# Calculating a value of force using vectors?

• xllx
In summary, to find the value of p in this problem, you can add the i components of the forces and divide by the corresponding i component of the resultant force. This will give you k, which can then be used to find the j component of the resultant force, which will be equal to 96+j. From there, you can solve for p by subtracting 96 from both sides and getting p = -84.9.
xllx
A box is being pulled with a resultant force of (33i+96j)N by 3 people. Another person starts pulling the box with a force of (100i+pj)N. With all 4 people pulling the box, it moves in the direction of (12i +j). I need to work out the value of p.

For this would I add 100 and 33, and then divide by 12 to find the proportions of i. And then with that times it by the 1j to get what j is.
E.g.
100+33=133
133/12=11.1

1x11.1=11.1
96+j=11.1
j= -84.9

Or is this totally wrong?

Any help at all would be greatly appreciated. Many Thanks!

Correct!
Might be easier to follow if you put
33i+96j + 100i+pj = k(12i+j)
Separate the i part from the j part. Use the i part to evaluate k, then use it in the j part to find p.

xllx said:
A box is being pulled with a resultant force of (33i+96j)N by 3 people. Another person starts pulling the box with a force of (100i+pj)N. With all 4 people pulling the box, it moves in the direction of (12i +j). I need to work out the value of p.

For this would I add 100 and 33, and then divide by 12 to find the proportions of i. And then with that times it by the 1j to get what j is.
E.g.
100+33=133
133/12=11.1

1x11.1=11.1
96+j=11.1
j= -84.9

Or is this totally wrong?

Any help at all would be greatly appreciated. Many Thanks!

That looks correct. Of course you are finding p and not j, but the method looks ok.

## 1. What is a vector and how is it used to calculate force?

A vector is a mathematical representation of a physical quantity that has both magnitude and direction. To calculate force using vectors, the vector representing the force acting on an object is multiplied by the vector representing the object's displacement.

## 2. How do you determine the magnitude and direction of a force using vectors?

The magnitude of a force can be determined by finding the length of the vector representing the force. The direction of the force can be determined by finding the angle between the force vector and a known reference direction, such as the positive x-axis.

## 3. Can vectors be added or subtracted to calculate force?

Yes, vectors can be added or subtracted to calculate force. This is done by using vector addition or subtraction rules, which involve breaking down the vectors into their x and y components and then adding or subtracting them separately.

## 4. What units are used to measure force calculated using vectors?

The units used to measure force calculated using vectors are typically Newtons (N) or pounds (lbs).

## 5. What are some common applications of calculating force using vectors in science?

Calculating force using vectors is commonly used in physics and engineering to analyze the motion and interactions of objects. It is also used in fields such as geology and meteorology to study the effects of forces on natural systems.

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