The spring in the figure has a spring constant of 1000N/m . It is compressed 13.

Question

The spring in the figure has a spring constant of 1000N/m . It is compressed 13.0cm , then launches a 200gblock. The horizontal surface is frictionless, but the block's coefficient of kinetic friction on the incline is 0.220.

What distance d does the block sail through the air?

The spring in the figure has a spring constant of 1000N/m . It is compressed 13.0cm , then launches a 200gblock. The horizontal surface is frictionless, but the block's coefficient of kinetic friction on the incline is 0.220. What distance d does the block sail through the air?

Explanation / Answer

Here ,

we will use conservation of energy

Let the speed of launch of block is u

then

Using conservation of energy at the bottom and top of incline

0.5kx^2 = 0.5mv^2 + mg*h + mg*u*h/sin(45)

0.5*1000*0.13^2 = 0.200(0.5*v^2 + 9.8 * 2 + 0.22 * 9.8 *2/sin(45))

solvng for v

v = 5.75 m/s

Now , range of projectile

d = v^2*sin(2*theta)/g

d = 5.75^2*sin(90)/9.8

d = 3.37 m

the block sails in air for 3.37 m

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