Problem Analysis and Solution
The worksheet is about calculating
net force acting on objects and determining whether the net force results in motion or no motion. Let's solve each problem step by step.
---
####
1. Net Force Calculation for Opposite Directions
-
Forces: Two forces of 5 N each acting in opposite directions.
-
Calculation:
\[
F_{\text{net}} = F_1 - F_2 = 5 \, \text{N} - 5 \, \text{N} = 0 \, \text{N}
\]
-
Result: The net force is \(0 \, \text{N}\), which means there is
no motion.
Answer: \( F_{\text{net}} = 0 \, \text{N} \)
---
####
2. Net Force Calculation for Same Direction
-
Forces: Two forces of 3 N and 5 N acting in the same direction.
-
Calculation:
\[
F_{\text{net}} = F_1 + F_2 = 3 \, \text{N} + 5 \, \text{N} = 8 \, \text{N}
\]
-
Result: The net force is \(8 \, \text{N}\), which means there is
motion.
Answer: \( F_{\text{net}} = 8 \, \text{N} \)
---
####
3. Which Team Will Push the Box Farther?
-
Team 1:
- Forces: Four forces of 5 N each acting in the same direction.
- Net Force:
\[
F_{\text{net, Team 1}} = 5 \, \text{N} + 5 \, \text{N} + 5 \, \text{N} + 5 \, \text{N} = 20 \, \text{N}
\]
-
Team 2:
- Forces: One force of 12 N acting in one direction and another force of 5 N acting in the opposite direction.
- Net Force:
\[
F_{\text{net, Team 2}} = 12 \, \text{N} - 5 \, \text{N} = 7 \, \text{N}
\]
-
Comparison:
- Team 1 has a net force of \(20 \, \text{N}\).
- Team 2 has a net force of \(7 \, \text{N}\).
- Therefore,
Team 1 will push the box farther.
Answer: Team 1 will push the box farther.
---
####
4. Net Force on the Shopping Cart
-
Forces:
- Applied force by Sally: \(20 \, \text{N}\) (forward).
- Frictional force: \(8 \, \text{N}\) (opposite to the applied force).
-
Calculation:
\[
F_{\text{net}} = F_{\text{applied}} - F_{\text{friction}} = 20 \, \text{N} - 8 \, \text{N} = 12 \, \text{N}
\]
-
Direction: The net force is in the direction of the applied force (forward).
Answer: \( F_{\text{net}} = 12 \, \text{N} \) (forward)
---
####
5. Net Force on the Rock
-
Forces:
- Jeff's force: \(85 \, \text{N}\) (uphill).
- Chris's force: \(60 \, \text{N}\) (uphill).
-
Calculation:
\[
F_{\text{net}} = F_{\text{Jeff}} + F_{\text{Chris}} = 85 \, \text{N} + 60 \, \text{N} = 145 \, \text{N}
\]
-
Direction: The net force is in the uphill direction.
Answer: \( F_{\text{net}} = 145 \, \text{N} \) (uphill)
---
Final Answers
1. \( \boxed{0 \, \text{N}} \)
2. \( \boxed{8 \, \text{N}} \)
3. Team 1 will push the box farther.
4. \( \boxed{12 \, \text{N}} \) (forward)
5. \( \boxed{145 \, \text{N}} \) (uphill)
Parent Tip: Review the logic above to help your child master the concept of net force worksheet with answers.
