Question

calculating net forces
interpret each drawing of forces on the box. calculate and write the resulting net force
on the blank below the box (make sure to include the correct unit of measure). on the
next blank, write the word balanced or unbalanced and circle the arrow for the direction
of the resulting net force.
1
50 n
100 n
75 n
net force
2
545 n
732 n
732 n
545 n
net force
3
61 n
192 n
61 n
net force
4
1231 n
562 n
489 n
956 n
net force
5
653 n
352 n
1000 n
net force
6
8732 n
net force
7
577 n
2957 n
net force
8
83 n
96 n
net force

Explanation:

Step1: Analyze Forces on Box 1

Right force: \( 100\,\text{N} \), Left forces: \( 50\,\text{N} + 75\,\text{N} = 125\,\text{N} \). Net force: \( 100 - 125 = -25\,\text{N} \) (magnitude \( 25\,\text{N} \) left, but let's check direction sum. Wait, right is positive, left negative: \( 100 - 50 - 75 = -25 \), so net force \( 25\,\text{N} \) left? Wait, no: \( 100\) right, \( 50 + 75 = 125\) left. So \( 125 - 100 = 25\) left? Wait, net force is \( F_{\text{net}} = F_{\text{right}} - F_{\text{left}} \) (if right positive). So \( 100 - (50 + 75) = 100 - 125 = -25\,\text{N} \), meaning \( 25\,\text{N} \) to the left. But maybe the problem wants magnitude with direction? Wait, let's do each box:

Step1 (Box 1):

Right force: \( 100\,\text{N} \)
Left forces: \( 50\,\text{N} + 75\,\text{N} = 125\,\text{N} \)
Net force: \( 100 - 125 = -25\,\text{N} \) (or \( 25\,\text{N} \) left, but let's compute as \( F_{\text{net}} = \sum F \), right positive: \( 100 - 50 - 75 = -25\,\text{N} \), so magnitude \( 25\,\text{N} \), direction left. But maybe the answer is \( 25\,\text{N} \) left, but let's check the format. Wait, the problem says "net force" – maybe just the magnitude with sign or direction. Wait, let's do Box 2:

Step2 (Box 2):

Right forces: \( 545 + 732 = 1277\,\text{N} \)
Left forces: \( 732 + 545 = 1277\,\text{N} \)
Net force: \( 1277 - 1277 = 0\,\text{N} \), balanced.

Step3 (Box 3):

Right forces: \( 61 + 192 = 253\,\text{N} \)
Left force: \( 61\,\text{N} \)
Net force: \( 253 - 61 = 192\,\text{N} \) right? Wait, no: right forces \( 61 + 192 = 253 \), left force \( 61 \). So \( 253 - 61 = 192\,\text{N} \) right.

Step4 (Box 4):

Right forces: \( 1231 + 562 = 1793\,\text{N} \)
Left forces: \( 489 + 956 = 1445\,\text{N} \)
Net force: \( 1793 - 1445 = 348\,\text{N} \) right.

Step5 (Box 5):

Right forces: \( 653 + 352 = 1005\,\text{N} \)
Left force: \( 1000\,\text{N} \)
Net force: \( 1005 - 1000 = 5\,\text{N} \) right.

Step6 (Box 6):

Right force: \( 8732\,\text{N} \), left force: \( 0\,\text{N} \)
Net force: \( 8732\,\text{N} \) right.

Step7 (Box 7):

Right force: \( 577\,\text{N} \), left force: \( 2957\,\text{N} \)
Net force: \( 577 - 2957 = -2380\,\text{N} \) (or \( 2380\,\text{N} \) left).

Step8 (Box 8):

Right force: \( 83\,\text{N} \), left force: \( 96\,\text{N} \)
Net force: \( 83 - 96 = -13\,\text{N} \) (or \( 13\,\text{N} \) left).

Wait, let's recheck Box 1:
Right: \( 100\,\text{N} \)
Left: \( 50 + 75 = 125\,\text{N} \)
Net: \( 100 - 125 = -25\,\text{N} \) → \( 25\,\text{N} \) left.

Box 2:
Right: \( 545 + 732 = 1277\)
Left: \( 732 + 545 = 1277\)
Net: \( 0\,\text{N} \), balanced.

Box 3:
Right: \( 61 + 192 = 253\)
Left: \( 61\)
Net: \( 253 - 61 = 192\,\text{N} \) right.

Box 4:
Right: \( 1231 + 562 = 1793\)
Left: \( 489 + 956 = 1445\)
Net: \( 1793 - 1445 = 348\,\text{N} \) right.

Box 5:
Right: \( 653 + 352 = 1005\)
Left: \( 1000\)
Net: \( 1005 - 1000 = 5\,\text{N} \) right.

Box 6:
Right: \( 8732\), left: \( 0\)
Net: \( 8732\,\text{N} \) right.

Box 7:
Right: \( 577\), left: \( 2957\)
Net: \( 577 - 2957 = -2380\,\text{N} \) → \( 2380\,\text{N} \) left.

Box 8:
Right: \( 83\), left: \( 96\)
Net: \( 83 - 96 = -13\,\text{N} \) → \( 13\,\text{N} \) left.

Now, let's present each net force:

1. \( 25\,\text{N} \) left (or \( -25\,\text{N} \), but maybe magnitude with direction: \( 25\,\text{N} \) left)
2. \( 0\,\text{N} \) (balanced)
3. \( 192\,\text{N} \) right
4. \( 348\,\text{N} \) right
5. \( 5\,\text{N} \) right
6. \( 8732\,\text{N} \) right
7. \( 2380\,\text{N} \) left
8. \( 13\,\text{N} \) left

But let's confirm the calculation for Box 1 again: \( 100 - 50 - 75 = -25 \), so net force \( 25\,\text{N} \) to the left (or \( 25\,\text{N} \) left, magnitude \( 25\,\text{N} \), direction left).

Answer:

1. Net Force: \( \boldsymbol{25\,\text{N}} \) (left, or \( -25\,\text{N} \))
2. Net Force: \( \boldsymbol{0\,\text{N}} \) (balanced)
3. Net Force: \( \boldsymbol{192\,\text{N}} \) (right)
4. Net Force: \( \boldsymbol{348\,\text{N}} \) (right)
5. Net Force: \( \boldsymbol{5\,\text{N}} \) (right)
6. Net Force: \( \boldsymbol{8732\,\text{N}} \) (right)
7. Net Force: \( \boldsymbol{2380\,\text{N}} \) (left)
8. Net Force: \( \boldsymbol{13\,\text{N}} \) (left)

(Note: Directions are inferred from the sign; positive for right, negative for left. Magnitudes are as calculated.)