LIFE SAVER RATING FOR ALL PARTS CORRECT- THANK YOU PLEASE DO NOT ROUND ANYTHING

Question

LIFE SAVER RATING FOR ALL PARTS CORRECT- THANK YOU 

PLEASE DO NOT ROUND ANYTHING WHILE DOING YOUR CALCULATION

(a) ALREADY DONE

If the mass is not attached to the spring, how far up the slope will the mass move before coming to rest?

ANSWER=0.72 (m)

(b)

If the mass is attached to the spring, how far up the slope will the mass move before coming to rest?

THE ANSWER IS NOT 0.5 (m), I REPEAT THE ANSWER IS NOT 0.5 (m), AGAIN THE ANSWER IS NOT 0.5 (m)

(c)

IF YOU GET VALUES OF (0.93) or (0.87) THEY ARE WRONG

Explanation / Answer

Let the mass be m Spring length l = 0.5 m Angle of inclined plane A = 41o The force acting on the mass in x and y directions are Fx = F - w * sinA --------(1) and Fy = n + (-w * cosA) = 0 or n = w * cosA ----------(2) where w = m * g,g = 9.8 m/s^2 From (1) m * ax = k * l - w * sinA where k is spring constant of spring or ax = (1/m) * (k * l - w * sinA) We know that v = u + ax * t where v = 0 or t = (u/ax) where t is time The kinetic energy of mass is K = (1/2)m * u^2 The kinetic energy of spring is E = (1/2)k * l^2 Here,K = E or (1/2)m * u^2 = (1/2)k * l^2 or u = (k/m)^1/2 * l The distance travelled by mass before coming to rest is S = ut + (1/2)ax * t^2

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