If the velocity of an object increases and its mass triples how much does the momentum increase by?

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gsenviro's profile pic

gsenviro | College Teacher | (Level 1) Educator Emeritus

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Momentum of an object is related to its mass, m and velocity, v. The product of mass and velocity of an object is termed as its momentum. If any of these quantities (mass or velocity or both) changes, object's momentum will change. 

In the given case, the mass triples, i.e. new mass is 3m. Nothing is mentioned about its velocity (except that it increases). Let us assume that it also triples, i.e. new velocity is 3v. Thus, the new momentum of the body is given by 3m x 3v = 9 mv. That is the momentum changes by a factor of 9, the final momentum is 9 times the original momentum. Similarly, any other change in mass or velocity or both can be used to determine the change in momentum.

Hope this helps.

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loves2learn | (Level 3) Salutatorian

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The formula for momentum is,


This is very important because it shows by how much the momentum will increase when either the mass or the velocity is increased because there is a direct relationship (as mass or velocity increases, momentum also increases or vice versa).

Therefore, if `m ` is the initial mass and `v ` is the initial velocity, then the initial momentum would be,

`p_o=mv `

Since you did not say how much the velocity increases by, I will choose some arbitrary number, like 2. The mass increases by a factor of 3

Therefore, we get that

`(3m)(2v)=6mv `

Therefore, the momentum of the object increases by a factor of 6 in this scenario.