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A toy car is made from a rectangular block of mass M and four disk wheels of mass m and radii r . The car is attached to a vertical wall by a massless horizontal spring with spring constant k and constrained to move perpendicular to the wall. The coefficient of static friction between the wheel of the car and the floor is . The maximum amplitude of oscillations of the car above which the wheels start slipping is?
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A toy car is made from a rectangular block of mass M and four disk whe...
Problem:
A toy car is made from a rectangular block of mass M and four disk wheels of mass m and radii r. The car is attached to a vertical wall by a massless horizontal spring with spring constant k and constrained to move perpendicular to the wall. The coefficient of static friction between the wheel of the car and the floor is μ. Find the maximum amplitude of oscillations of the car above which the wheels start slipping.
Solution:
To find the maximum amplitude of oscillations of the car above which the wheels start slipping, we need to consider the forces acting on the car and analyze the conditions for slipping.
Forces acting on the car:
1. Weight of the car (Mg) acting vertically downwards.
2. Normal force (N) exerted by the floor perpendicular to the surface.
3. Tension force (T) in the spring, directed towards the wall.
4. Friction force (F) acting parallel to the surface.
Conditions for slipping:
For the wheels to start slipping, the maximum friction force (F_max) must be equal to the product of the coefficient of static friction (μ) and the normal force (N).
Analysis:
1. At the maximum amplitude, when the car is at the extreme end of its oscillation, the only force acting in the horizontal direction is the friction force (F).
2. The friction force (F) can be calculated as the product of the coefficient of static friction (μ) and the normal force (N).
3. The normal force (N) can be calculated as the sum of the weight of the car (Mg) and the vertical component of the tension force (T).
4. The vertical component of the tension force (T) can be calculated as T*sin(θ), where θ is the angle between the spring and the vertical.
5. The angle θ can be calculated as θ = tan^(-1)(A/L), where A is the amplitude of oscillation and L is the length of the spring.
6. The tension force (T) can be calculated as kA, where k is the spring constant and A is the amplitude of oscillation.
Calculation:
1. Calculate the normal force (N) = Mg + T*sin(θ).
2. Calculate the friction force (F) = μN.
3. Set F = F_max and solve for the maximum amplitude (A).
Conclusion:
The maximum amplitude of oscillations of the car above which the wheels start slipping can be calculated by setting the maximum friction force (F_max) equal to the product of the coefficient of static friction (μ) and the normal force (N). By analyzing the forces acting on the car and considering the conditions for slipping, we can calculate the maximum amplitude of oscillations.
A toy car is made from a rectangular block of mass M and four disk wheels of mass m and radii r. The car is attached to a vertical wall by a massless horizontal spring with spring constant k and constrained to move perpendicular to the wall. The coefficient of static friction between the wheel of the car and the floor is μ. Find the maximum amplitude of oscillations of the car above which the wheels start slipping.
Solution:
To find the maximum amplitude of oscillations of the car above which the wheels start slipping, we need to consider the forces acting on the car and analyze the conditions for slipping.
Forces acting on the car:
1. Weight of the car (Mg) acting vertically downwards.
2. Normal force (N) exerted by the floor perpendicular to the surface.
3. Tension force (T) in the spring, directed towards the wall.
4. Friction force (F) acting parallel to the surface.
Conditions for slipping:
For the wheels to start slipping, the maximum friction force (F_max) must be equal to the product of the coefficient of static friction (μ) and the normal force (N).
Analysis:
1. At the maximum amplitude, when the car is at the extreme end of its oscillation, the only force acting in the horizontal direction is the friction force (F).
2. The friction force (F) can be calculated as the product of the coefficient of static friction (μ) and the normal force (N).
3. The normal force (N) can be calculated as the sum of the weight of the car (Mg) and the vertical component of the tension force (T).
4. The vertical component of the tension force (T) can be calculated as T*sin(θ), where θ is the angle between the spring and the vertical.
5. The angle θ can be calculated as θ = tan^(-1)(A/L), where A is the amplitude of oscillation and L is the length of the spring.
6. The tension force (T) can be calculated as kA, where k is the spring constant and A is the amplitude of oscillation.
Calculation:
1. Calculate the normal force (N) = Mg + T*sin(θ).
2. Calculate the friction force (F) = μN.
3. Set F = F_max and solve for the maximum amplitude (A).
Conclusion:
The maximum amplitude of oscillations of the car above which the wheels start slipping can be calculated by setting the maximum friction force (F_max) equal to the product of the coefficient of static friction (μ) and the normal force (N). By analyzing the forces acting on the car and considering the conditions for slipping, we can calculate the maximum amplitude of oscillations.
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A toy car is made from a rectangular block of mass M and four disk wheels of mass m and radii r . The car is attached to a vertical wall by a massless horizontal spring with spring constant k and constrained to move perpendicular to the wall. The coefficient of static friction between the wheel of the car and the floor is . The maximum amplitude of oscillations of the car above which the wheels start slipping is?
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A toy car is made from a rectangular block of mass M and four disk wheels of mass m and radii r . The car is attached to a vertical wall by a massless horizontal spring with spring constant k and constrained to move perpendicular to the wall. The coefficient of static friction between the wheel of the car and the floor is . The maximum amplitude of oscillations of the car above which the wheels start slipping is? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about A toy car is made from a rectangular block of mass M and four disk wheels of mass m and radii r . The car is attached to a vertical wall by a massless horizontal spring with spring constant k and constrained to move perpendicular to the wall. The coefficient of static friction between the wheel of the car and the floor is . The maximum amplitude of oscillations of the car above which the wheels start slipping is? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A toy car is made from a rectangular block of mass M and four disk wheels of mass m and radii r . The car is attached to a vertical wall by a massless horizontal spring with spring constant k and constrained to move perpendicular to the wall. The coefficient of static friction between the wheel of the car and the floor is . The maximum amplitude of oscillations of the car above which the wheels start slipping is?.
A toy car is made from a rectangular block of mass M and four disk wheels of mass m and radii r . The car is attached to a vertical wall by a massless horizontal spring with spring constant k and constrained to move perpendicular to the wall. The coefficient of static friction between the wheel of the car and the floor is . The maximum amplitude of oscillations of the car above which the wheels start slipping is? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about A toy car is made from a rectangular block of mass M and four disk wheels of mass m and radii r . The car is attached to a vertical wall by a massless horizontal spring with spring constant k and constrained to move perpendicular to the wall. The coefficient of static friction between the wheel of the car and the floor is . The maximum amplitude of oscillations of the car above which the wheels start slipping is? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A toy car is made from a rectangular block of mass M and four disk wheels of mass m and radii r . The car is attached to a vertical wall by a massless horizontal spring with spring constant k and constrained to move perpendicular to the wall. The coefficient of static friction between the wheel of the car and the floor is . The maximum amplitude of oscillations of the car above which the wheels start slipping is?.
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