Use the exact values you enter to make later calculations.

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.

(a) If m₁ falls down 2.9 m, what is the change in potential energy ΔU₁ of m₁? Leave your answer in terms of m₁ and g. Note: 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.)
ΔU₁ =

(b) Notice that the string connecting m₁ and m₂ does not stretch but remains taut. What is the corresponding change in potential energy ΔU₂ of m₂? Leave your answer in terms of m₂, g, and θ. Note: 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.)
ΔU₂ =

(c) Use m₁ = 5 kg, m₂ = 8 kg, and θ = 27°. Calculate the total change in potential energy ΔU_system of the system. Note: A positive answer indicates an increase in potential energy and a negative answer indicates a decrease in potential energy.
ΔU_system =

(d) What is the total change in kinetic energy ΔK_system of the system. Note: A positive answer indicates an increase in kinetic energy and a negative answer indicates a decrease in kinetic energy.
ΔK_system =

(e) What is the final velocity v of the system?
v =

(f) What are the advantages in using Conservation of Energy to solve this problem instead of Newton's Second Law of Motion? (Select all that apply.)

Both methods have the same level of complexity.

We have to find the components of the force vectors regardless of the method used.

Conservation of Energy involves only scalar quantities.

Using Conservation of Energy is simpler.

Conservation of Energy method does not require free body diagrams showing the force vectors.

Question

Use the exact values you enter to make later calculations.

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.

(a) If m₁ falls down 2.9 m, what is the change in potential energy ΔU₁ of m₁? Leave your answer in terms of m₁ and g. Note: 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.)
ΔU₁ =

(b) Notice that the string connecting m₁ and m₂ does not stretch but remains taut. What is the corresponding change in potential energy ΔU₂ of m₂? Leave your answer in terms of m₂, g, and θ. Note: 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.)
ΔU₂ =

(c) Use m₁ = 5 kg, m₂ = 8 kg, and θ = 27°. Calculate the total change in potential energy ΔU_system of the system. Note: A positive answer indicates an increase in potential energy and a negative answer indicates a decrease in potential energy.
ΔU_system =

(d) What is the total change in kinetic energy ΔK_system of the system. Note: A positive answer indicates an increase in kinetic energy and a negative answer indicates a decrease in kinetic energy.
ΔK_system =

(e) What is the final velocity v of the system?
v =

(f) What are the advantages in using Conservation of Energy to solve this problem instead of Newton's Second Law of Motion? (Select all that apply.)

Both methods have the same level of complexity.

We have to find the components of the force vectors regardless of the method used.

Conservation of Energy involves only scalar quantities.

Using Conservation of Energy is simpler.

Conservation of Energy method does not require free body diagrams showing the force vectors.

Accepted Answer

(a)Find the change in potential energy for mass m1 moving down.

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