A wall is hit elastically and normally by ‘n’ balls per second. All the balls have the same mass ‘m’ and are moving with the same velocity ‘u’. the force exerted by the balls on the wall is
A wall is hit elastically and normally by ‘n’ balls per second. All the balls have the same mass ‘m’ and are moving with the same velocity ‘u’. the force exerted by the balls on the wall is
2mnu
\(\frac {1}{2}\)mnu2
mnu
2mnu2
The Correct Option is A
Solution and Explanation
The change in momentum of a ball is given by Δp = 2mu, where m is the mass of the ball and u is the velocity of the ball.
Since there are 'n' balls hitting the wall per second, the total change in momentum per second (rate of change of momentum) is given by:
Δptotal = n * Δp
Δptotal = n * 2mu
Δptotal = 2mnu
Therefore, the force exerted by the balls on the wall is equal to the rate of change of momentum:
F = \(\frac {Δp_{total}}{t}\)
Since the balls are hitting the wall per second, the time interval 't' is equal to 1 second.
F = Δptotal
Substituting the value of Δp_total:
F = 2mnu
Therefore, the correct answer is (A) 2mnu.
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Concepts Used:
Collision Theory
The collision theory states that a chemical reaction can only occur between particles when they collide (hit each other). The collision between reactant particles is necessary but not sufficient for a reaction to take place. The collisions also have to be effective. It is important to understand the exact nature of an effective collision since this determines whether particles react with each other and form new products.
Molecular Collisions
- The more molecules are present, the more collisions will happen.
- Molecules must collide before they can react.
- To effectively initiate a reaction, collisions must be sufficiently energetic
(kinetic energy) to bring about this bond disruption. - As the temperature rises, molecules move faster and collide more vigorously,
greatly increasing the likelihood of bond cleavages and rearrangements. - Most reactions involving neutral molecules cannot take place at all until they have acquired the activation energy needed to stretch, bend, or otherwise distort one or more bonds.