Sure, let’s break down the questions one by one:
### Question 9
Whenever an object exerts a force on another object, the second object exerts a force of the same magnitude on the first object, but in the opposite direction.
- True for all objects interacting
- True for only objects at rest
- False because these would cancel
- False because two forces cannot happen
Answer: The correct answer is the first option, "True for all objects interacting." This statement is a direct application of Newton's Third Law of Motion, which states that for every action, there is an equal and opposite reaction. Therefore, whenever an object exerts a force on another object, the second object will exert a force of the same magnitude but in the opposite direction.
### Question 10
A force of 265.1 N acts on an object to produce an acceleration of 12.52 m/s². What is the mass of the object?
To solve this, we use Newton's Second Law of Motion, which states that [tex]\( F = m \times a \)[/tex], where:
- [tex]\( F \)[/tex] is the force applied,
- [tex]\( m \)[/tex] is the mass of the object,
- [tex]\( a \)[/tex] is the acceleration.
We can rearrange the formula to solve for mass ([tex]\( m \)[/tex]):
[tex]\[ m = \frac{F}{a} \][/tex]
Plugging the given values into the formula:
- Force ([tex]\( F \)[/tex]) = 265.1 N
- Acceleration ([tex]\( a \)[/tex]) = 12.52 m/s²
So:
[tex]\[ m = \frac{265.1 \, \text{N}}{12.52 \, \text{m/s}^2} \][/tex]
Doing the division:
[tex]\[ m \approx 21.1741214057508 \, \text{kg} \][/tex]
Therefore, the mass of the object is approximately 21.174 kg.
I hope these detailed solutions help clarify the concepts for you!
