Qns on Motion & Work: Find 1/2(M+m)v^2

In summary, the man of mass "m" jumping off the initially stationary boat causes the boat of mass "M" to move to the right at speed v. The work done by the man during the leap, taking into account both the man's body and the boat, is equal to 1/2(M+(M^2/m))v^2. This is found by using conservation of momentum to find the speed of the man and adding the kinetic energies of the boat and man.
  • #1
Delzac
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A man of mass "m" on an initially stationary boat gets off the boat by jumping to the left in an exactly horizontal direction. Immediately after he leaps, the boat of mass "M", is observed to be moving to the right at speed v. how much work did the man do during the leap ( both to his own body and on the boat)?

is the ans as simple as " 1/2(M+m)v^2 " , or is there on to it?
 
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  • #2
Delzac said:
A man of mass "m" on an initially stationary boat gets off the boat by jumping to the left in an exactly horizontal direction. Immediately after he leaps, the boat of mass "M", is observed to be moving to the right at speed v. how much work did the man do during the leap ( both to his own body and on the boat)?

is the ans as simple as " 1/2(M+m)v^2 " , or is there on to it?
Careful. It is true that the answer will be the sum of the kinetic energies of the boat and man but the man will not have the same speed as the boat. Use conservation of momentum to find the speed of the man then add the kinetic energies of the boat and man.
Patrick
 
  • #3
got it! the ans is 1/2(M+(M^2/m))v^2 right? thanks a bunch!
 

FAQ: Qns on Motion & Work: Find 1/2(M+m)v^2

What does "1/2(M+m)v^2" represent in the equation?

The expression "1/2(M+m)v^2" represents the kinetic energy of an object in motion, where M is the mass of the object, m is the mass of the surrounding medium, and v is the velocity of the object.

Why is the mass of the surrounding medium included in the equation?

The mass of the surrounding medium is included in the equation because it affects the amount of energy required to move an object through it. This is particularly important when considering the movement of objects through air or water, where the medium can have a significant impact on the object's velocity and kinetic energy.

How is kinetic energy related to an object's motion?

Kinetic energy is directly proportional to an object's mass and the square of its velocity. This means that as an object's mass or velocity increases, its kinetic energy also increases. Additionally, kinetic energy is a measure of the work that an object can do, so it is closely tied to an object's ability to move and exert force.

What is the significance of the "1/2" in the equation?

The "1/2" in the equation is a constant that represents the conversion factor between the units of mass (kilograms) and the units of energy (joules). This constant ensures that the result of the equation is in the correct units of energy.

Can this equation be used for all types of motion and work?

No, this equation is specifically used for calculating the kinetic energy of an object in motion. It cannot be used for calculating work done by other forces, such as gravity or friction. Different equations exist for calculating the work done by these forces.

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