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a block of mass 1.2 kg moving at a speed 20 cm/s collides head on with a similar block kept at rest the coefficient of restitution is 3/5 find the loss of kinetic energy during collision
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a block of mass 1.2 kg moving at a speed 20 cm/s collides head on with...
Here, m1=1.2 kg, u1=20cm/s, m2=1.2kg, u2=0
If v1 and v2 are velocities of the two blocks after collision, then according to the principle of conservation of momentum, m1u1 + m2u2 = m1v1 + m2v2 1.2 x 20 + 0 = 1.2v1 + 1.2v2 ... (i)
velocity of approach = u1 − u2 = 20cm/s
velocity of separation = v2 − v1
By definition, e = v2 − v1/u1 − u2 = 3/5 = v2 − v1/u1 − u2
Therefore, v2 − v1 = 20 x 3/5 = 12 --- (ii)
From (i) and (ii),
v1 = 4cm/s, v2 = 16cm/s,
Loss in K.E. = 1/2m1u1^2 − 1/2(m1)v1^2 − 1/2m2v2^2 = 1/2 x 1.2(20/100)^2 − 1/2(1.2)(4/100)^2 − 1/2 x 1.2(16/100)^2 = 2.4 x 10^−2 − 0.096 x 10^−2 − 1.536 x 10^−2
Loss in K.E. = 0.768 x 10^−2 = 7.7 x 10^−3 J
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Most Upvoted Answer
a block of mass 1.2 kg moving at a speed 20 cm/s collides head on with...
Given:
Mass of the first block (m1) = 1.2 kg
Initial velocity of the first block (u1) = 20 cm/s
Mass of the second block (m2) = 1.2 kg (similar to the first block)
Coefficient of restitution (e) = 3/5
To find:
Loss of kinetic energy during the collision
Solution:
Step 1: Calculate the initial momentum of the first block
The initial momentum (P1) of the first block can be calculated using the formula:
P1 = m1 * u1
= 1.2 kg * 20 cm/s
Step 2: Calculate the final velocity of the first block
The final velocity of the first block (v1) can be calculated using the formula:
v1 = e * u1
= (3/5) * 20 cm/s
Step 3: Calculate the final momentum of the first block
The final momentum (P1') of the first block can be calculated using the formula:
P1' = m1 * v1
= 1.2 kg * [(3/5) * 20 cm/s]
Step 4: Calculate the loss of kinetic energy during the collision
The loss of kinetic energy (K.E. loss) during the collision can be calculated using the formula:
K.E. loss = (1/2) * m1 * (u1^2 - v1^2)
Step 5: Substitute the values and calculate the loss of kinetic energy
K.E. loss = (1/2) * 1.2 kg * [(20 cm/s)^2 - [(3/5) * 20 cm/s]^2]
Simplifying the equation further will give us the loss of kinetic energy during the collision.
Explanation:
During a head-on collision between two objects, the coefficient of restitution (e) is used to determine how elastic or inelastic the collision is. In this case, the coefficient of restitution is given as 3/5, which means the collision is somewhat elastic.
To find the loss of kinetic energy during the collision, we first calculate the initial momentum of the first block using its mass and initial velocity. Then, we use the coefficient of restitution to find the final velocity of the first block. The final momentum of the first block is then calculated using its mass and final velocity.
Finally, we use the formula for loss of kinetic energy to calculate the actual energy lost during the collision. The loss of kinetic energy is calculated by subtracting the final kinetic energy from the initial kinetic energy. The difference in kinetic energy represents the energy that was dissipated or converted into other forms, such as heat or sound, during the collision.
It is important to note that the loss of kinetic energy can vary depending on the nature of the collision and the properties of the objects involved. In this case, the loss of kinetic energy can be calculated using the given values and formulas.
Mass of the first block (m1) = 1.2 kg
Initial velocity of the first block (u1) = 20 cm/s
Mass of the second block (m2) = 1.2 kg (similar to the first block)
Coefficient of restitution (e) = 3/5
To find:
Loss of kinetic energy during the collision
Solution:
Step 1: Calculate the initial momentum of the first block
The initial momentum (P1) of the first block can be calculated using the formula:
P1 = m1 * u1
= 1.2 kg * 20 cm/s
Step 2: Calculate the final velocity of the first block
The final velocity of the first block (v1) can be calculated using the formula:
v1 = e * u1
= (3/5) * 20 cm/s
Step 3: Calculate the final momentum of the first block
The final momentum (P1') of the first block can be calculated using the formula:
P1' = m1 * v1
= 1.2 kg * [(3/5) * 20 cm/s]
Step 4: Calculate the loss of kinetic energy during the collision
The loss of kinetic energy (K.E. loss) during the collision can be calculated using the formula:
K.E. loss = (1/2) * m1 * (u1^2 - v1^2)
Step 5: Substitute the values and calculate the loss of kinetic energy
K.E. loss = (1/2) * 1.2 kg * [(20 cm/s)^2 - [(3/5) * 20 cm/s]^2]
Simplifying the equation further will give us the loss of kinetic energy during the collision.
Explanation:
During a head-on collision between two objects, the coefficient of restitution (e) is used to determine how elastic or inelastic the collision is. In this case, the coefficient of restitution is given as 3/5, which means the collision is somewhat elastic.
To find the loss of kinetic energy during the collision, we first calculate the initial momentum of the first block using its mass and initial velocity. Then, we use the coefficient of restitution to find the final velocity of the first block. The final momentum of the first block is then calculated using its mass and final velocity.
Finally, we use the formula for loss of kinetic energy to calculate the actual energy lost during the collision. The loss of kinetic energy is calculated by subtracting the final kinetic energy from the initial kinetic energy. The difference in kinetic energy represents the energy that was dissipated or converted into other forms, such as heat or sound, during the collision.
It is important to note that the loss of kinetic energy can vary depending on the nature of the collision and the properties of the objects involved. In this case, the loss of kinetic energy can be calculated using the given values and formulas.
Community Answer
a block of mass 1.2 kg moving at a speed 20 cm/s collides head on with...
2304×(10^-5)
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a block of mass 1.2 kg moving at a speed 20 cm/s collides head on with a similar block kept at rest the coefficient of restitution is 3/5 find the loss of kinetic energy during collision
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a block of mass 1.2 kg moving at a speed 20 cm/s collides head on with a similar block kept at rest the coefficient of restitution is 3/5 find the loss of kinetic energy during collision for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about a block of mass 1.2 kg moving at a speed 20 cm/s collides head on with a similar block kept at rest the coefficient of restitution is 3/5 find the loss of kinetic energy during collision covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for a block of mass 1.2 kg moving at a speed 20 cm/s collides head on with a similar block kept at rest the coefficient of restitution is 3/5 find the loss of kinetic energy during collision.
a block of mass 1.2 kg moving at a speed 20 cm/s collides head on with a similar block kept at rest the coefficient of restitution is 3/5 find the loss of kinetic energy during collision for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about a block of mass 1.2 kg moving at a speed 20 cm/s collides head on with a similar block kept at rest the coefficient of restitution is 3/5 find the loss of kinetic energy during collision covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for a block of mass 1.2 kg moving at a speed 20 cm/s collides head on with a similar block kept at rest the coefficient of restitution is 3/5 find the loss of kinetic energy during collision.
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