Question

thinking mathematically: out of balance?
a resting object will keep resting and a moving object will keep moving unless it encounters an unbalanced force. look at the boxes pictured in the card set below and observe the forces they are experiencing. (note that forces are measured in newtons n.) how will each box move—to the right, to the left, or will it stay in place? cut out the cards and sort them into the three categories listed. then circle the category that shows balanced forces.
box will move right
2
3
box will move left
5
6
box will stay in place
1
4
forces on boxes card set
1
75 n → □ ←75 n
2
20 n → □ ←75 n
3
40 n →
40 n → □ ←75 n
4
75 n → □ ←15 n
←30 n
←30 n
5
←40 n
←20 n □ →80 n
6
←40 n □ →25 n

Explanation:

Step1: Calculate net force for Card 1

Right force: $75\ \text{N}$, Left force: $75\ \text{N}$
Net force: $75 - 75 = 0\ \text{N}$

Step2: Calculate net force for Card 2

Right force: $20\ \text{N}$, Left force: $75\ \text{N}$
Net force: $20 - 75 = -55\ \text{N}$ (negative = left)

Step3: Calculate net force for Card 3

Right force: $40 + 40 = 80\ \text{N}$, Left force: $75\ \text{N}$
Net force: $80 - 75 = 5\ \text{N}$ (positive = right)

Step4: Calculate net force for Card 4

Right force: $75\ \text{N}$, Left force: $15 + 30 + 30 = 75\ \text{N}$
Net force: $75 - 75 = 0\ \text{N}$

Step5: Calculate net force for Card 5

Right force: $80\ \text{N}$, Left force: $40 + 20 = 60\ \text{N}$
Net force: $80 - 60 = 20\ \text{N}$ (positive = right)

Step6: Calculate net force for Card 6

Right force: $25\ \text{N}$, Left force: $40\ \text{N}$
Net force: $25 - 40 = -15\ \text{N}$ (negative = left)

Step7: Sort boxes by net force

• Right movement: positive net force
• Left movement: negative net force
• Stay in place: zero net force

Answer:

Box Will Move Right

Card 3, Card 5

Box Will Move Left

Card 2, Card 6

Box Will Stay in Place

Card 1, Card 4
Balanced forces category: Box Will Stay in Place