A thrill-seeking cat with mass 4.00 kg is attached by a harness to an ideal spring of negligible mass and oscillates vertically in SHM. The amplitude is 0.050 m, and at the highest point of the motion the spring has its natural unstretched length. Calculate the elastic potential energy of the spring (take it to be zero for the unstretched spring), the kinetic energy of the cat, the gravitational potential energy of the system relative to the lowest point of the motion, and the sum of these three energies
Calculate the elastic potential energy of the spring (take it to be zero for the unstretched spring) when the cat is at its highest point.
Solve:
vbr{lr<5vvx><f(nn)/.bbn>
vbr<lr><5.12>(9.8)^3
.bbn=%ff
%ff=F(9x)
.bbn=%ff9x
.bbn=.133%tri
.bbn=.tri
t.ri=vbr
v=31.4
b=59.3
r=28.6
KE___?
^^^Wrong!
10c-<0.06>=f(n)(l1/l3+l2/l4)
uf=f(x)_ln<1.962>
fx/%fl
%fl=1.333
2C-<0.09>=f(1.33)
ANS:___?
dude I have no idea what you just typed..
can you please clarify what all the variables you used stand for?
fl= flux
uf= kinetic flux
fx= potential flux
l= lib
C= constant
To calculate the elastic potential energy of the spring when the cat is at its highest point, we need the formula for elastic potential energy, which is given by:
Elastic Potential Energy = (1/2) * k * x^2
Where:
- Elastic Potential Energy is the energy stored in the spring
- k is the spring constant
- x is the displacement from the equilibrium position (amplitude)
In this case, since the spring is ideal and has negligible mass, its spring constant can be determined using Hooke's Law:
F = -k * x
Where:
- F is the force applied on the spring
- x is the displacement from the equilibrium position (amplitude)
At the highest point, the displacement is equal to the amplitude, so we can substitute the values into the formulas to solve for the elastic potential energy.
Given:
- Mass of the cat (m) = 4.00 kg
- Amplitude (x) = 0.050 m
Let's calculate the spring constant (k) using the formula:
k = -F / x
To find the force (F), we need to use Newton's second law:
F = m * g
Where:
- g is the acceleration due to gravity (9.8 m/s^2)
Now substituting the values:
F = (4.00 kg) * (9.8 m/s^2) = 39.2 N
Now, we can calculate the spring constant:
k = -F / x = -39.2 N / 0.050 m = -784 N/m
Substituting the values into the formula for elastic potential energy:
Elastic Potential Energy = (1/2) * k * x^2
Elastic Potential Energy = (1/2) * (-784 N/m) * (0.050 m)^2
Now you can solve the equation to find the elastic potential energy.