Kinematics: force along x-axis problem

  • Thread starter Thread starter vsage
  • Start date Start date
  • Tags Tags
    Force Kinematics
AI Thread Summary
The discussion revolves around calculating the velocity of a 2.7 kg body moving along the x-axis under the influence of a force given by Fx = -6x N. The initial velocity at x = 3.0 m is 8.0 m/s, and the user calculates the velocity at x = 4.0 m to be approximately 0.22 m/s. However, there is confusion regarding the method used, particularly the derivation of acceleration and velocity from force. Participants emphasize the importance of using work and energy principles, specifically noting that the work done is the integral of force over distance. The conversation highlights the need for correct application of physics concepts to solve the problem accurately.
vsage
The only force acting on a 2.7 kg body as it moves along the positive x-axis has an x component Fx = - 6x N, where x is in meters. The velocity of the body at x = 3.0 m is 8.0 m/s.

What is the velocity at x = 4?

I found it to be 0.22m/s but my friends swear up and down it's not. Could I get a second opinion on this answer? My work is something like this:

F = -6x
a = -6/2.7 * x
v = -3/2.7 * x^2 +c

v(3) = 8

8 = -3/2.7 * 3^2 + c
c = 18

v(4) = -3/2.7 * 4^2 + 18
v(4) = 0.222

Corrections please? Thanks in advance.
 
Physics news on Phys.org
W = d(Kinetic energy) = (Integral from inital to final ) F dx

that's waht you're missing
 
heh that makes sense. I had forgotten the point of the entire homework assignment I was helping with was work-related. I still can't figure out why my way didn't work though oh well.
 
It didn't work BECAUSE!

vsage said:
F = -6x
a = -6/2.7 * x
v = -3/2.7 * x^2 +c

First of all what are you thinking about here how did you figure (ASSUME) that a = 6 / 2.7 x
and how did you derive v from that ?

v(3) = 8

8 = -3/2.7 * 3^2 + c
c = 18

v(4) = -3/2.7 * 4^2 + 18
v(4) = 0.222

Seems you tried to find the difference betwee nthe two points on force

Remember that is W is the integral because it is the area under the graph of force and the only way to do that is to find the integral
 
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...
Thread 'Variable mass system : water sprayed into a moving container'
Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
Back
Top