Question
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One end of a cord is fixed and a small 0.510-kg object is attached to the other end, where it swings in a section of a vertical circle of radius 2.50 m as shown in the figure below. When theta = 28.0 degree, the speed of the object is 4.00 m/s. At this instant, find each of the following. the tension in the string T = N the tangential and radial components of acceleration ar = m/s2 inward at = m/s2 downward tangent to the circle the total acceleration a total = m/s2 inward and below the cord at degree A block of the mass 2.30 kg is accelerated across a rough surface by a light cord passing over a small pulley as shown in the figure below. The tension T in the cord is maintained at 10.0 N, and the pulley is 0.130 m above the top of the block. The coefficient of kinetic friction is 0.300. Determine the acceleration of the block when x = .400 m. m/s2 Describe the general behavior of the acceleration as the block slides from a location where x is large to x = 0. increasing, then decreasing no change decreasing, then increasing Find the maximum value of the acceleration and the position x for which it occurs. x = m a = m/s2 Find the largest value of x for which the acceleration is zero. m
Explanation / Answer
1) T=8.262N
ar=6.4
at=gsin(28)=4.6
a(total)=7.88
26.3 deg with horizontal i.e 63.7 with vertical
2)f=0.3(mg-Tcos(theta))
a) a=(Tsin(theta)-f)/m=1.6
b)correct
c)x=0.468
a=3.68
d)0.057m
