Civil Engineering (CE) Exam > Civil Engineering (CE) Questions > A body of mass 10 kg is hanging freely and a...
Start Learning for Free
A body of mass 10 kg is hanging freely and another body of mass 15 kg is lying on a rough inclined surface. If the coefficient of friction and angle of inclination respectively are 0.3 and 30°, then the acceleration of the system (in m/s2) is __________. (Answer up to two decimal places)
Correct answer is '0.02'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
A body of mass 10 kg is hanging freely and another body of mass 15 kg...
Given: m1 = 10 kg, m2 = 15 kg, μ = 0.3 and α = 30o
Acceleration of the system is
= 0.022 m/s2
= 0.02 m/s2
Free Test
FREE
| Start Free Test |
Community Answer
A body of mass 10 kg is hanging freely and another body of mass 15 kg...
Given data:
Mass of body hanging freely (m1) = 10 kg
Mass of body on inclined surface (m2) = 15 kg
Coefficient of friction (μ) = 0.3
Angle of inclination (θ) = 30°
Free body diagram of the hanging body:
- The weight of the body (m1g) acts vertically downwards.
- There is no other external force acting on the body.
Free body diagram of the body on the inclined surface:
- The weight of the body (m2g) acts vertically downwards.
- The normal force (N) acts perpendicular to the inclined surface.
- The friction force (f) acts parallel to the inclined surface, opposing the motion.
- The component of the weight (m2g sinθ) acts parallel to the inclined surface, in the direction of motion.
- The component of the weight (m2g cosθ) acts perpendicular to the inclined surface.
Equations of motion:
For the hanging body:
m1g - T = m1a ...(1)
For the body on the inclined surface:
m2g sinθ - f = m2a ...(2)
N - m2g cosθ = 0 ...(3)
Calculating the tension in the string:
From equation (1):
T = m1g - m1a
Calculating the friction force:
From equation (2):
f = m2g sinθ - m2a
Calculating the normal force:
From equation (3):
N = m2g cosθ
Substituting the values:
m1 = 10 kg
m2 = 15 kg
g = 9.8 m/s^2
θ = 30°
Calculating the acceleration:
Substituting the values of T, f, and N in equation (2):
m2g sinθ - (m2g sinθ - m2a) = m2a
a = (m2g sinθ) / (m1 + m2)
a = (15 * 9.8 * sin30°) / (10 + 15)
a = 0.02 m/s^2
Therefore, the acceleration of the system is 0.02 m/s^2.
Mass of body hanging freely (m1) = 10 kg
Mass of body on inclined surface (m2) = 15 kg
Coefficient of friction (μ) = 0.3
Angle of inclination (θ) = 30°
Free body diagram of the hanging body:
- The weight of the body (m1g) acts vertically downwards.
- There is no other external force acting on the body.
Free body diagram of the body on the inclined surface:
- The weight of the body (m2g) acts vertically downwards.
- The normal force (N) acts perpendicular to the inclined surface.
- The friction force (f) acts parallel to the inclined surface, opposing the motion.
- The component of the weight (m2g sinθ) acts parallel to the inclined surface, in the direction of motion.
- The component of the weight (m2g cosθ) acts perpendicular to the inclined surface.
Equations of motion:
For the hanging body:
m1g - T = m1a ...(1)
For the body on the inclined surface:
m2g sinθ - f = m2a ...(2)
N - m2g cosθ = 0 ...(3)
Calculating the tension in the string:
From equation (1):
T = m1g - m1a
Calculating the friction force:
From equation (2):
f = m2g sinθ - m2a
Calculating the normal force:
From equation (3):
N = m2g cosθ
Substituting the values:
m1 = 10 kg
m2 = 15 kg
g = 9.8 m/s^2
θ = 30°
Calculating the acceleration:
Substituting the values of T, f, and N in equation (2):
m2g sinθ - (m2g sinθ - m2a) = m2a
a = (m2g sinθ) / (m1 + m2)
a = (15 * 9.8 * sin30°) / (10 + 15)
a = 0.02 m/s^2
Therefore, the acceleration of the system is 0.02 m/s^2.
Attention Civil Engineering (CE) Students!
To make sure you are not studying endlessly, EduRev has designed Civil Engineering (CE) study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Civil Engineering (CE).
|
Explore Courses for Civil Engineering (CE) exam
|
|
Top Courses for Civil Engineering (CE)View all
A body of mass 10 kg is hanging freely and another body of mass 15 kg is lying on a rough inclined surface. If the coefficient of friction and angle of inclination respectively are 0.3 and 30°, then the acceleration of the system (in m/s2) is __________. (Answer up to two decimal places)Correct answer is '0.02'. Can you explain this answer?
Question Description
A body of mass 10 kg is hanging freely and another body of mass 15 kg is lying on a rough inclined surface. If the coefficient of friction and angle of inclination respectively are 0.3 and 30°, then the acceleration of the system (in m/s2) is __________. (Answer up to two decimal places)Correct answer is '0.02'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about A body of mass 10 kg is hanging freely and another body of mass 15 kg is lying on a rough inclined surface. If the coefficient of friction and angle of inclination respectively are 0.3 and 30°, then the acceleration of the system (in m/s2) is __________. (Answer up to two decimal places)Correct answer is '0.02'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A body of mass 10 kg is hanging freely and another body of mass 15 kg is lying on a rough inclined surface. If the coefficient of friction and angle of inclination respectively are 0.3 and 30°, then the acceleration of the system (in m/s2) is __________. (Answer up to two decimal places)Correct answer is '0.02'. Can you explain this answer?.
A body of mass 10 kg is hanging freely and another body of mass 15 kg is lying on a rough inclined surface. If the coefficient of friction and angle of inclination respectively are 0.3 and 30°, then the acceleration of the system (in m/s2) is __________. (Answer up to two decimal places)Correct answer is '0.02'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about A body of mass 10 kg is hanging freely and another body of mass 15 kg is lying on a rough inclined surface. If the coefficient of friction and angle of inclination respectively are 0.3 and 30°, then the acceleration of the system (in m/s2) is __________. (Answer up to two decimal places)Correct answer is '0.02'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A body of mass 10 kg is hanging freely and another body of mass 15 kg is lying on a rough inclined surface. If the coefficient of friction and angle of inclination respectively are 0.3 and 30°, then the acceleration of the system (in m/s2) is __________. (Answer up to two decimal places)Correct answer is '0.02'. Can you explain this answer?.
Solutions for A body of mass 10 kg is hanging freely and another body of mass 15 kg is lying on a rough inclined surface. If the coefficient of friction and angle of inclination respectively are 0.3 and 30°, then the acceleration of the system (in m/s2) is __________. (Answer up to two decimal places)Correct answer is '0.02'. Can you explain this answer? in English & in Hindi are available as part of our courses for Civil Engineering (CE).
Download more important topics, notes, lectures and mock test series for Civil Engineering (CE) Exam by signing up for free.
Here you can find the meaning of A body of mass 10 kg is hanging freely and another body of mass 15 kg is lying on a rough inclined surface. If the coefficient of friction and angle of inclination respectively are 0.3 and 30°, then the acceleration of the system (in m/s2) is __________. (Answer up to two decimal places)Correct answer is '0.02'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
A body of mass 10 kg is hanging freely and another body of mass 15 kg is lying on a rough inclined surface. If the coefficient of friction and angle of inclination respectively are 0.3 and 30°, then the acceleration of the system (in m/s2) is __________. (Answer up to two decimal places)Correct answer is '0.02'. Can you explain this answer?, a detailed solution for A body of mass 10 kg is hanging freely and another body of mass 15 kg is lying on a rough inclined surface. If the coefficient of friction and angle of inclination respectively are 0.3 and 30°, then the acceleration of the system (in m/s2) is __________. (Answer up to two decimal places)Correct answer is '0.02'. Can you explain this answer? has been provided alongside types of A body of mass 10 kg is hanging freely and another body of mass 15 kg is lying on a rough inclined surface. If the coefficient of friction and angle of inclination respectively are 0.3 and 30°, then the acceleration of the system (in m/s2) is __________. (Answer up to two decimal places)Correct answer is '0.02'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A body of mass 10 kg is hanging freely and another body of mass 15 kg is lying on a rough inclined surface. If the coefficient of friction and angle of inclination respectively are 0.3 and 30°, then the acceleration of the system (in m/s2) is __________. (Answer up to two decimal places)Correct answer is '0.02'. Can you explain this answer? tests, examples and also practice Civil Engineering (CE) tests.
|
|
Explore Courses for Civil Engineering (CE) exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup