Answer :
Sure! Let's work through the problem step by step to find out at what height the blender was placed.
We're given the following information:
- The mass of the blender is [tex]\(2.5\)[/tex] kg.
- The gravitational acceleration is [tex]\(9.8 \, \text{m/s}^2\)[/tex].
- The potential energy the blender has is [tex]\(70\)[/tex] joules.
We want to find the height at which the blender is placed. To do this, we'll use the formula for potential energy:
[tex]\[ \text{Potential Energy (PE)} = \text{mass} \times \text{gravity} \times \text{height} \][/tex]
This can be written as:
[tex]\[ PE = m \times g \times h \][/tex]
Where:
- [tex]\(PE\)[/tex] is the potential energy,
- [tex]\(m\)[/tex] is the mass,
- [tex]\(g\)[/tex] is the gravitational acceleration,
- [tex]\(h\)[/tex] is the height.
We need to solve for height ([tex]\(h\)[/tex]), so rearrange the formula to:
[tex]\[ h = \frac{PE}{m \times g} \][/tex]
Now, plug in the given values:
- The potential energy ([tex]\(PE\)[/tex]) is [tex]\(70\)[/tex] joules.
- The mass ([tex]\(m\)[/tex]) is [tex]\(2.5\)[/tex] kg.
- The gravitational acceleration ([tex]\(g\)[/tex]) is [tex]\(9.8 \, \text{m/s}^2\)[/tex].
[tex]\[ h = \frac{70}{2.5 \times 9.8} \][/tex]
After calculating, we find:
[tex]\[ h \approx 2.86 \, \text{meters} \][/tex]
So, the blender was placed at a height of approximately [tex]\(2.86\)[/tex] meters.
We're given the following information:
- The mass of the blender is [tex]\(2.5\)[/tex] kg.
- The gravitational acceleration is [tex]\(9.8 \, \text{m/s}^2\)[/tex].
- The potential energy the blender has is [tex]\(70\)[/tex] joules.
We want to find the height at which the blender is placed. To do this, we'll use the formula for potential energy:
[tex]\[ \text{Potential Energy (PE)} = \text{mass} \times \text{gravity} \times \text{height} \][/tex]
This can be written as:
[tex]\[ PE = m \times g \times h \][/tex]
Where:
- [tex]\(PE\)[/tex] is the potential energy,
- [tex]\(m\)[/tex] is the mass,
- [tex]\(g\)[/tex] is the gravitational acceleration,
- [tex]\(h\)[/tex] is the height.
We need to solve for height ([tex]\(h\)[/tex]), so rearrange the formula to:
[tex]\[ h = \frac{PE}{m \times g} \][/tex]
Now, plug in the given values:
- The potential energy ([tex]\(PE\)[/tex]) is [tex]\(70\)[/tex] joules.
- The mass ([tex]\(m\)[/tex]) is [tex]\(2.5\)[/tex] kg.
- The gravitational acceleration ([tex]\(g\)[/tex]) is [tex]\(9.8 \, \text{m/s}^2\)[/tex].
[tex]\[ h = \frac{70}{2.5 \times 9.8} \][/tex]
After calculating, we find:
[tex]\[ h \approx 2.86 \, \text{meters} \][/tex]
So, the blender was placed at a height of approximately [tex]\(2.86\)[/tex] meters.
