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A cart loaded with water having mass m=1000 kg moves on a straight horizontal road starting from rest under the force of 100N.the water spills from the small hole at the bottom at the rate of 0.1kg/s.the velocity of cart after 300s will be??
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A cart loaded with water having mass m=1000 kg moves on a straight hor...
Introduction
To determine the velocity of the cart after 300 seconds, we can apply the principles of momentum and Newton's second law of motion. The cart starts with an initial mass and experiences a continuous loss of mass due to the spillage of water.
Given Data
- Initial mass of the cart (m): 1000 kg
- Force applied (F): 100 N
- Rate of water spillage (dm/dt): 0.1 kg/s
- Time (t): 300 s
Calculating the Mass Loss
- The total mass lost after 300 seconds:
- Mass lost = Rate of spillage × Time
- Mass lost = 0.1 kg/s × 300 s = 30 kg
- Remaining mass of the cart after 300 seconds:
- Remaining mass = Initial mass - Mass lost
- Remaining mass = 1000 kg - 30 kg = 970 kg
Calculating Acceleration
Using Newton's second law (F = ma):
- The net force acting on the cart after the mass loss:
- F = 100 N (constant)
- m = 970 kg (remaining mass)
- Acceleration (a):
- a = F/m = 100 N / 970 kg ≈ 0.1031 m/s²
Calculating Final Velocity
Using the formula for velocity (v = u + at), where u is the initial velocity:
- Initial velocity (u) = 0 m/s (starts from rest)
- Time (t) = 300 s
- Final velocity (v):
- v = 0 + (0.1031 m/s² × 300 s) = 30.93 m/s
Conclusion
The velocity of the cart after 300 seconds will be approximately 30.93 m/s.
To determine the velocity of the cart after 300 seconds, we can apply the principles of momentum and Newton's second law of motion. The cart starts with an initial mass and experiences a continuous loss of mass due to the spillage of water.
Given Data
- Initial mass of the cart (m): 1000 kg
- Force applied (F): 100 N
- Rate of water spillage (dm/dt): 0.1 kg/s
- Time (t): 300 s
Calculating the Mass Loss
- The total mass lost after 300 seconds:
- Mass lost = Rate of spillage × Time
- Mass lost = 0.1 kg/s × 300 s = 30 kg
- Remaining mass of the cart after 300 seconds:
- Remaining mass = Initial mass - Mass lost
- Remaining mass = 1000 kg - 30 kg = 970 kg
Calculating Acceleration
Using Newton's second law (F = ma):
- The net force acting on the cart after the mass loss:
- F = 100 N (constant)
- m = 970 kg (remaining mass)
- Acceleration (a):
- a = F/m = 100 N / 970 kg ≈ 0.1031 m/s²
Calculating Final Velocity
Using the formula for velocity (v = u + at), where u is the initial velocity:
- Initial velocity (u) = 0 m/s (starts from rest)
- Time (t) = 300 s
- Final velocity (v):
- v = 0 + (0.1031 m/s² × 300 s) = 30.93 m/s
Conclusion
The velocity of the cart after 300 seconds will be approximately 30.93 m/s.
Community Answer
A cart loaded with water having mass m=1000 kg moves on a straight hor...
(1k/.97k)/3O=31 nearest value
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A cart loaded with water having mass m=1000 kg moves on a straight horizontal road starting from rest under the force of 100N.the water spills from the small hole at the bottom at the rate of 0.1kg/s.the velocity of cart after 300s will be??
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A cart loaded with water having mass m=1000 kg moves on a straight horizontal road starting from rest under the force of 100N.the water spills from the small hole at the bottom at the rate of 0.1kg/s.the velocity of cart after 300s will be?? 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 cart loaded with water having mass m=1000 kg moves on a straight horizontal road starting from rest under the force of 100N.the water spills from the small hole at the bottom at the rate of 0.1kg/s.the velocity of cart after 300s will be?? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A cart loaded with water having mass m=1000 kg moves on a straight horizontal road starting from rest under the force of 100N.the water spills from the small hole at the bottom at the rate of 0.1kg/s.the velocity of cart after 300s will be??.
A cart loaded with water having mass m=1000 kg moves on a straight horizontal road starting from rest under the force of 100N.the water spills from the small hole at the bottom at the rate of 0.1kg/s.the velocity of cart after 300s will be?? 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 cart loaded with water having mass m=1000 kg moves on a straight horizontal road starting from rest under the force of 100N.the water spills from the small hole at the bottom at the rate of 0.1kg/s.the velocity of cart after 300s will be?? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A cart loaded with water having mass m=1000 kg moves on a straight horizontal road starting from rest under the force of 100N.the water spills from the small hole at the bottom at the rate of 0.1kg/s.the velocity of cart after 300s will be??.
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