# Simple problem involving moment and force

• RKOwens4
In summary, the two given systems are equivalent and the task is to find the values of F' and M. The position vector for System 1 is r = 6i + 0j + 6k and the cross product of that with F = 30i - 100j + 40k gives M = 600i - 222j - 600k. To find F' for System 2, the position vector is r = 6i + 4j + 6k. Attempting to solve for F' using the known answer of M' = 40i - 80j + 120k is not a feasible method. It is necessary to ensure the numbers in the problem statement
RKOwens4

## Homework Statement

The two systems are equivalent. If F = 30i - 100j + 40k lb and M' = 40i - 80j + 120k lb*in, determine F' and M.

Here's a pic of the problem: http://img214.imageshack.us/img214/339/fc1g.jpg

M = r x F

## The Attempt at a Solution

To find M, I started out finding the position vector for System 1 and got r = 6i + 0j +6k, and then did the cross product of that with F = 3i - 100j + 40k, and got M = 600i - 222j - 600k. To find F' for System 2, I took r to be 6i + 4j + 6k. I then set up the cross product box, with the F' row blank, and tried finding F' with the known answer of M' = 40i - 80j + 120k, however it is practically impossible to solve for F' that way and something tells me that's not the right way to try to solve it anyway. Also, something tells me that I didn't solve for M in the first part correctly either.

Last edited by a moderator:
RKOwens4: Hint 1: Ensure you copied the numbers given in the problem statement correctly in your calculations. Hint 2: If F' is not identical to F, would the system be subjected to different forces?

Sorry but I'm really not getting anything helpful from that. Of course it would be subjected to different forces, I just don't know how to calculate F' or M.

Come on, guys. EIGHTY-FIVE views and not one person can help me? EIGHTY-FIVE?

RKOwens4: What do you think it means to say "the two systems are equivalent"? Have you used that property?

## What is the definition of moment?

Moment is the measure of the turning effect of a force around a point or axis. It is a vector quantity and is calculated by multiplying the force by the perpendicular distance from the point/axis.

## What is the difference between a moment and a force?

A force is a push or pull applied to an object, while a moment is the measure of the rotational effect of a force. While a force can be applied in any direction, a moment is always applied around a fixed point or axis.

## How do you calculate the moment of a force?

The moment of a force can be calculated by multiplying the magnitude of the force by the perpendicular distance from the point/axis to the line of action of the force. This can also be expressed as the cross product of the force and the perpendicular distance vector.

## What is the unit of measurement for moment?

The SI unit of measurement for moment is Newton-meter (Nm) or Joule (J). In US customary units, the unit is pound-foot (lb-ft) or foot-pound (ft-lb).

## How does the moment of a force affect an object?

The moment of a force causes an object to rotate around a fixed point or axis. The magnitude of the moment determines the amount of rotation, while the direction of the moment determines the direction of rotation (clockwise or counterclockwise).

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