a block with mass 1.6g compresses A block with mass 1.6 g compresses a spring wi

Question

a block with mass 1.6g compresses A block with mass 1.6 g compresses a spring with spring constant k = 24 N/m by 15.2 cm cm before being released. After being released, the block slides up an inclined plane with a slope of 24.8 degree. How much potential energy does the spring have when fully compressed? How much kinetic energy does the block have after it is released? How fast is it going. Using conservation of energy, determine how far up the inclined plane the block goes? Give the distance travelled, nor the height.

Explanation / Answer

1) potential energy;

FORCE DUE TO STRETCHED SPRING:

F = -KX

K is spring constant

x is displacement

F=- 24 * 15.2 /100

= - 3.648 N

potential energy is calculated from spring energy,

potential energy = 1/2 k x2

= 1/2 * 24 * (15.2/100)2

   = 0.2772 joules

2)kinetic energy = 0.2772 joules

to calculate velocity:

1/2 * 1.6/1000 * v2 cos224.8 =0.2772

v2= 554.4 / 1.318

v2 = 420.637

v=20.509 m/sec

velocity is equal to 20.509 m/sec

c) distance travelled=420.637/2*10

= 21.032 m

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