A spring is mounted at angle ? = 35? on a frictionless incline as illustrated in

Question

A spring is mounted at angle ? = 35? on a frictionless incline as illustrated in the figure below. The spring is compressed by 15 cm where it is allowed to propel a mass of4.4 kg up the incline.

(a) If the spring constant is 640 N/m, how fast is the mass moving when it leaves the spring?
cm/s

(b) To what maximum distance from the starting point will the mass rise up the incline?
cm

A spring is mounted at angle ? = 35½ on a frictionless incline as illustrated in the figure below. The spring is compressed by 15 cm where it is allowed to propel a mass of4.4 kg up the incline. (a) If the spring constant is 640 N/m, how fast is the mass moving when it leaves the spring? cm/s (b) To what maximum distance from the starting point will the mass rise up the incline? cm

Explanation / Answer

Here

A)

Here , let the speed of block be u when it leaves the spring

Using conservation of energy ,

0.5 kx^2 = mgx*sin(35) + 0.5mu^2

0.5*640*.15^2 = 4.4*9.8*.15 sin(35)+0.5*4.4*u^2

solving for u

u = 1.313 m/s

the speed of mass is 1.313 m/s when it leaves spring

B)

Here , Using conservation of energy

0.5kx^2 = mgd*sin(35)

0.5*640*0.15^2 = 4.4*9.7*d*sin(35)

d = 0.291 m

it will fo 0.291 m from starting point

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