Answer :
To solve this problem, we have to determine the weight of a crate in different units, given that it's acted upon by a net force and has a certain acceleration.
Let's break it down:
1. Identify the Given Information:
- Net force acting on the crate: 100 N (Newtons)
- Acceleration of the crate: [tex]\(4.0 \, \text{m/s}^2\)[/tex]
2. Determine the Mass of the Crate:
- We can use Newton's second law, which states that Force ([tex]\(F\)[/tex]) is the product of mass ([tex]\(m\)[/tex]) and acceleration ([tex]\(a\)[/tex]):
[tex]\[ F = m \cdot a \][/tex]
- Rearrange this formula to solve for mass ([tex]\(m\)[/tex]):
[tex]\[ m = \frac{F}{a} \][/tex]
- Plug in the given values:
[tex]\[ m = \frac{100 \, \text{N}}{4.0 \, \text{m/s}^2} = 25 \, \text{kg} \][/tex]
3. Calculate the Weight in Newtons:
- Weight can be calculated using the formula:
[tex]\[ \text{Weight} = \text{mass} \times g \][/tex]
- Where [tex]\(g\)[/tex] (acceleration due to gravity) is approximately [tex]\(9.8 \, \text{m/s}^2\)[/tex].
- Substitute the mass we found:
[tex]\[ \text{Weight} = 25 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 245 \, \text{N} \][/tex]
4. Convert the Weight to Pounds:
- To convert from Newtons to pounds, use the conversion factor: [tex]\(1 \, \text{lb} = 4.44822 \, \text{N}\)[/tex].
- Calculate the weight in pounds:
[tex]\[ \text{Weight in pounds} = \frac{245 \, \text{N}}{4.44822 \, \text{N/lb}} \approx 55.08 \, \text{lb} \][/tex]
Therefore, for the options given in the question, the correct choices would be:
- Mass of the crate: 25 kg
- Weight of the crate: 245 N
Those are the values that match the scenario described in the problem.
Let's break it down:
1. Identify the Given Information:
- Net force acting on the crate: 100 N (Newtons)
- Acceleration of the crate: [tex]\(4.0 \, \text{m/s}^2\)[/tex]
2. Determine the Mass of the Crate:
- We can use Newton's second law, which states that Force ([tex]\(F\)[/tex]) is the product of mass ([tex]\(m\)[/tex]) and acceleration ([tex]\(a\)[/tex]):
[tex]\[ F = m \cdot a \][/tex]
- Rearrange this formula to solve for mass ([tex]\(m\)[/tex]):
[tex]\[ m = \frac{F}{a} \][/tex]
- Plug in the given values:
[tex]\[ m = \frac{100 \, \text{N}}{4.0 \, \text{m/s}^2} = 25 \, \text{kg} \][/tex]
3. Calculate the Weight in Newtons:
- Weight can be calculated using the formula:
[tex]\[ \text{Weight} = \text{mass} \times g \][/tex]
- Where [tex]\(g\)[/tex] (acceleration due to gravity) is approximately [tex]\(9.8 \, \text{m/s}^2\)[/tex].
- Substitute the mass we found:
[tex]\[ \text{Weight} = 25 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 245 \, \text{N} \][/tex]
4. Convert the Weight to Pounds:
- To convert from Newtons to pounds, use the conversion factor: [tex]\(1 \, \text{lb} = 4.44822 \, \text{N}\)[/tex].
- Calculate the weight in pounds:
[tex]\[ \text{Weight in pounds} = \frac{245 \, \text{N}}{4.44822 \, \text{N/lb}} \approx 55.08 \, \text{lb} \][/tex]
Therefore, for the options given in the question, the correct choices would be:
- Mass of the crate: 25 kg
- Weight of the crate: 245 N
Those are the values that match the scenario described in the problem.
