The set up in the diagram below relates to a classic inclined plane problem that

Question

The set up in the diagram below relates to a classic inclined plane problem that is typically solved using free body diagrams and Newton's Second Law of Motion. You will work through this inclined plane problem using Conservation of Mechanical Energy instead. You may ignore friction and assume that the system is initially at rest. If m_1 falls down 2.6 m, what is the change in potential energy deltaU_1 of m_1? Leave your answer in terms of m_1 and g. A positive answer indicates an increase in potential energy and a negative answer indicates a decrease in potential energy. (Assume any numerical value for height is in meters, but do not enter units.) Notice that the string connecting m_1 and m_2 does not stretch but remains taut. What is the corresponding change in potential energy deltaU_2 of m_2? Leave your answer in terms of m_2, g, and 6. A positive answer indicates an increase in potential energy and a negative answer indicates a decrease in potential energy. (Assume any numerical value for height is in meters, but do not enter units.) Use m_1 = 6 kg, m_2 = 9 kg, and theta = 25degree. Calculate the total change in potential energy delta U_system of the system. A positive answer indicates an increase in potential energy and a negative answer indicates a decrease in potential energy. What is the total change in kinetic energy deltaK_system of the system. A positive answer indicates an increase in kinetic energy and a negative answer indicates a decrease in kinetic energy. What is the final velocity v of the system?

Explanation / Answer

part A)

change in potential energy of m1 = - m1 * g * h1

change in potential energy of m1 = -2.6 * m1*g

partt B)

for the mass m2 ,

change in height , h2 = 2.6 * sin(theta)

change in potential energy of m2 = m2 * g * 2.6 * sin(theta)

the change in potential energy of m2 is m2 * g * 2.6 * sin(theta)

part C)

Total change in potential energy = -2.6 * m1*g + m2 * g * 2.6 * sin(theta)

Total change in potential energy = -2.6 * 9.8 * (6 - 9 * sin(25))

Total change in potential energy = - 56 J

part D)

Total change in kinetic energy = - change in potential energy

Total change in kinetic energy = 56 J

the Total change in kinetic energy is 56 J

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