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Two blocks of masses m and M are placed on a horizontal frictionless table connected by light spring. Mass M is pulled to right with a force F. If the acceleration of mass m is a . Then acceleration of mass M will be ________
Most Upvoted Answer
Two blocks of masses m and M are placed on a horizontal frictionless t...
Explanation:
When a force is applied to the mass M, it will cause both masses to move together due to the spring connecting them. The acceleration of both masses will depend on the force applied to mass M and the mass of both masses.
Free Body Diagram:
To understand the acceleration of both masses, we need to draw the free body diagram of both masses.
For mass m:
- Weight (mg) acts downwards
- Tension (T) acts upwards
For mass M:
- Weight (Mg) acts downwards
- Force (F) acts towards the right
- Tension (T) acts towards the left
Equations:
Using the free body diagram, we can write the equations of motion for both masses.
For mass m:
- T - mg = ma
For mass M:
- F - T = Ma
Substitute:
We know that the spring force is equal to the tension in the spring. Therefore, we can substitute T with the spring force (kx) in both equations.
For mass m:
- kx - mg = ma
For mass M:
- F - kx = Ma
Acceleration of Mass M:
We are given that the acceleration of mass m is a. Therefore, we can substitute a with its value in the equation of mass m.
kx - mg = ma
kx = ma + mg
x = (ma + mg)/k
Now, we can substitute x in the equation of mass M.
F - k(ma+mg)/k = Ma
F - ma - mg = Ma
a(M + m) = F - mg
a = (F - mg)/(M + m)
Therefore, the acceleration of mass M is (F - mg)/(M + m).
When a force is applied to the mass M, it will cause both masses to move together due to the spring connecting them. The acceleration of both masses will depend on the force applied to mass M and the mass of both masses.
Free Body Diagram:
To understand the acceleration of both masses, we need to draw the free body diagram of both masses.
For mass m:
- Weight (mg) acts downwards
- Tension (T) acts upwards
For mass M:
- Weight (Mg) acts downwards
- Force (F) acts towards the right
- Tension (T) acts towards the left
Equations:
Using the free body diagram, we can write the equations of motion for both masses.
For mass m:
- T - mg = ma
For mass M:
- F - T = Ma
Substitute:
We know that the spring force is equal to the tension in the spring. Therefore, we can substitute T with the spring force (kx) in both equations.
For mass m:
- kx - mg = ma
For mass M:
- F - kx = Ma
Acceleration of Mass M:
We are given that the acceleration of mass m is a. Therefore, we can substitute a with its value in the equation of mass m.
kx - mg = ma
kx = ma + mg
x = (ma + mg)/k
Now, we can substitute x in the equation of mass M.
F - k(ma+mg)/k = Ma
F - ma - mg = Ma
a(M + m) = F - mg
a = (F - mg)/(M + m)
Therefore, the acceleration of mass M is (F - mg)/(M + m).
Community Answer
Two blocks of masses m and M are placed on a horizontal frictionless t...
for the string not to slack or break the both blocks must have same acceleration. so M also have acceleration a
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Two blocks of masses m and M are placed on a horizontal frictionless table connected by light spring. Mass M is pulled to right with a force F. If the acceleration of mass m is a . Then acceleration of mass M will be ________
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Two blocks of masses m and M are placed on a horizontal frictionless table connected by light spring. Mass M is pulled to right with a force F. If the acceleration of mass m is a . Then acceleration of mass M will be ________ for Software Development 2025 is part of Software Development preparation. The Question and answers have been prepared according to the Software Development exam syllabus. Information about Two blocks of masses m and M are placed on a horizontal frictionless table connected by light spring. Mass M is pulled to right with a force F. If the acceleration of mass m is a . Then acceleration of mass M will be ________ covers all topics & solutions for Software Development 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two blocks of masses m and M are placed on a horizontal frictionless table connected by light spring. Mass M is pulled to right with a force F. If the acceleration of mass m is a . Then acceleration of mass M will be ________.
Two blocks of masses m and M are placed on a horizontal frictionless table connected by light spring. Mass M is pulled to right with a force F. If the acceleration of mass m is a . Then acceleration of mass M will be ________ for Software Development 2025 is part of Software Development preparation. The Question and answers have been prepared according to the Software Development exam syllabus. Information about Two blocks of masses m and M are placed on a horizontal frictionless table connected by light spring. Mass M is pulled to right with a force F. If the acceleration of mass m is a . Then acceleration of mass M will be ________ covers all topics & solutions for Software Development 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two blocks of masses m and M are placed on a horizontal frictionless table connected by light spring. Mass M is pulled to right with a force F. If the acceleration of mass m is a . Then acceleration of mass M will be ________.
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