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From the formula of K, K = 1/2mv^2 So, K is directly proportional to mass. But we can derive that p = (under root of) 2Km. So, K is inversely proportional to mass. But don’t both these statements contradict each other? Then how can they be right?

 
From the formula of K, K = 1/2mv^2
So, K is directly proportional to mass.
But we can derive that p = (under root of) 2Km.
So, K is inversely proportional to mass.
But don’t both these statements contradict each other? Then how can they be right?
 

Grade:12

2 Answers

Harsh Patodia IIT Roorkee
askIITians Faculty 907 Points
6 years ago
Hi Student

p= (2km)½
It does not mean k is inversely proportinal to m
because p itself depends on mass
when you write k= ½ mv2 in this m and v are independent quantities

if you look at 2km= m.m.v2 =(mv)2
Now we know that p=mv which square root of above expression

So the second formula is just the one to relate momentum to knectic energy. When you look at proportionality the quantities should be independent.

Saurabh Kumar
askIITians Faculty 2411 Points
6 years ago
Kinetic energy is the energy an object has due to its motion.

Quantity: Kinetic energy Unit name: Joule

Kinetic energy is the energy an object has because of its motion. This means that any moving object has kinetic energy. Kinetic energy is defined as:(1)where is the kinetic energy (measured in joules, J)

m = mass of the the object (measured in kg)

v = velocity of the object (measured in m·s−1).

Therefore the kinetic energy depends on the mass and velocity of an object. The faster it moves, and the more massive it is, the more kinetic energy it has. A truck of 2000 kg, moving at 100 km·hr−1 will have more kinetic energy than a car of 500 kg, also moving at 100 km·hr−1.
While in the second case, keeping Linear momentum to be constant (if given), then K.E. is inversly proportional to mass.

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