Energy Problem

Classical Mechanics Level 3

Calculate the final speed of the system after it has traveled a distance S in m/s. G = 10.


The answer is 4.

Kevin Tran by Kevin Tran , 19, USA

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1 solution

Steven Chase
Dec 23, 2017

Net conversion of gravitational potential energy = Kinetic energy of system + friction losses

m 2 g S − m 1 g S s i n ( θ ) = 1 2 ( m 1 + m 2 ) v 2 + μ k m 1 g c o s ( θ ) S \large{m_2 \, g \, S - m_1 \, g \, S \, sin(\theta) = \frac{1}{2} (m_1 + m_2) \, v^2 + \mu_k m_1 \, g \, cos(\theta) \, S}

Plugging in numbers yields v = 4 v= 4 . Note that for integer results, μ k = 3 \mu_k = \sqrt{3} and g = 10 g = 10

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