The spring in the figure has a spring constant of 1300N/m . It is compressed 17.

Question

The spring in the figure has a spring constant of 1300N/m . It is compressed 17.0cm , 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 1300N/m . It is compressed 17.0cm , 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

let u is the speed of the block at the bottom of the ramp.

0.5*m*u^2 = 0.5*k*x^2

==> u = x*sqrt(k/m)

= 0.17*sqrt(1300/0.2)

= 13.7 m/s

acceleration of the block on the inclined surface,

a = -g*sin(45) - mue_k*g*cos(45)

= -9.8*sin(45) - 0.22*9.8*cos(45)

= -8.45 m/s^2

distance travelled, d = 2/sin(45) = 2.83 m/s

let v is the speed of the block at the top of the incline

Apply, v^2 - u^2 = 2*a*d

v = sqrt(u^2 + 2*a*d)

= sqrt(13.7^2 - 2*8.45*2.83)

= 11.82 m/s

now, Horizontal range, d = v^2*sin(2*theta)/g

= 11.82^2*sin(2*45)/9.8

= 14.2 m

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