Sure! Let's go through the steps to determine the kinetic energy of the block when it reaches the bottom of the inclined plane.
### Step-by-Step Solution
1. Identify Given Data:
- Mass of the block [tex]\(m = 1.5\)[/tex] kg
- Angle of the inclined plane [tex]\(\theta = 15^\circ\)[/tex] (we won't need this directly since it slides without friction)
- Height from which the block starts [tex]\(h = 1\)[/tex] meter
- Acceleration due to gravity [tex]\(g = 9.8\)[/tex] m/s²
2. Calculate Potential Energy at the Top:
- Potential energy ([tex]\(PE\)[/tex]) is given by the formula:
[tex]\[
PE = m \cdot g \cdot h
\][/tex]
- Substituting the given values:
[tex]\[
PE = 1.5 \, \text{kg} \times 9.8 \, \text{m/s}^2 \times 1 \, \text{m}
\][/tex]
- This calculates to:
[tex]\[
PE = 14.7 \, \text{J}
\][/tex]
3. Energy Conservation Principle:
- In an ideal scenario with no friction, the mechanical energy is conserved. This means that all the potential energy at the top will convert into kinetic energy ([tex]\(KE\)[/tex]) at the bottom.
- Therefore, the kinetic energy at the bottom of the plane will be equal to the potential energy at the top:
[tex]\[
KE = PE
\][/tex]
- Thus:
[tex]\[
KE = 14.7 \, \text{J}
\][/tex]
### Conclusion:
The block will have a kinetic energy of 14.7 Joules when it reaches the bottom of the inclined plane.
Given the options in the question:
A. 44.1 J
B. 50.9 J
C. 0 J
D. 6.8 J
None of these options match the calculated kinetic energy of 14.7 J, so you might want to double-check the provided multiple-choice options for any potential errors.
