Question

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.

Answer 1

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

Method for solving:

The equations for kinetic energy is:

k= 1/2*m*$v^{2}$

The equation for elastic potential energy is:

U= 1/2*ks*$x^{2}$

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*$v{2}$

U= 1/2*552*$(0)^{2}$

 = 0 J

Kinetic energy:

k= 1/2*m*$x^{2}$

k= 1/2*(1.05)*$(0.855)^{2}$

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*$(0.01)^{2}$

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*$(0.02)^{2}$

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*$(0.03)^{2}$

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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