12/20/2017 12.00:00 AM (U%) Problem 5: A block of mass 5.1 kg is sitting on a fr

Question

12/20/2017 12.00:00 AM (U%) Problem 5: A block of mass 5.1 kg is sitting on a frictionless ramp with a spring at the bottom that has a spring constant of 545 N/m (refer to the figure). The angle of the ramp with respect to the honzontal is 16 Randomized Variables m=5.1 kg k 545 Nm t Status re for view Status Completed Completed Ctheexpertta. The block, starting fom rest, slides down the ramp a distance 67 cm before hitting the spring How far, in centimeters, 33% Part (b) After the block comes to rest, the spring pushes the block back up the ramp How fast, in meters per second is the blo of the block the top 33% Part (a) spring compressed as the block comes to momentary rest? moving right after it comes off the spring? & 33% Part (c) what is the change of the gravitational potential energy, nj ules between he riginal post ramp and the postion of the block when the spring is fully compressed? Grade Sumo an Dedoction Potential Submissioni cos0 tan) 8 sinO

Explanation / Answer

mass = m= 5.1kg

spring constant = k = 545 N/m

part(a)

Ei = Ef

m*g*(d+x)*sintheta = (1/2)*k*x^2

5.1*9.8*(0.67+x)*sin16 = (1/2)*545*x^2

x = 0.211 = 21.1 cm

part b

KE = PE

(1/2)*m*v^2 = (1/2)*k*x^2

m*v^2 = k*x^2

v = x*sqrt(k/m)

v = 0.211*sqrt(545/5.1) = 2.18 m/s

part(c)

dU = m*g*(d+x)*sintheta = 5.1*9.8*(0.67+0.211)*sin16 = 12.14 J

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