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Answer :
Let's solve the problem step-by-step to find the kinetic energy of the object.
1. Identify the given information:
- Weight ([tex]\(W\)[/tex]) of the object: 19.6 N
- Velocity ([tex]\(v\)[/tex]) of the object: 10 m/s
2. Find the mass of the object:
- We know that weight can be calculated using the formula:
[tex]\[
W = m \cdot g
\][/tex]
where [tex]\(m\)[/tex] is the mass and [tex]\(g\)[/tex] is the acceleration due to gravity (9.8 m/s² on Earth).
- Rearrange the formula to solve for mass ([tex]\(m\)[/tex]):
[tex]\[
m = \frac{W}{g} = \frac{19.6 \, \text{N}}{9.8 \, \text{m/s}^2} = 2.0 \, \text{kg}
\][/tex]
3. Calculate the kinetic energy ([tex]\(E_c\)[/tex]):
- The kinetic energy is given by the formula:
[tex]\[
E_c = \frac{1}{2} \cdot m \cdot v^2
\][/tex]
where [tex]\(m\)[/tex] is the mass and [tex]\(v\)[/tex] is the velocity.
- Substitute the known values:
[tex]\[
E_c = \frac{1}{2} \cdot 2.0 \, \text{kg} \cdot (10 \, \text{m/s})^2
\][/tex]
[tex]\[
E_c = \frac{1}{2} \cdot 2.0 \cdot 100
\][/tex]
[tex]\[
E_c = 1.0 \cdot 100 = 100.0 \, \text{J}
\][/tex]
So, the mass of the object is 2.0 kg and its kinetic energy is 100.0 Joules.
1. Identify the given information:
- Weight ([tex]\(W\)[/tex]) of the object: 19.6 N
- Velocity ([tex]\(v\)[/tex]) of the object: 10 m/s
2. Find the mass of the object:
- We know that weight can be calculated using the formula:
[tex]\[
W = m \cdot g
\][/tex]
where [tex]\(m\)[/tex] is the mass and [tex]\(g\)[/tex] is the acceleration due to gravity (9.8 m/s² on Earth).
- Rearrange the formula to solve for mass ([tex]\(m\)[/tex]):
[tex]\[
m = \frac{W}{g} = \frac{19.6 \, \text{N}}{9.8 \, \text{m/s}^2} = 2.0 \, \text{kg}
\][/tex]
3. Calculate the kinetic energy ([tex]\(E_c\)[/tex]):
- The kinetic energy is given by the formula:
[tex]\[
E_c = \frac{1}{2} \cdot m \cdot v^2
\][/tex]
where [tex]\(m\)[/tex] is the mass and [tex]\(v\)[/tex] is the velocity.
- Substitute the known values:
[tex]\[
E_c = \frac{1}{2} \cdot 2.0 \, \text{kg} \cdot (10 \, \text{m/s})^2
\][/tex]
[tex]\[
E_c = \frac{1}{2} \cdot 2.0 \cdot 100
\][/tex]
[tex]\[
E_c = 1.0 \cdot 100 = 100.0 \, \text{J}
\][/tex]
So, the mass of the object is 2.0 kg and its kinetic energy is 100.0 Joules.
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