2
Dig= mg[h + x(sin20.0)]

The Attempt at a Solution


Kf,Disp, and Dfg all Equal zero
so by substitution:

-1/2mv^2+1/2kx^2-mg[h + x(sin20.0)]=0
-(2.71)(.75^2)/2+455/2x^2-(2.71*9.8)[0.33+xsin(20)]=0

which simplifies to
227.5x^2-9.084x-9.52=0

My answer is .226, which is the incorrect answer. What am I doing wrong?

Thanks!
 
Last edited:
Physics news on Phys.org
I forgot to post the picture. Here it is:
7-p-063.gif
 
Last edited:
I multiplied the values first without the error limit. Got 19.38. rounded it off to 2 significant figures since the given data has 2 significant figures. So = 19. For error I used the above formula. It comes out about 1.48. Now my question is. Should I write the answer as 19±1.5 (rounding 1.48 to 2 significant figures) OR should I write it as 19±1. So in short, should the error have same number of significant figures as the mean value or should it have the same number of decimal places as...
Thread 'A cylinder connected to a hanging mass'
Let's declare that for the cylinder, mass = M = 10 kg Radius = R = 4 m For the wall and the floor, Friction coeff = ##\mu## = 0.5 For the hanging mass, mass = m = 11 kg First, we divide the force according to their respective plane (x and y thing, correct me if I'm wrong) and according to which, cylinder or the hanging mass, they're working on. Force on the hanging mass $$mg - T = ma$$ Force(Cylinder) on y $$N_f + f_w - Mg = 0$$ Force(Cylinder) on x $$T + f_f - N_w = Ma$$ There's also...
Back
Top