A block of rock with a mass of 72 kg slides on a surface inclined at an angle of 30° as shown in the figure. Assuming no cohesion and friction, the force \( F \) is ........... Newton (answer in one decimal place; acceleration due to gravity = 9.8 m/s²).
A block of rock with a mass of 72 kg slides on a surface inclined at an angle of 30° as shown in the figure. Assuming no cohesion and friction, the force \( F \) is ........... Newton (answer in one decimal place; acceleration due to gravity = 9.8 m/s²).
Show Hint
Correct Answer: 352.8
Solution and Explanation
Step 1: Understand the problem setup.
The force \( F \) is the component of the weight of the rock that acts parallel to the inclined surface. The force is calculated as:
\[
F = m \cdot g \cdot \sin(\theta)
\]
where \( m \) is the mass of the rock, \( g \) is the acceleration due to gravity, and \( \theta \) is the angle of inclination.
Step 2: Calculation.
Substitute the known values:
\[
F = 72 \, \text{kg} \times 9.8 \, \text{m/s}^2 \times \sin(30^\circ)
\]
\[
F = 72 \times 9.8 \times 0.5 = 352.8 \, \text{N}
\]
Step 3: Conclusion.
The force \( F \) is 352.8 N.
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