3 boys pulling at the end of 3 ropes held together on a knot. one boy pulls with a force of 20 Newton eastward, while a 2nd boy pulls with the same magnitude force northward. in what direction and with what force must a 3rd boy be pulling if his pull of the knot is to be equal and opposite to the combine pulls of the other 2 boys.

Question

3 boys pulling at the end of 3 ropes held together on a knot. one boy pulls with a force of 20 Newton eastward, while a 2nd boy pulls with the same magnitude force northward. in what direction and with what force must a 3rd boy be pulling if his pull of the knot is to be equal and opposite to the combine pulls of the other 2 boys.

Answer 1

The three forces must have a resultant of zero.

The third force must be 20*sqrt2 Newtons, in a SW direction.

Answer 2

F1 + F2 = 20N.[0o] * 20N.[90o].

F1+F2 = 20 + 20i = 28.3N.[45o].
F3 must be equal to -(F1+F2).

F3 = -28.3[45o] = 28.3[45+180] = 28.3[225] = 28.3N.[45o] S. of W.

Answer 3

To find the direction and magnitude of the force the third boy must exert to balance the combined forces of the first two boys, we can break down the forces into their components.

1. The first boy pulls with a force of 20 Newton eastward.
2. The second boy pulls with the same magnitude force northward.

Let's break down the forces into their x and y components:

1. The first boy's force can be split into an x-component and a y-component:

- The x-component is 20 Newton in the positive east direction.
- The y-component is 0 Newton since there is no force in the north or south direction.

2. The second boy's force can also be split into an x-component and a y-component:

- The x-component is 0 Newton since there is no force in the east or west direction.
- The y-component is 20 Newton in the positive north direction.

To balance these forces, the third boy's force must have equal magnitudes but opposite directions:

- The x-component of the third boy's force should be -20 Newton to balance the first boy's force.
- The y-component of the third boy's force should be -20 Newton to balance the second boy's force.

Now, let's find the resultant force by combining the x and y components:

- Resultant x-component: 20 Newton - 20 Newton = 0 Newton
- Resultant y-component: 0 Newton + (-20 Newton) = -20 Newton

The resultant force has no magnitude in the x-direction (east-west) and a magnitude of 20 Newton in the negative y-direction (south). Therefore, the third boy must pull with a force of 20 Newton in the south direction to balance the combined forces of the other two boys.

The three forces must have a resultant of zero.

40

F1 + F2 = 20N.[0o] * 20N.[90o].

To find the direction and magnitude of the force the third boy must exert to balance the combined forces of the first two boys, we can break down the forces into their components.