# Question Details

Three masses m1= 5.0 kg ; m2= 10.0 kg ; m1= 15.0 kg are attached by a strings over frictionless pulleys. The horizontal surface exerts a force of friction of 30N on m2. If the system is released from rest, use energy concepts to find the speed of m2 after it moves 4.0 meter

You need to describe the figure that goes with this. Are m1 and m3 hanging from pulleys at the ends of the horizontal surface? Is 15kg supposed to be m3? You call it m1.

The energy concepts you can use are to equate
Potential energy decrease = (frictional work done) + (kinetic energy increase).

The frictional work done is 30Nx4m = 120 J.
Get the new velocity V from the kinetic energy increase. I assume all three masses will have that velocity.

If one mass rises while another falls an amount X, the potential energy decrease will be (mass difference)* g * X

Sorry there was a mistake on my part

M1=5 kg
M2=10 kg
M3=15 kg

while m1 and m3 are hanging with a support of a pulley and M2 reside on the horizontal surface

## No problem! Thank you for the clarification.

To find the speed of m2 after it moves 4.0 meters, we can use energy concepts. In this case, we can equate the potential energy decrease to the work done against friction and the increase in kinetic energy.

First, let's find the potential energy decrease. Since m1 and m3 are hanging from a pulley, and m2 is on the horizontal surface, we can treat m2 as the only mass that moves vertically. The potential energy decrease is given by:
Potential energy decrease = (mass of m2) * g * (distance moved vertically)

In this case, the distance moved vertically is equal to the distance traveled horizontally, which is given as 4.0 meters. Therefore, the potential energy decrease is:
Potential energy decrease = (m2) * g * (4.0 meters)

Next, let's find the work done against friction. The force of friction is given as 30 N, and the distance traveled is 4.0 meters. The work done against friction is:
Work done against friction = (force of friction) * (distance traveled)

Now, let's calculate the kinetic energy increase. We can assume that all three masses will have the same velocity after the movement. The kinetic energy increase is given by:
Kinetic energy increase = (1/2) * (total mass) * (velocity)^2

Now, we can set up the equation using the principle of conservation of energy:
Potential energy decrease = Work done against friction + Kinetic energy increase

Substitute the expressions we found earlier for each term:
(m2) * g * (4.0 meters) = (30 N) * (4.0 meters) + (1/2) * (m1 + m2 + m3) * (velocity)^2

Now, you can solve this equation to find the velocity of m2 after it moves 4.0 meters.