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A 1. 30 kg block slides with a speed of 0. 855 m/s on a frictionless horizontal surface until it encounters a spring with a force constant of 552 n/m. The block comes to rest after compressing the spring 4. 15 cm. Part a. Find the spring potential energy, u , the kinetic energy of the block, k , and the total mechanical energy of the system, e , for compressions of 0 cm. Part b. Find the spring potential energy, u , the kinetic energy of the block, k , and the total mechanical energy of the system, e , for compressions of 1. 00 cm. Part c. Find the spring potential energy, u , the kinetic energy of the block, k , and the total mechanical energy of the system, e , for compressions of.

Sagot :

a) U =  0 J

k = 0.383 J

E = 0.383 J

b) U = 0.0228 J

k = 0.155 J

E = 0.383 J

c) U = 0.1104 J

k = 0.272 J

E = 0.383 J

d) U = 0.248 J

k = 0.177 J

E = 0.383 J

Method for solving:

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*

= 0 J

Kinetic energy:

k= 1/2*m*[tex]v^{2}[/tex]

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*[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

To learn more about spring potential energy visit:

https://brainly.com/question/28168175

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