finding mass from kinetic energy?

Question

im having trouble with this so please explain it to me

a cat ran the distance (d) over a period of time (t) .
if the cat's kinetic energy was (j) whats the formula to find the cat's mass ?

not to sound stupid (already did) but could someone put m = 2 j t² / d² in words i got most of it but need a little more help.

Answer 1

KE =1/2 m v^2

and

v = d/t

in your case...

KE = j

so....

j = 1/2 m (d/t)^2

2j / (d/t)^2 = m

m = 2j / (d/t)^2 = 2j / (d^2/t^2) = 2jt^2/d^2

if you prefer....

m = 2 j t² / d²


************* update ************

mass = 2 x kinetic energy x time squared / distance squared

where kinetic energy has units kilogram x meter squared / second squared

time is in seconds

and distance is in meters

Answer 2

This is a little vague since kinetic energy is usually given as a function of time. From what you have given we can only find what we would take to be the average kinetic energy of the cat since we do not know the instantaneous velocity of the cat, which would give you the cat's true mass. So in effect, we can find the average mass of the cat as well.

technically,

d = integral(v(t)*dt) from time t=0 to T
and
j = 1/2*m*v(t)^2

if we take
d/T = 1/T*integral(v(t)*dt, 0,T) = V_ave over t=[0,T]

then
j = 1/2*m*V_ave^2 = 1/2*m*d^2/T^2

m = 2j*T^2/d^2, but this is basically an average because we had to average the velocity of the cat over the time. This is the same thing as assuming the cat had a constant velocity over that time, which is what all these answers assume.

Answer 3

Well use law of conservation of energy... ps bear with the calculations. a. Loss in GPE of system = Gain in KE 5*g*h - 1*g*h = 1/2*5*v^2 + 1/2* 1* v^2 where, g= 9.81, h= o.13 m, v= common to both the blocks,,,, solve the above =n to find v, b. If air resistance acts,, we have to subtrct its w.d. from Lhs of the above =n, simply subtract 2*o.8*o.13 { 2 s there are 2 blocks, ... WD = F.s, f=o.8, s=o.13} find the new velo. which would be lesser thn the prev. one

Answer 4

KE = 1/2 mv^2

KE = j
v = d/t

Plug an' chug.

Answer 5

KE = ½mv² and v = x/t, therefore:

j = ½m(d/t)², then

m = 2jt²/d²