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(7%) Problem i 4: A block of mass m = 3.5 kg is attached to a spring with spring

ID: 1778971 • Letter: #

Question

(7%) Problem i 4: A block of mass m = 3.5 kg is attached to a spring with spring constant k = 910 N/m. It is initially at rest on an inclined plane that is at an angle of 1-26" with respect to the horizontal, and the coefficientof kinetic friction between the block and the plane is A = 0.19. In the initial position, where the spring is compressed by a distance of d= 0.11 m, the mass is at its lowest position and the spring is compressed the maximum amount. Take the initial gravitational energy of the block as zero. I d l 0 Randomized Variables m-3.5 kg k=910 N/m d=0.11 m = 260 ,-0.19 Otheexpertta.c / 50% Part (a) What is the block's initial mechanical energy, EO in J? G, 50% Part (b) If the spring pushes the block up the incline, what distance, L in meters, will the block travel before coming to rest? The spring remains attached to both the block and the fixed wall throughout its motion.

Explanation / Answer

Given values  

m = 3.5 kg , k = 910 N/m

d = 0.11 m , theta =26 degrees

mue_k = 0.19

when the spring pushes the block , by utilising the elastic potential energy = 0.5*k*d^2 so that the block will move up

the forces acting down ward are the component of the gravitational force and the frictional force

work done = F*S

F_down = (mg sin theta + mue_k*mg cos theta)

work done  

0.5*k*d^2 = (mg sin theta + mue_k*mg cos theta)L

L =( 0.5*k*d^2 )/ (mg sin theta + mue_k*mg cos theta)

L = (0.5*910*0.11^2)/((3.5*9.8)(sin26+0.19 cos26)) m

L = 0.2635 m