# Use the energy method to find the distance moved by particle

• chwala
In summary, the energy method is used to find the distance traveled by a particle when only the initial and final energy states are known. The steps to use this method are to identify the initial and final energy states, calculate the difference in energy, use this energy difference to find the work done, and then determine the distance moved. The energy method involves both kinetic and potential energy, and can be used for any type of particle as long as the initial and final energy states are known. However, it has limitations such as assuming that all work is converted to kinetic energy and assuming a constant force acting on the particle.

#### chwala

Gold Member
Homework Statement
A particle with mass ##0.4## kgs is projected with a speed of ##12## m/s up a line of greatest slope of a smooth plane inclined at ##30^0## to the horizontal.

i. Find the initial kinetic energy of the particle.

ii. Use an energy method to find the distance moved by the particle up the plane before coming to instantaneous rest.
Relevant Equations
kinetic energy
This is from an examination paper -A level. My interest is on part (ii). Ok my take;

i. ##KE_{initial} = \dfrac {1}{2} mu^2= \dfrac {1}{2}× 0.4 ×12^2=28.8## Joules.

ii. ##\dfrac {1}{2} mv^2=\dfrac {1}{2} mu^2-mgh##

##0=28.8-(0.4×10×h)## where h is the vertical perpendiculor distance.

##h=\dfrac{28.8}{4}=7.2##

It follows that;

##\sin 30^0=\dfrac{7.2}{s}##

##s=7.2×2=14.4## m

where ##s## is the distance travelled by the particle before coming to rest.