Here are the step-by-step solutions for each problem on the worksheet.
1. Wagon and Dog
*
Formula: $F = m \times a$
*
Given: Mass ($m$) = 45 kg, Acceleration ($a$) = 0.85 m/s²
*
Calculation: $45 \times 0.85 = 38.25$
*
Answer: 38.25 N
2. Car Acceleration
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Formula: $F = m \times a$
*
Given: Mass ($m$) = 1650 kg, Acceleration ($a$) = 4.0 m/s²
*
Calculation: $1650 \times 4 = 6600$
*
Answer: 6600 N
3. Runner's Acceleration
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Formula: $a = \frac{F}{m}$
*
Given: Force ($F$) = 59 N, Mass ($m$) = 68 kg
*
Calculation: $59 \div 68 \approx 0.8676$
*
Answer: 0.87 m/s² (rounded)
4. Crate on Ice
*
Formula: $m = \frac{F}{a}$
*
Given: Force ($F$) = 47 N, Acceleration ($a$) = 0.08 m/s²
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Calculation: $47 \div 0.08 = 587.5$
*
Answer: 587.5 kg
5. Women Pushing Car
*
Formula: $m = \frac{F_{\text{total}}}{a}$
*
Step 1 (Total Force): 3 women $\times$ 425 N each = 1275 N
*
Given: Total Force ($F$) = 1275 N, Acceleration ($a$) = 0.85 m/s²
*
Calculation: $1275 \div 0.85 = 1500$
*
Answer: 1500 kg
6. Sports Car Mass
*
Formula: $m = \frac{F}{a}$
*
Step 1 (Find Acceleration): Acceleration is change in speed divided by time.
* Change in speed = 27 m/s - 0 m/s = 27 m/s
* Time = 6.3 seconds
* $a = \frac{27}{6.3} \approx 4.2857 \text{ m/s}^2$
*
Given: Force ($F$) = 4106 N
*
Calculation: $m = \frac{4106}{4.2857} \approx 958.06$
*
Answer: 958 kg (rounded)
7. Book on Table
*
Part a) Net Force
*
Concept: Net force is the applied force minus the friction force.
*
Calculation: $2.8 \text{ N} - 2.6 \text{ N} = 0.2 \text{ N}$
*
Answer: 0.2 N
*
Part b) Mass of the Book
*
Formula: $m = \frac{F_{\text{net}}}{a}$
*
Given: Net Force ($F$) = 0.2 N, Acceleration ($a$) = 0.11 m/s²
*
Calculation: $0.2 \div 0.11 \approx 1.818$
*
Answer: 1.82 kg (rounded)
Final Answer:
1. 38.25 N
2. 6600 N
3. 0.87 m/s²
4. 587.5 kg
5. 1500 kg
6. 958 kg
7. a) 0.2 N, b) 1.82 kg
Parent Tip: Review the logic above to help your child master the concept of newton s second law problems worksheet.
