How Does Friction Affect the Acceleration of Stacked Blocks?

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    Exam F=ma
In summary, to find the acceleration of the lower block in this scenario, we can use the equation a = ((F - (μ * (m1 + m2) g)) / m2, where F is the applied force, μ is the coefficient of kinetic friction for all surfaces, m1 and m2 are the masses of the two blocks, and g is the acceleration due to gravity. This equation accounts for the normal force and frictional force acting on the lower block, as well as the additional friction from the top block when it slips on the lower block.
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Homework Statement


A block of mass m1 is on top of a block of mass m2. The lower block is on a horizontal surface, and a rope can pull horizontally on the lower block. The coefficient of kinetic friction for all surfaces is μ. What is the resulting acceleration of the lower block if a force F is applied to the rope? Assume that F is sufficiently large so that the top block slips on the lower block.

Homework Equations



F = ma
Frictional Force = Normal Force * μ

The Attempt at a Solution



Normal Force (for lower block) = (m1 + m2) g
Frictional Force (for lower block) = μ * (m1 + m2) g
F - (μ * (m1 + m2) g) = m2 * a
a = ((F - (μ * (m1 + m2) g)) / m2

Correct Answer should be: a2 = (F - μg(2m1 + m2)) / m2
 
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welcome to pf!

hi vjnmath! welcome to pf! :smile:
vjnmath said:
… Assume that F is sufficiently large so that the top block slips on the lower block.

… sooo, you'll need to include the friction force from the top block :wink:
 

FAQ: How Does Friction Affect the Acceleration of Stacked Blocks?

What is the significance of F=MA?

F=MA is a fundamental equation in physics that relates force (F), mass (M), and acceleration (A). It is often referred to as Newton's second law of motion and is a key concept in understanding the behavior of objects in motion.

What does the F=MA equation represent?

The F=MA equation represents the relationship between the net force applied to an object, its mass, and the resulting acceleration. It states that the force applied to an object is directly proportional to its mass and the resulting acceleration.

How is the F=MA equation used in real-world applications?

The F=MA equation is used in a wide range of real-world applications, including engineering, mechanics, and motion analysis. It is used to calculate the force required to move objects, the acceleration of objects in motion, and to design structures and machines that can withstand various forces.

What is the difference between force, mass, and acceleration?

Force is a measure of the push or pull on an object, mass is the amount of matter in an object, and acceleration is the rate of change of an object's velocity. In the F=MA equation, force is directly proportional to mass and acceleration, meaning that an increase in either mass or acceleration will result in an increase in force.

How does F=MA relate to other equations in classical mechanics?

F=MA is a key equation in classical mechanics, which also includes Newton's first and third laws of motion. It is often used in conjunction with other equations, such as the equations of motion and the laws of conservation of momentum and energy, to analyze and predict the behavior of objects in motion.

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