What is the Displacement and Force Acting on a Particle in the xy Plane?

  • Thread starter Thread starter vinnyzwrx
  • Start date Start date
  • Tags Tags
    Force Particle
AI Thread Summary
The discussion focuses on calculating various properties of a particle moving in the xy plane under a constant force. The magnitude of the displacement is determined using the Pythagorean theorem, resulting in a value derived from the components sx and sy. The magnitude of the force is identified as the length of the force vector, while the work done by the force is calculated using the dot product of the displacement and force vectors. Additionally, the angle between the force and displacement is found using trigonometric functions. The thread emphasizes the simplicity of these calculations and the importance of understanding the correct methods to solve the problem.
vinnyzwrx
Messages
14
Reaction score
0

Homework Statement



A particle moving in the xy plane undergoes a displacement ⃗s = (sx ˆi + sy ˆj), with sx = 1.74 m, sy = 4.3 m, while a constant force
F⃗ = (Fxˆi+Fyˆj), with Fx = 5.1 N, Fy = 1.95 N, acts on the particle.
Calculate the magnitude of the displacement.
Answer in units of m.

Find the magnitude of the force. Answer in units of N.

Calculate the work done by F⃗ . Answer in units of J.

Calculate the angle between F⃗ and ⃗s. Answer in units of degrees.

Homework Equations



The Attempt at a Solution



i took the dot product of the two thinking i would get the magnitude of the displacement. I am lost as to why it is incorrect?

1.74*5.1 + 4.3*1.95 = 17.259
 
Physics news on Phys.org
its simple, i figured it out... i feel like an idiot

pythagorean theorm, magnitude = sqrt(1.74^2 + 4.3^2)
 
the entire problem is simple, i figured it out so i thought i would post it in case anyone would stumble upon this in the future

Find the magnitude of the force. Answer in units of N.

this is just the length force vector, duh...

Calculate the work done by F⃗ . Answer in units of J.

this is the dot product of the two

Calculate the angle between F⃗ and ⃗s. Answer in units of degrees.

this angle is found by taking the inverse of any trig function, provided that you use the correct sides that coorespond to that function, of the larger angle, - the smaller angle.
 
Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
Back
Top