Step-by-Step Solution:
Problem 1:
*
Given: Mass ($m$) = $45\text{ kg}$, Acceleration ($a$) = $0.85\text{ m/s}^2$
*
Formula: $F = m \times a$
*
Calculation: $F = 45 \times 0.85 = 38.25\text{ N}$
Problem 2:
*
Given: Mass ($m$) = $1650\text{ kg}$, Acceleration ($a$) = $4.0\text{ m/s}^2$
*
Formula: $F = m \times a$
*
Calculation: $F = 1650 \times 4.0 = 6600\text{ N}$
Problem 3:
*
Given: Mass ($m$) = $68\text{ kg}$, Force ($F$) = $59\text{ N}$
*
Formula: $a = F / m$
*
Calculation: $a = 59 / 68 \approx 0.8676...$
*
Rounding: $\approx 0.87\text{ m/s}^2$ (to 2 significant figures)
Problem 4:
*
Given: Force ($F$) = $47\text{ N}$, Acceleration ($a$) = $0.08\text{ m/s}^2$
*
Formula: $m = F / a$
*
Calculation: $m = 47 / 0.08 = 587.5\text{ kg}$
Problem 5:
*
Given: 3 women push with $425\text{ N}$ each. Total Force ($F$) = $3 \times 425 = 1275\text{ N}$. Acceleration ($a$) = $0.85\text{ m/s}^2$
*
Formula: $m = F / a$
*
Calculation: $m = 1275 / 0.85 = 1500\text{ kg}$
Problem 6:
*
Given: Initial velocity = $0$, Final velocity = $27\text{ m/s}$, Time ($t$) = $6.3\text{ s}$, Force ($F$) = $4106\text{ N}$
*
Step 1 (Find Acceleration): $a = (v_f - v_i) / t = (27 - 0) / 6.3 \approx 4.2857\text{ m/s}^2$
*
Step 2 (Find Mass): $m = F / a$
*
Calculation: $m = 4106 / 4.2857 \approx 958.06\text{ kg}$
*
Rounding: $\approx 958\text{ kg}$
Problem 7:
*
Part a) Net Force:
* Applied Force = $2.8\text{ N}$, Frictional Force = $2.6\text{ N}$
* Formula: $F_{net} = F_{applied} - F_{friction}$
* Calculation: $F_{net} = 2.8 - 2.6 = 0.2\text{ N}$
*
Part b) Mass of Book:
* Given: $F_{net} = 0.2\text{ N}$, Acceleration ($a$) = $0.11\text{ m/s}^2$
* Formula: $m = F_{net} / a$
* Calculation: $m = 0.2 / 0.11 \approx 1.8181...$
* Rounding: $\approx 1.82\text{ kg}$
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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 newtons second law worksheet.
