Instructions. For each question, show all work leading to an answer and simplify
ID: 3280664 • Letter: I
Question
Instructions. For each question, show all work leading to an answer and simplify as much as reasonably possible 1. A block of mass m 0.500 kg is pushed against a horizontal spring of negligible mass until the spring is compressed a distance See the accompanying figure. The force constant of the spring is k450 N mI When the block is released from rest, it travels along a frictionless, horizontal surface to point A (which is the bottom of a vertical circular track of radius R 100 m) and continues to move along the track. The speed of the block at A is v12.0 m 1, and the block experiences an average kinetic frictional force of magnitude 7.00 N while sliding up the track. Neglect air resistance (a) Determine the value of z. (b) For a particle that is subject to a kinetic frictional force of constant magnitude Fe, the work done over a distance d by that force is WfreFd. What speed do you predict for the block at point B (which is the top of the track)? (c) Does the block actually reach the top of the track, or does it fall off before reaching the top? Explain your answer. VAExplanation / Answer
a] By eenergy conservationn,
0.5 mv^2 = 0.5 kx^2
x = sqrt(m/k) v
= sqrt(0.5/450) *12
= 0.4 m
b] by work energy theorem, KE change = total work done
0.5 mv^2 = 0.5 kx^2 - mg*2R - Fk*(pi R)
= 0.5*450*0.4^2 - 0.5*9.8*2*1 - 7*pi*1
0.5*0.5 v^2 = 4.209
v = sqrt(4*4.209) = 4.1 m/s answer
c] minimum velocity at top to complete circular motion,Vmin = sqrt(rg) = sqrt(1*9.8) = 3.13 m/s
since v > Vmin, it will reach top of the loop.