Finding work done by object along circular helix: Line Integral

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Homework Help Overview

The problem involves calculating the work done by an object moving along a helical path defined by parametric equations in a gravitational field. The object has a weight of 1.2 pounds, and the context is set within the framework of physics involving forces and work.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss the need to define the force acting on the object and explore the relationship between weight, mass, and gravitational force. There is uncertainty about how to apply the equations of motion and the definitions of weight and force.

Discussion Status

Some participants have provided clarifications regarding the nature of weight as a force and its implications for calculating work. There is ongoing exploration of the definitions and relationships between mass, weight, and gravitational force, with no explicit consensus reached yet.

Contextual Notes

Participants are navigating the differences between the English and SI systems of measurement, particularly in relation to force and weight. There is a focus on ensuring the correct application of physical principles without resolving the underlying confusion about units and definitions.

yolanda
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Homework Statement


An object weighing 1.2 pounds travels along a helix given by x=cost, y=sint, z=4t, 0<=t<=8pi. Find the work done by the object.

Let's keep this in ft.

Homework Equations


g=32.174 ft/s2
f=m*g
f=w*d

The Attempt at a Solution



r(t)=cos(t)i+sin(t)j+4(t)k

I know I need an F function, but I'm not sure how to find it.

w=\int F(dot)dr
w=\intF(r(t)) (dot) r'(t) dt

Any help would be appreciated, thanks in advance!
 
Last edited:
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You are working against gravity, which is directed downward. So figure out the force f of gravity on your object and use

\vec F = \langle 0,0,-f\rangle

This is the work done by the force, opposite the work done by the object.
 
Thank you for your response. This may sound a bit stupid, but I want to make sure I'm getting the right force here...

Weight is the mass of an object with a force acting upon it. I'm not sure how much the equations f=ma and weight=m*gravity "overlap", if you will. Can I just say 1.2=mass*gravity? That would mean that the force is 1.2 pounds... do you see what I'm confused about here?

Thanks again for your help!
 
1.2 pounds is a unit of force in the English system. And work is measured in foot-pounds which gives the right units for w = fd in the English system.
 
yolanda said:
Weight is the mass of an object with a force acting upon it.
Weight is a force. The formula F = ma gives the force F acting on an object of mass m under an acceleration a.

In the SI system, a mass of 1 kg at the surface of the Earth exerts a force downward of 1kg * 9.8 m/s^2 = 1 Nt. In the English system, a mass of 1 slug at the surface of the Earth exerts a force downward of 1 slug* 32 ft/sec^2 = 32 lb.
yolanda said:
I'm not sure how much the equations f=ma and weight=m*gravity "overlap", if you will. Can I just say 1.2=mass*gravity? That would mean that the force is 1.2 pounds... do you see what I'm confused about here?

They overlap considerably, but the F = ma formula applies more generally for any kind of acceleration, not just that due to gravity.
 

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