Certainly! Let's address each problem step by step.
### Problem 3:
Question: A truck is subjected to a net force of 5000 N and it accelerates at 2 m/s². What is the mass of the truck?
Solution:
1. Identify the given values:
- Net force on the truck, [tex]\( F_{\text{truck}} = 5000 \)[/tex] N
- Acceleration of the truck, [tex]\( a_{\text{truck}} = 2 \)[/tex] m/s²
2. Recall Newton's Second Law:
Newton's Second Law states that [tex]\( F = m \cdot a \)[/tex], where [tex]\( F \)[/tex] is the force, [tex]\( m \)[/tex] is the mass, and [tex]\( a \)[/tex] is the acceleration.
3. Rearrange the formula to solve for mass:
[tex]\( m = \frac{F}{a} \)[/tex]
4. Substitute the given values into the equation:
[tex]\[
m_{\text{truck}} = \frac{F_{\text{truck}}}{a_{\text{truck}}} = \frac{5000 \, \text{N}}{2 \, \text{m/s}^2}
\][/tex]
5. Perform the division:
[tex]\[
m_{\text{truck}} = 2500 \, \text{kg}
\][/tex]
So, the mass of the truck is 2500 kg.
### Problem 4:
Question: An object experiences an acceleration of 8 m/s² when a force of 96 N is applied. Determine the mass of the object.
Solution:
1. Identify the given values:
- Force on the object, [tex]\( F_{\text{object}} = 96 \)[/tex] N
- Acceleration of the object, [tex]\( a_{\text{object}} = 8 \)[/tex] m/s²
2. Recall Newton's Second Law:
Newton's Second Law states that [tex]\( F = m \cdot a \)[/tex], where [tex]\( F \)[/tex] is the force, [tex]\( m \)[/tex] is the mass, and [tex]\( a \)[/tex] is the acceleration.
3. Rearrange the formula to solve for mass:
[tex]\( m = \frac{F}{a} \)[/tex]
4. Substitute the given values into the equation:
[tex]\[
m_{\text{object}} = \frac{F_{\text{object}}}{a_{\text{object}}} = \frac{96 \, \text{N}}{8 \, \text{m/s}^2}
\][/tex]
5. Perform the division:
[tex]\[
m_{\text{object}} = 12 \, \text{kg}
\][/tex]
So, the mass of the object is 12 kg.
### Summary:
- The mass of the truck is 2500 kg.
- The mass of the object is 12 kg.
