Calculate Acceleration of 5kg Box w/ μ=.5 & 2kg Mass Falling

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To calculate the acceleration of a 5kg box with a coefficient of friction (μ) of 0.5, attached to a 2kg mass over a frictionless pulley, one must consider the net forces acting on both masses. The friction force acting on the box is determined by multiplying μ by the weight of the box, which impacts the overall acceleration. The formula for acceleration (a) is derived from the net force divided by the total mass of the system. It's important to differentiate between static and kinetic friction coefficients, as they affect the resistance to acceleration differently. Understanding these concepts is crucial for accurately determining the system's acceleration.
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1. Calculate the acceleration of a box with a mass of 5kg and μ=.5 when attached by a massless cord over frictionless pulley to a 2kg mass that is allowed to fall freely. The box is on a table, the pulley is hanging off.



2. I know a = (Fnet/total mass) but I am not sure what to do with μ! Can someone explain it to me?
 
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When you pull a sled on ice, it is easy to pull because μ is small.
When you pull it on gravel, it is hard to pull because μ is larger.
μ is the fraction of the weight that the friction force is.
Force of friction = μ*weight.
(When on a slope at an angle, you have to use the normal force - the component of the weight that pushes against the slope.)
 
Think of mu (μ) as the magnitude of how much an object cancels out the forces trying to accelerate it.

There are two mu values for any object. The static and kinetic friction coefficients. Static is the resistance for an object to acceleration, kinetic is the resistance to acceleration after it starts moving.
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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