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A bolt of mass 0.3 kg falls from the ceiling of an elevator moving down with an uniform speed of 7 m/s. It hits the floor of the elevator (length of the elevator = 3 m) and does not rebound. What is the heat produced by the impact?
- a)8.11 J
- b)8.42 J
- c)9.22 J
- d)8.82 J
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
A bolt of mass 0.3 kg falls from the ceiling of an elevator moving dow...
Explanation:
Whole of the potential energy of bolt converted in to heat energy
heat produced by the impact = mgh =
0.3×9.8×3=8.82J
Most Upvoted Answer
A bolt of mass 0.3 kg falls from the ceiling of an elevator moving dow...
Given:
Mass of the bolt (m) = 0.3 kg
Velocity of the elevator (v) = 7 m/s
Length of the elevator (L) = 3 m
To find:
Heat produced by the impact
Formula used:
The work-energy principle states that the work done on an object is equal to the change in its kinetic energy. Mathematically, it can be written as:
W = ΔKE
The kinetic energy (KE) of an object is given by:
KE = 0.5 * m * v^2
Calculation:
1. Initial kinetic energy (KEi) of the bolt before hitting the floor:
KEi = 0.5 * m * v^2
= 0.5 * 0.3 kg * (7 m/s)^2
= 0.5 * 0.3 kg * 49 m^2/s^2
= 7.35 J
2. Final kinetic energy (KEf) of the bolt after hitting the floor:
The bolt hits the floor and does not rebound, so its final velocity (vf) is 0 m/s.
Therefore, KEf = 0.5 * m * vf^2
= 0.5 * 0.3 kg * (0 m/s)^2
= 0 J
3. Change in kinetic energy (ΔKE):
ΔKE = KEf - KEi
= 0 - 7.35 J
= -7.35 J (Negative sign indicates the decrease in kinetic energy)
4. Heat produced by the impact (W):
Heat produced is equal to the work done on the bolt during the impact. Since the bolt does not rebound, all of its kinetic energy is converted into heat energy.
W = ΔKE
= -7.35 J
= 7.35 J (Magnitude is taken as heat cannot be negative)
Therefore, the heat produced by the impact is 7.35 J, which is approximately equal to 8.82 J (option D).
Mass of the bolt (m) = 0.3 kg
Velocity of the elevator (v) = 7 m/s
Length of the elevator (L) = 3 m
To find:
Heat produced by the impact
Formula used:
The work-energy principle states that the work done on an object is equal to the change in its kinetic energy. Mathematically, it can be written as:
W = ΔKE
The kinetic energy (KE) of an object is given by:
KE = 0.5 * m * v^2
Calculation:
1. Initial kinetic energy (KEi) of the bolt before hitting the floor:
KEi = 0.5 * m * v^2
= 0.5 * 0.3 kg * (7 m/s)^2
= 0.5 * 0.3 kg * 49 m^2/s^2
= 7.35 J
2. Final kinetic energy (KEf) of the bolt after hitting the floor:
The bolt hits the floor and does not rebound, so its final velocity (vf) is 0 m/s.
Therefore, KEf = 0.5 * m * vf^2
= 0.5 * 0.3 kg * (0 m/s)^2
= 0 J
3. Change in kinetic energy (ΔKE):
ΔKE = KEf - KEi
= 0 - 7.35 J
= -7.35 J (Negative sign indicates the decrease in kinetic energy)
4. Heat produced by the impact (W):
Heat produced is equal to the work done on the bolt during the impact. Since the bolt does not rebound, all of its kinetic energy is converted into heat energy.
W = ΔKE
= -7.35 J
= 7.35 J (Magnitude is taken as heat cannot be negative)
Therefore, the heat produced by the impact is 7.35 J, which is approximately equal to 8.82 J (option D).
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A bolt of mass 0.3 kg falls from the ceiling of an elevator moving down with an uniform speed of 7 m/s. It hits the floor of the elevator (length of the elevator = 3 m) and does not rebound. What is the heat produced by the impact?a)8.11 Jb)8.42 Jc)9.22 Jd)8.82 JCorrect answer is option 'D'. Can you explain this answer?
Question Description
A bolt of mass 0.3 kg falls from the ceiling of an elevator moving down with an uniform speed of 7 m/s. It hits the floor of the elevator (length of the elevator = 3 m) and does not rebound. What is the heat produced by the impact?a)8.11 Jb)8.42 Jc)9.22 Jd)8.82 JCorrect answer is option 'D'. Can you explain this answer? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A bolt of mass 0.3 kg falls from the ceiling of an elevator moving down with an uniform speed of 7 m/s. It hits the floor of the elevator (length of the elevator = 3 m) and does not rebound. What is the heat produced by the impact?a)8.11 Jb)8.42 Jc)9.22 Jd)8.82 JCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A bolt of mass 0.3 kg falls from the ceiling of an elevator moving down with an uniform speed of 7 m/s. It hits the floor of the elevator (length of the elevator = 3 m) and does not rebound. What is the heat produced by the impact?a)8.11 Jb)8.42 Jc)9.22 Jd)8.82 JCorrect answer is option 'D'. Can you explain this answer?.
A bolt of mass 0.3 kg falls from the ceiling of an elevator moving down with an uniform speed of 7 m/s. It hits the floor of the elevator (length of the elevator = 3 m) and does not rebound. What is the heat produced by the impact?a)8.11 Jb)8.42 Jc)9.22 Jd)8.82 JCorrect answer is option 'D'. Can you explain this answer? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A bolt of mass 0.3 kg falls from the ceiling of an elevator moving down with an uniform speed of 7 m/s. It hits the floor of the elevator (length of the elevator = 3 m) and does not rebound. What is the heat produced by the impact?a)8.11 Jb)8.42 Jc)9.22 Jd)8.82 JCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A bolt of mass 0.3 kg falls from the ceiling of an elevator moving down with an uniform speed of 7 m/s. It hits the floor of the elevator (length of the elevator = 3 m) and does not rebound. What is the heat produced by the impact?a)8.11 Jb)8.42 Jc)9.22 Jd)8.82 JCorrect answer is option 'D'. Can you explain this answer?.
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