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a) For 0 compressions:
potential energy = U = 0 J
kinetic energy = k = 0.383 J
total mechanical energy = E = 0.383 J
b) For compression of 1 cm:
potential energy = U = 0.0228 J
kinetic energy = k = 0.155 J
total mechanical energy = E = 0.383 J
c) For compression of 2 cm :
potential energy = U = 0.1104 J
kinetic energy = k = 0.272 J
total mechanical energy = E = 0.383 J
d) For compression of 3cm:
potential energy = U = 0.248 J
kinetic energy = k = 0.177 J
total mechanical energy = E = 0.383 J
<h3>Method for solving:</h3>The equations for kinetic energy is:
k= 1/2*m*
The equation for elastic potential energy is:
U= 1/2*ks*
Where,
m= mass of the block
v= velocity
ks= spring constant
x= displacement of the spring
(a)when compression= 0 cm
U= 1/2*ks*
U= 1/2*552*
= 0 J
Kinetic energy:
k= 1/2*m*
k= 1/2*(1.05)*
k= 0.383 J
Mechanical energy:
E= k + U
E= 0.383+0
E= 0.383 J
There will be no work done by friction or any other dissipative force, hence this energy will be conserved, or it will remain constant (like air resistance). This indicates that only spring potential energy will be created from the kinetic energy (there is no thermal energy due to friction, for example).
(b) spring potential = ?
U= 1/2* 457 N/m*
U= 0.0228 J
Since the mechanical energy must remain constant, we may calculate the kinetic energy using the mechanical energy equation:
E= k + U
0.383= k + 0.0228
k= 0.383 - 0.228
k= 0.155
(c)spring constant when x= 0.02
U= 1/2*552*
U= 0.1104 J
Using the equation of mechanical energy:
E= k +U
0.383= k+ 0.1104
k= 0.383 - 0.1104
k= 0.272 J
(d) U= 1/2*552*
U= 0.2484 J
E= 0.383 J
k = E - U
k= 0.383- 0.206
k= 0.177
To learn more about spring potential energy visit:
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Answer:
Final speed, v = 54.64 m/s.
Explanation:
Given that,
Mass of a car, m = 2000 kg
Initial speed of the car, u = 23 mph = 10.28 m/s
height, h = 144 m
We need to find the speed of the car at the bottom of the hill. Let v is the speed. Applying conservation of energy as :
a = g here
So, the speed at the bottom of the hill is 54.64 m/s.