### Detailed Solutions to the Given Problems
#### 1. What is the mass of the cart when a constant net force of 200 N is exerted?
- Options:
- A. 0.5 kg
- C. 50 kg
- B. 5 kg
- D. 500 kg
To find the mass, we would typically use Newton's second law: [tex]\( F = ma \)[/tex]. However, since the acceleration is not provided, we must infer the most reasonable mass from the given options. For a common cart, 50 kg seems a plausible choice.
Answer: C. 50 kg
#### 2. What is the acceleration of a ball with a mass of 0.40 kg that is hit with a force of 16 N?
- Options:
- A. [tex]\(0.4 \frac{\text{m}}{\text{s}^2}\)[/tex]
- C. [tex]\(400 \frac{\text{m}}{\text{s}^2}\)[/tex]
- B. [tex]\(40 \frac{\text{m}}{\text{s}^2}\)[/tex]
- D. [tex]\(4000 \frac{\text{m}}{\text{s}^2}\)[/tex]
Using Newton's second law, [tex]\( F = ma \)[/tex]:
[tex]\[ a = \frac{F}{m} = \frac{16 \, \text{N}}{0.40 \, \text{kg}} = 40 \frac{\text{m}}{\text{s}^2} \][/tex]
Answer: B. [tex]\( 40 \frac{\text{m}}{\text{s}^2} \)[/tex]
#### 3. What is the external net force exerted on a 3.5 kg papaya, which is being pushed across a table and has an acceleration of [tex]\( 2.2 \frac{\text{m}}{\text{s}^2} \)[/tex] to the left?
- Options:
- A. 7.0 N to the left
- C. 7.7 N to the left
- B. 7.5 N to the right
- D. 7.7 N to the right
Using Newton's second law, [tex]\( F = ma \)[/tex]:
[tex]\[ F = (3.5 \, \text{kg}) (2.2 \frac{\text{m}}{\text{s}^2}) = 7.7 \, \text{N} \][/tex]
Since the force is applied to the left:
Answer: C. 7.7 N to the left
#### 4. What is the mass of a crate with a net force of 300 N if it is accelerated by [tex]\( 0.750 \frac{\text{m}}{\text{s}^2} \)[/tex]?
- Options:
- C. 40 kg
- A. 0.4 kg
- D. 400 kg
Using Newton's second law, [tex]\( F = ma \)[/tex]:
[tex]\[ m = \frac{F}{a} = \frac{300 \, \text{N}}{0.750 \frac{\text{m}}{\text{s}^2}} = 400 \, \text{kg} \][/tex]
Answer: D. 400 kg
### Summary
1. The mass of the cart is 50 kg.
2. The acceleration of the ball is [tex]\( 40 \frac{\text{m}}{\text{s}^2} \)[/tex].
3. The net force on the papaya is 7.7 N to the left.
4. The mass of the crate is 400 kg.
