# Work and force problem with vectors

• J-dizzal
In summary, the machine applied a constant force of 10.9, 13.25, and 9.94 N to a 4.0 kg package over the course of 15 seconds. The work done by the force was 10.9 N, the average power of the force was 5.0 W.
J-dizzal

## Homework Statement

A machine carries a 4.0 kg package from an initial position of di=0.6m##\hat i## + 0.7m##\hat j## + 0.26m##\hat k## at t = 0 to a final position of df= 11.5m##\hat i## + 14.0m##\hat j## + 10.2m##\hat k## at t = 15.0 s. The constant force applied by the machine on the package is F= 10.9N##\hat i## + 13.25N##\hat j## + 9.94N##\hat k##. For that displacement, find (a) the work done on the package by the machine's force and (b) the average power of the machine's force on the package.

w=Fd

## The Attempt at a Solution

im attempting to use the dot product here to get work but not working, i don't know why[/B]

Quick question: should you have a vector as the result of the dot product?

Scott Redmond said:
Quick question: should you have a vector as the result of the dot product?
never

Scott Redmond said:
Quick question: should you have a vector as the result of the dot product?
thanks, i have been doing that lately i don't know why, i must stop doing that with the dot product.

Scott Redmond
Is the j component of the initial position 0.7m or 0.75m? (You said 0.7 in the OP but I think it's a typo.)

Also what is the force supposed to be? Your OP says <10.9, 13.25, 9.94>N but your work treats the force as <5, 5, 7>N

J-dizzal
Nathanael said:
Is the j component of the initial position 0.7m or 0.75m? (You said 0.7 in the OP but I think it's a typo.)

Also what is the force supposed to be? Your OP says <10.9, 13.25, 9.94>N but your work treats the force as <5, 5, 7>N

yes your right its 0.75j for initial pos.
the force is supposed to be (5,5,7)

i made a few typos on the OP sorry Nathanael.

Ok, your only mistake is miscalculating the dot product. ##\vec a\cdot \vec b=a_xb_x+a_yb_y+a_zb_z##

J-dizzal said:
thanks, i have been doing that lately i don't know why, i must stop doing that with the dot product.

Ha ha.. We all do stuff like that sometimes, and it's much better to do that here than on the exam!

## 1. How do you calculate the net force in a work and force problem with vectors?

The net force in a work and force problem with vectors can be calculated by finding the sum of all the forces acting on an object. This includes both the magnitude and direction of each force.

## 2. What is the difference between a scalar and a vector quantity?

A scalar quantity only has magnitude, while a vector quantity has both magnitude and direction. In a work and force problem, the magnitude of a force would be a scalar quantity, while the direction would be a vector quantity.

## 3. Can you give an example of a work and force problem with vectors?

Sure! Imagine a person pushing a box across a flat surface. The person applies a force of 50 newtons at an angle of 30 degrees above the horizontal. The box has a weight of 100 newtons acting straight down. To calculate the net force on the box, both the magnitude and direction of each force would be taken into account.

## 4. How do you determine if an object is in equilibrium in a work and force problem with vectors?

An object is in equilibrium if the net force acting on it is equal to zero. In other words, the forces are balanced and there is no acceleration in any direction. In a work and force problem, this can be determined by calculating the net force and seeing if it is equal to zero.

## 5. What is the relationship between work and force in a work and force problem with vectors?

Work is defined as the force applied to an object multiplied by the distance the object moves in the direction of the force. Therefore, in a work and force problem, the work done on an object would be equal to the magnitude of the force multiplied by the displacement of the object in the direction of the force.

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