Kinetic and potential energy?
Posted in xn--kfs74mzzid01b.com edit by admin on January 7th, 2009
a)what is the kinetic energy of the ball as it leaves the bat
b)ignoring air resistance what is the max height the ball reaches. please explain what you do and why.
if u have mass is kg and velocity in m/s u get k.e in joules
convert 160g to kg to get the rt answer.
for part 2 of yr qn:
use the following eqns:
s=ut + 1/2at^2
v^2 = u^2+2as
u=init velocity (u have it as 16.8m/s)
v= final velocity =0 (it "stops" when it reaches max ht)
a=acc due to gravity which is 9.8m/s^2
s is the distance travelled so far at time t
(hint: if u put v=0, u'll get a -ve sign to ake care of this
view acc as -9.8 as this is against the direction of earth's gravity)
hi. i never occurred to me to use k.e = p.e as the other two have answered. their approach is simpler and st fwd and comes directly from one of the 1st principles: ke+p.e=constant.
but u can check for yrself that both the answers are right.
there is an element of mass in these two answers which is not there in the one which i've given. there is no problem with that as mass gets cancelled out if u equate p.e and k.e.
so here's the insight u get: the max ht reached by the body does not depend on its mass (assuming an ideal situation without air friction) and that all objects experience the same acceleration (g) -- a fact first understood by Galileo.
Ek = 0.5*0.16*16.8²
Ek = 22.58J
Kinetic energy = 22.58J
Potential energy at top = kinetic energy at bottom
Potential energy = mgh
mgh = 22.58
0.16*9.8*h = 22.58
h = 14.4m
height = 14.4m
An exam tip: when the question obviously deals with kinetic and potential energy do not attempt to derive the answer using for example equations of motion. The examiner will not mark you correct, even if the result is correct.
Potential energy (in Joules) = mass (in kg) x height (in metres) x gravity (usually, value is 9.8 N/kg)
a) Kinetic energy of the ball (as it leaves the bat) = 0.5 x 0.16 x (16.8)^2 = 22.5792 Joules
b) As the ball reaches its max. height, kinetic energy is 0J (no more kinetic energy to move on further), which means all the kinetic energy has been converted to potential energy.
Potential energy = mass x height x gravity
22.5792 Joules = 0.16kg x height x 9.8N/kg
height = 22.5792J / (0.16kg x 9.8N/kg) = 14.4metres
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