Answer :
a) Spring potential energy U = 0 J
Kinetic energy of the block k = 0.383 J
Total mechanical energy of the system E = 0.383 J
b) Spring potential energy U = 0.0228 J
Kinetic energy of the block k = 0.155 J
Total mechanical energy of the system E = 0.383 J
c) Spring potential energy U = 0.1104 J
Kinetic energy of the block k = 0.272 J
Total mechanical energy of the system E = 0.383 J
d) Spring potential energy U = 0.248 J
Kinetic energy of the block k = 0.177 J
Total mechanical energy of the system E = 0.383 J
The equations for kinetic energy is:
k= (1/2) × m × [tex]v^{2}[/tex]
The equation for elastic potential energy is:
U= (1/2) × ks × [tex]x^{2}[/tex]
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 × [tex]x^{2}[/tex]
U= (1/2) ×552 × [tex]0^{2}[/tex]
= 0 J
Kinetic energy:
k= (1/2) × m × [tex]v^{2}[/tex]
k= (1/2) × 1.05 × [tex]0.855^{2}[/tex]
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 × [tex]0.01^{2}[/tex]
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 × [tex]0.02^{2}[/tex]
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 × [tex]0.03^{2}[/tex]
U= 0.2484 J
E= 0.383 J
k = E - U
k= 0.383- 0.206
k= 0.177
Therefore,
a) Spring potential energy U = 0 J
Kinetic energy of the block k = 0.383 J
Total mechanical energy of the system E = 0.383 J
b) Spring potential energy U = 0.0228 J
Kinetic energy of the block k = 0.155 J
Total mechanical energy of the system E = 0.383 J
c) Spring potential energy U = 0.1104 J
Kinetic energy of the block k = 0.272 J
Total mechanical energy of the system E = 0.383 J
d) Spring potential energy U = 0.248 J
Kinetic energy of the block k = 0.177 J
Total mechanical energy of the system E = 0.383 J
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