Conservation of momentum problems

[ownedbyphysics]

The larges grand piano in the world is really grand. Built in London, it has a mass of 1250 kg. Suppose a pianist finishes playing this piano and pushes herself from the piano so that she rolls backwards with a speed of 1.4m/s. Meanwhile, the piano rolls forward so that in 4.0s it travels 24 cm at constant velocity. Assuming the stool that the pianist is istting on has a negligible mass, what is the pianist's mass?

a. v of piano= s/t= .24/4=.06m/s
b. mp2= -mpvp,f/vp2,f= (-1250*.06)/-1.4 = 54kg

Correct me if I'm wrong, thanks!

 

[radou]

Looks correct.

 

[kyle8921]

Your calculations are correct. Conservation of momentum states that in a closed system, the total momentum before an event must equal the total momentum after the event. In this case, the total momentum of the system (piano and pianist) before the pianist pushes off the piano is zero, since they are both at rest. After the pianist pushes off, the total momentum of the system is still zero, as the piano and pianist are moving in opposite directions with equal and opposite momenta. Therefore, we can set up the equation:
mpvp,i + mpvp,f = 0
Where mp is the mass of the pianist and vp is the velocity of the piano. Solving for mp, we get:
mp = -mpvp,f/vp,i
Substituting in the values given, we get mp = (-1250*.06)/-1.4 = 54 kg. This means that the pianist has a mass of 54 kg.