Worksheet on Newton's Second Law calculations with problems involving force, mass, and acceleration.

Problem: Solving Newton's Second Law Calculations

We will solve each problem step by step using Newton's Second Law of Motion, which is given by the equation:

\[
F = m \cdot a
\]

Where:
- \( F \) is the force (in Newtons, N),
- \( m \) is the mass (in kilograms, kg),
- \( a \) is the acceleration (in meters per second squared, m/s²).

---

Problem 1:

Question: With what force will a car hit a telephone pole if the car has a mass of 4,000 kg and an acceleration of 2 m/s²?

#### Steps:
1. Identify the given values:
- Mass (\( m \)) = 4,000 kg
- Acceleration (\( a \)) = 2 m/s²

2. Use Newton's Second Law:
\[
F = m \cdot a
\]

3. Substitute the values:
\[
F = 4,000 \, \text{kg} \cdot 2 \, \text{m/s}^2
\]

4. Calculate:
\[
F = 8,000 \, \text{N}
\]

#### Final Answer:
\[
\boxed{8000 \, \text{N}}
\]

---

Problem 2:

Question: What force would be needed to make a 5 kg skateboard accelerate down a hill with an acceleration of 3 m/s²?

#### Steps:
1. Identify the given values:
- Mass (\( m \)) = 5 kg
- Acceleration (\( a \)) = 3 m/s²

2. Use Newton's Second Law:
\[
F = m \cdot a
\]

3. Substitute the values:
\[
F = 5 \, \text{kg} \cdot 3 \, \text{m/s}^2
\]

4. Calculate:
\[
F = 15 \, \text{N}
\]

#### Final Answer:
\[
\boxed{15 \, \text{N}}
\]

---

Problem 3:

Question: What would be the mass of a vehicle if it is accelerating at a rate of 5 m/s² and hits a parked car with a force of 15,000 N?

#### Steps:
1. Identify the given values:
- Force (\( F \)) = 15,000 N
- Acceleration (\( a \)) = 5 m/s²

2. Rearrange Newton's Second Law to solve for mass:
\[
m = \frac{F}{a}
\]

3. Substitute the values:
\[
m = \frac{15,000 \, \text{N}}{5 \, \text{m/s}^2}
\]

4. Calculate:
\[
m = 3,000 \, \text{kg}
\]

#### Final Answer:
\[
\boxed{3000 \, \text{kg}}
\]

---

Problem 4:

Question: What is the acceleration of a football with a mass of 0.40 kg and hits the receiver’s hands with a force of 25 N?

#### Steps:
1. Identify the given values:
- Force (\( F \)) = 25 N
- Mass (\( m \)) = 0.40 kg

2. Rearrange Newton's Second Law to solve for acceleration:
\[
a = \frac{F}{m}
\]

3. Substitute the values:
\[
a = \frac{25 \, \text{N}}{0.40 \, \text{kg}}
\]

4. Calculate:
\[
a = 62.5 \, \text{m/s}^2
\]

#### Final Answer:
\[
\boxed{62.5 \, \text{m/s}^2}
\]

---

Problem 5:

Question: How much does a refrigerator weigh if it has a mass of 131 kg? (Hint: you need to recall the acceleration due to gravity)

#### Steps:
1. Identify the given values:
- Mass (\( m \)) = 131 kg
- Acceleration due to gravity (\( g \)) = 9.8 m/s²

2. The weight of an object is the force due to gravity, which can be calculated using:
\[
W = m \cdot g
\]

3. Substitute the values:
\[
W = 131 \, \text{kg} \cdot 9.8 \, \text{m/s}^2
\]

4. Calculate:
\[
W = 1,283.8 \, \text{N}
\]

#### Final Answer:
\[
\boxed{1283.8 \, \text{N}}
\]

---

Problem 6:

Question: What would be the mass of an asteroid falling from the sky if it hits the ground with a force of 147 N? (Hint: think about the acceleration all falling objects have)

#### Steps:
1. Identify the given values:
- Force (\( F \)) = 147 N
- Acceleration due to gravity (\( g \)) = 9.8 m/s²

2. Use Newton's Second Law to solve for mass:
\[
m = \frac{F}{a}
\]
Here, \( a = g = 9.8 \, \text{m/s}^2 \).

3. Substitute the values:
\[
m = \frac{147 \, \text{N}}{9.8 \, \text{m/s}^2}
\]

4. Calculate:
\[
m = 15 \, \text{kg}
\]

#### Final Answer:
\[
\boxed{15 \, \text{kg}}
\]

---

Problem 7:

Question: What is the acceleration of the stack of books below if the total mass of the books is 1.5 kg? (Hint: you will need to calculate the NET Force)

#### Steps:
1. Identify the given values:
- Total mass (\( m \)) = 1.5 kg
- Forces acting on the books:
- Rightward force (\( F_{\text{right}} \)) = 3 N
- Leftward force (\( F_{\text{left}} \)) = 2 N + 1 N = 3 N

2. Calculate the net force:
\[
F_{\text{net}} = F_{\text{right}} - F_{\text{left}}
\]
\[
F_{\text{net}} = 3 \, \text{N} - 3 \, \text{N} = 0 \, \text{N}
\]

3. Use Newton's Second Law to solve for acceleration:
\[
a = \frac{F_{\text{net}}}{m}
\]
\[
a = \frac{0 \, \text{N}}{1.5 \, \text{kg}} = 0 \, \text{m/s}^2
\]

#### Final Answer:
\[
\boxed{0 \, \text{m/s}^2}
\]

---

Final Answers:

1. \(\boxed{8000 \, \text{N}}\)
2. \(\boxed{15 \, \text{N}}\)
3. \(\boxed{3000 \, \text{kg}}\)
4. \(\boxed{62.5 \, \text{m/s}^2}\)
5. \(\boxed{1283.8 \, \text{N}}\)
6. \(\boxed{15 \, \text{kg}}\)
7. \(\boxed{0 \, \text{m/s}^2}\)