Hmm, lost in PE = gain in KE + work done against force of friction ?
A box of mass is resting on a sloping platform which is inclined at to the horizontal. The coefficient of friction between the box and the platform is . The box is released from rest and slides down the platform. Calculate:
a) the speed of the box after it has been moving for seconds.
b) the potential energy lost by the box during this time.
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I've done part (a) but I cannot get my head around energy. Can I have help on part (b) please. Thanks.
hi,
Part 1)
Weight of the mass,
normal force acting on the mass by the platform, N =
force from the weight that is pulling the mass parallel down the slope
frictional force,
resultant force pulling the mass down parallel to the slope,
from Newton's second law, F = ma
Part 2)
Using principle of conservation of energy,
Gain in kinetic energy + other energy lost(due to friction) = Lost in gravitational potential energy
where,
v = final velocity of mass after 3 sec under acceleration
S = distance moved by the mass during the 3 second acceleration
h = vertical distance moved by the mass
Finding the final velocity of the mass:
using :
u = 0
a = 1.511451
t = 3
Kinetic energy obtained:
Finding the distance moved parallel to the plane:
using
u = 0
t = 3
a = 1.511451
Other energy lost(due to friction):
Substituting into the principle of conservation of energy:
Gain in kinetic energy + other energy lost(due to friction) = Lost in gravitational potential energy
102.8017856 + 125.398167 = Lost in potential energy
Lost in potential energy = 228.2121958 Joule
There is another method to obtain the lost in gravitational potential energy. Much faster but if you are to answer in an exam this method of using the principle of conservation of energy is the best method to use. Good luck
directly finding the gravitational potential energy:
Lost in gravitational potential energy = mgh
we already found that the mass will travel 6.801529 m down the plane. this corresponds to a drop in vertically
hence from:
Lost in gravitational potential energy = mgh