Conservation of momentum problems

In summary, the largest grand piano in the world is located in London and has a mass of 1250 kg. After a pianist finishes playing the piano and pushes herself off, she rolls backwards with a speed of 1.4m/s. The piano simultaneously rolls forward at a constant velocity and travels 24cm in 4.0s. Assuming the stool has negligible mass, the pianist's mass is 54 kg.
  • #1
ownedbyphysics
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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!
 
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  • #2
Looks correct.
 
  • #3


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.
 

Related to Conservation of momentum problems

What is conservation of momentum?

Conservation of momentum is a fundamental principle in physics that states that the total momentum of a closed system remains constant over time, regardless of any external forces acting on the system.

How is conservation of momentum applied in problem solving?

In conservation of momentum problems, we use the principle to analyze and predict the motion of objects in a system. This involves setting up equations to represent the initial and final momenta of the objects and solving for any unknown quantities.

What is an elastic collision?

An elastic collision is a type of collision between two objects where both objects retain their original shapes and no kinetic energy is lost. This means that the total momentum before and after the collision remains the same.

What is an inelastic collision?

An inelastic collision is a type of collision where the objects deform or stick together after colliding, resulting in a loss of kinetic energy. In this case, the total momentum before the collision may not be equal to the total momentum after the collision.

Can conservation of momentum be violated?

No, conservation of momentum is a fundamental law of physics and cannot be violated. However, in some situations, it may appear that momentum is not conserved due to external forces acting on the system or errors in measurement.

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