A body ascends a slope with a speed of 10 m per s. If 105 J of energy of the body is lost due to...

Question:

A body ascends a slope with a speed of 10 m per s. If 105 J of energy of the body is lost due to friction , the height to which the body will rise is (take {eq}g =10 {/eq} m per s{eq}^2 {/eq})?

Law of Conservation of Energy:

The law states that the total sum of all energies associated with a system always remains constant or no change is possible in the magnitude of the sum of the total energy. If non-conservative forces come into play then mechanical energy does not remain conserved but total energy still remains conserved. Overall, new energy cannot be made and the current energy cannot be destroyed.

Given:

• Initial speed, {eq}v=10 \ \rm m/s {/eq}
• Energy lost, {eq}W=-105 \ \rm J {/eq}

According to the law of conservation of mechanical energy,

Change in energy is zero,

{eq}\Delta E=0 {/eq}

But the energy lost will be equal to the change in energy,

therefore,

{eq}\Delta E=W\\ E_2-E_1=-105\\ mgh-\frac{1}{2}mv^{2}=-105\\ \displaystyle h=\frac{v^{2}}{2g}-\frac{105}{mg}\\ {/eq}

Therefore, this is the expression for the required height and can be used to solve, now as the mass of the body is not given but if it was then by using this expression, easily the problem can be solved.