A particle of mass 0.6 kg is projected with a speed of 4 m s-1 down a line of greatest slope of a smooth plane inclined at 10° to the horizontal.
Use an energy method to find the speed of the particle after it has moved 15 m down the plane.
Solution
Initial kinetic energy (KE) is given by:
\(\frac{1}{2} \times 0.6 \times 4^2 = 4.8 \text{ J}\)
Potential energy (PE) loss is given by:
\(0.6 \times g \times 15 \times \sin 10^{\circ} = 15.628 \text{ J}\)
Final kinetic energy (KE) is given by:
\(\frac{1}{2} \times 0.6 \times v^2\)
Using the energy conservation equation:
\(0.6 \times g \times 15 \times \sin 10^{\circ} + \frac{1}{2} \times 0.6 \times 4^2 = \frac{1}{2} \times 0.6 \times v^2\)
Solving for \(v\):
\(v = 8.25 \text{ m s}^{-1}\)
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