In lab, you used an Atwood\'s Machine to verify Newton\'s Second Law of Motion.
ID: 1634027 • Letter: I
Question
In lab, you used an Atwood's Machine to verify Newton's Second Law of Motion. a. The acceleration of the masses in an Atwood's machine is given by a = (m_1 - m_2)g/m_1 + m_1, where m_1 represents the greater mass and g is the acceleration due to gravity. Use kinematics to calculate the final velocity of the masses after they have moved through a distance h. Assume that both masses are initially at rest. b. Use a work-energy approach to verify your answer to part a. c. Use the law of conservation of energy to verify your answer to part a. Assume that the pulley is frictionless.Explanation / Answer
a)
GIVEN THAT
accelaration is a = (m1-m2)*g/(m1+m2)
m1>m2
initial velocity of both the masses are Vo1 = 0 m/sec and Vo2 = 0 m/sec
distance travelled is S = h
using kinematic equations
for m1
V1^2 - Vo1^2 = 2*a*S
V1^2-0^2 = 2*[(m1-m2)*g / (m1+m2)]*h
V1 = sqrt[2*(m1-m2)*g*h / (m1+m2)]
gor m2 also same V2 = V1 = sqrt[2*(m1-m2)*g*h / (m1+m2)]
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b) using work energy theorem
work done by the net force = change in kinetic energy
W = Kf-Ki
initial kinetic energy is zero J
then
W = Kf
F*s = Kf
for m1
m1*a*h = (1/2)*m1*v1^2
m1 cancels on both sides
then
a*h = (1/2)*v1^2
(m1-m2)*g*h/(m1+m2) = (1/2)*v1^2
v1 = sqrt[2*(m1-m2)*g*h / (m1+m2)]
similarly for m2
v2 = v1 = sqrt[2*(m1-m2)*g*h / (m1+m2)]
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c)
using law of conservation of energy
energy at the initial position = energy at the final height h
0 = ((1/2)*m1*v^2) + ((1/2)*m2*v^2) - (m1*g*h) + (m2*g*h)
(m1-m2)*g*h = (1/2)*v^2*(m1+m2)
v^2 = 2*(m1-m2)*g*h/(m1+m2)
v = sqrt[2*(m1-m2)*g*h / (m1+m2)]
so v1 = v2 = sqrt[2*(m1-m2)*g*h / (m1+m2)]
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