Use the energy method to find the distance moved by particle

AI Thread Summary
The discussion focuses on using energy methods to calculate the distance moved by a particle in an A-level physics examination problem. The initial kinetic energy is calculated as 28.8 Joules, leading to the equation relating kinetic energy and gravitational potential energy. By solving for the vertical distance (h), it is determined to be 7.2 meters. Using the sine function for a 30-degree angle, the total distance traveled by the particle is found to be 14.4 meters. The calculations align with the mark scheme solution, confirming their accuracy.
chwala
Gold Member
Messages
2,827
Reaction score
415
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.

Your insight appreciated.

Mark scheme solution here

1671442190743.png
 
Physics news on Phys.org
Looks fine to me.
 
Thread 'Variable mass system : water sprayed into a moving container'
Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
Back
Top