Momentum is a vector quantity representing the product of an object’s mass and velocity, describing its motion and resistance to change.
Class 11 Physics, Chapter 5: Work, Energy and Power, emphasizes understanding concepts, solving problems and exploring applications, essential for mastering mechanics in CBSE EXAM 2024-25.
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To find the percentage decrease in kinetic energy (K.E.) when momentum decreases by 20%, we have the following relations:
1. Momentum (p) is defined as:
p = m * v
where m is the mass and v is the velocity.
2. Kinetic energy (K.E.) is defined as:
K.E. = (1/2) * m * v².
3. If momentum decreases by 20%, then the new momentum is given by p’.
p’ = p – 0.2p = 0.8p.
4. As momentum is directly proportional to mass and velocity, we can express the new velocity, v’, in terms of the original velocity, v, as:
p’ = m * v’ = 0.8(m * v).
5. Divide both sides by m
v’ = 0.8v.
6. We can now compute the new kinetic energy, K.E.’:
K.E.’ = (1/2) * m * (v’)²
= (1/2) * m * (0.8v)²
= (1/2) * m * 0.64v²
= 0.64 * (1/2) * m * v²
= 0.64 * K.E.
7. The percentage decrease in kinetic energy is:
Percentage decrease = [(K.E. – K.E.’) / K.E.] * 100
= [(K.E. – 0.64K.E.) / K.E.] * 100
= (0.36K.E. / K.E.) * 100 = 36%.
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