Can you tell me what formulas I need to use for the following problems: A 14.0 k
ID: 1464216 • Letter: C
Question
Can you tell me what formulas I need to use for the following problems:
A 14.0 kg hollow sphere with o radius of 0.20 m rolls (without slipping) 10.0 m down a romp Inclined at 35* to the horizontal, if the sphere starts from rest. what is its linear speed at the bottom of the romp? A 150.0 kg merry-go-round in the shape of a uniform solid disk of radius 1.50 m is rotating at 7.00 rad/s when a 50.0 kg child jumps on and stands 1.20 m from the center. Determine the final angular speed of the system. A 75.0 kg astronaut connected by a 20 m long tether to a satellite is initially rotating about the satellite a? 5.0 m/s. As the astronaut rotates the tether gets wrapped around the satellite. Find the speed of the astronaut when the tether is 7.0 m long.Explanation / Answer
let h is the vertical height travelled.
h = 10*sin(35)
= 5.74 m
1)
let v is the speed of cyllinder at th bottom,
Apply conservation of energy
0.5*m*v^2 + 0.5*I*w^2 = m*g*h
0.5*m*v^2 + 0.5*(2/5)*m*r^2*w^2 = m*g*h
0.5*m*v^2 + 0.2*m*(r^2*w^2) = m*g*h (since v = r*w)
0.5*m*v^2 + 0.25*m*v^2 = m*g*h
0.7*m*v^2 = m*g*h
v = sqrt(g*h/0.7)
= sqrt(9.8*5.74/0.7)
= 8.96 m/s <<<<<<<<-------------Answer
2)
Apply conservation of angular momentum
I2*w2 = I1*w1
w2 = I1*w1/I2
= (0.5*150*1.5^2)*7/(0.5*150*1.5^2 + 50*1.2^2)
= 4.9 RAD/S
3) Apply conservation of angular momentum
m*v2*r2 = m*v1*r1
v2 = v1*r1/r2
= 5*20/7
= 14.3 m/s <<<<<<<<-------------Answer
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