3 objects with masses m1=5kg, m2=10kg and m3=15kg are attached by massless string over two frictionless pulleys. The horizontal surface is frictionless and system is released from rest. Using energy concept calculate m3 speed after it has moved down 0.4m
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To calculate the speed of object m3 after it has moved down 0.4m, we can use the concept of energy.
First, let's consider the initial state of the system when it is released from rest. At this point, all three masses are at the same height and have zero velocity.
Next, let's consider the final state of the system when m3 has moved down 0.4m. We want to calculate the final velocity of m3 at this point.
Since the system is frictionless and there is a massless string connecting the objects, we can assume that the amount of potential energy lost by m3 is transferred to kinetic energy gained by m3.
The potential energy lost by m3 can be calculated using the formula:
ΔPE = m3 * g * h
where m3 is the mass of object m3, g is the acceleration due to gravity (9.8 m/s^2), and h is the distance m3 has moved down (0.4m in this case).
The kinetic energy gained by m3 can be calculated using the formula:
ΔKE = (1/2) * m3 * v^2
where v is the final velocity of m3.
According to the principle of conservation of energy, the potential energy lost by m3 (ΔPE) is equal to the kinetic energy gained by m3 (ΔKE).
Therefore, we can equate these two equations:
m3 * g * h = (1/2) * m3 * v^2
Now, we can solve for the final velocity of m3 (v):
v^2 = 2 * g * h
v = √(2 * g * h)
Substituting the given values:
v = √(2 * 9.8 * 0.4)
v ≈ 2.798 m/s
Therefore, the speed of object m3 after it has moved down 0.4m is approximately 2.798 m/s.