Gravitation topic doubt

Question

The Gravitation potential difference between the surface of planet and a point 20m above is 16 J/kg. Calculae the work done in moving a 4 kg mass by 8m on a slope of 60degree from the horizontal.

Answer 1

Since gravitation is a conservative force, the work done in moving a body from one point to another in the gravitational field depends only on the end points.  It does not depend on the path between the end points.  It equals the negative of the change in gravitational potential energy.

 

U(h) = mah, where a = gravitational acceleration on the planet

 

At h = 20 m, U/m = 16 J/kg

 

U/m = ah ⇒ a = (U/m) / h = (16 J/kg) / (20 m) = 0.80 m/s²

 

U₁ = gravitational potential energy at height h₁

 

h₁ is ground level = 0 m

 

U₁ = ma(0) = 0

 

U₂ = gravitational potential energy at height h₂

 

h₂ = 8 sin(60º) m = 6.93 m

 

W_1→2 = -(U₂ - U₁) = U₁ - U₂ = 0 - U₂ = -mah₂

 

W_1→2 = -(4 kg)(0.80 m/s²)(6.93 m) J = -22.2 J

 

The negative sign means work was done against the gravitational force.