Work, energy, and cats

Classical Mechanics Level 1

Find the mass, in kg , \text{kg}, of a cat whose gravitational potential energy decreases from 300 J \text{J} to 200 J \text{J} over 2 m . \text{m}. Take the acceleration due to gravity to be g = 10 m s 2 . g = 10 \frac{\text{m}}{\text{s}^2}.


The answer is 5.

July Thomas by July Thomas , 30, USA

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2 solutions

July Thomas
Apr 20, 2016

Relevant wiki: Work

Since gravitational force is conservative, use

W n e t = − Δ U F y d y = − ( U f − U i ) m g d y = U i − U f m = U i − U f g d y m = 300 − 200 ( 10 ) ( 2 ) = 5 kg \begin{aligned} W_{net} &= -\Delta U \\ \\ F_y d_y &= -(U_f - U_i) \\ \\ mgd_y &= U_i - U_f \\ \\ m &= \frac{U_i - U_f}{gd_y} \\ \\ m &= \frac{300-200}{(10)(2)} = 5\text{kg} \end{aligned}

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Tom Engelsman
May 1, 2021

Let h h be the cat's height where P E = 200 PE = 200 joules and h + 2 h+2 for 300 300 joules. We have the system of equations:

m g h = 200 , mgh = 200, (i)

m g ( h + 2 ) = 300 mg(h+2) = 300 (ii)

If we substitute (i) into (ii), we obtain 2 m g = 300 − m g h ⇒ m = 300 − 200 2 ( 10 ) = 5 2mg = 300 - mgh \Rightarrow m = \frac{300-200}{2(10)} = \boxed{5} kilograms.

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