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So if I compare how the accelerations are observed in two objects, a car and a block, both having the same mass of 100kg on a surface with [itex]μ_{s} = .5[/itex] and [itex]μ_{k} = .1[/itex]

Car:

The car will have Static Friction Force [itex] f_{s} = μ_{s}F_{N}=[μmg = ma] = [.5(100kg)(10m/s^{2}) = 100kg(a)][/itex] =>

so acceleration will be [itex] ==> [itex] \frac{f_{s}}{m}=\frac{μ_{s}F_{N}}{m}= \frac{μmg}{m} = \frac{.5(100kg(10)}{100kg}= \frac{500N}{100kg} = 5m/s^{s} = a = acceleration[/itex]

So the force on the car would need to be greater than 500N. And the acceleration would need to be 5m/s^2.

Block:

The block will have Static Friction Force [itex] f_{s} = μ_{s}F_{N}=[μmg = ma] = [.5(100kg)(10m/s^{2}) = 100kg(a)] [/itex] =>

so acceleration will be [itex] ==> \frac{f_{s}}{m}=\frac{μ_{s}F_{N}}{m}= \frac{μmg}{m} = \frac{.5(100kg(10)}{100kg}= \frac{500N}{100kg} = 5m/s^{s} = a = acceleration[/itex]

So the force on the block would also need to be greater than 500N. And the acceleration would need to be 5m/s^2.

So, no difference of between the car and block in terms of how much Force and acceleration need to be applied in order to break static friction.

However, there seems to be a visual difference that is confusing.

It looks as though as Force is being applied to the car and the block from 0 to 500N, there is an associated acceleration applied to the car and block from 0 to 2m/s^2. The difference is, the car can be viewed as literally accelerating while the block remains stationary. So the "a" in the formula [μmg = ma] seems to be manifesting into the vehicles accelerating motion. However, although the same force is being applied to the block, you don't see the force having any affect on the blocks motion.

So, my question now is, what happens to the acceleration of an object upon breaking past the maximum static friction?

Would I measure the block accelerating at a rate of just over 2m/s^2 exactly at the instant it breaks from static friction? Would I measure the acceleration quickly increase from 0 to 2m/s^2? Will it immediately drop to the net acceleration of [itex]\frac{f_{s}-f_{k}}{m} = a_{net}[/itex]? Or will the acceleration at the instant of breaking free from the static friction automatically start at [itex]\frac{f_{s}-f_{k}}{m} = a_{net}[/itex]?

Car:

The car will have Static Friction Force [itex] f_{s} = μ_{s}F_{N}=[μmg = ma] = [.5(100kg)(10m/s^{2}) = 100kg(a)][/itex] =>

so acceleration will be [itex] ==> [itex] \frac{f_{s}}{m}=\frac{μ_{s}F_{N}}{m}= \frac{μmg}{m} = \frac{.5(100kg(10)}{100kg}= \frac{500N}{100kg} = 5m/s^{s} = a = acceleration[/itex]

So the force on the car would need to be greater than 500N. And the acceleration would need to be 5m/s^2.

Block:

The block will have Static Friction Force [itex] f_{s} = μ_{s}F_{N}=[μmg = ma] = [.5(100kg)(10m/s^{2}) = 100kg(a)] [/itex] =>

so acceleration will be [itex] ==> \frac{f_{s}}{m}=\frac{μ_{s}F_{N}}{m}= \frac{μmg}{m} = \frac{.5(100kg(10)}{100kg}= \frac{500N}{100kg} = 5m/s^{s} = a = acceleration[/itex]

So the force on the block would also need to be greater than 500N. And the acceleration would need to be 5m/s^2.

So, no difference of between the car and block in terms of how much Force and acceleration need to be applied in order to break static friction.

However, there seems to be a visual difference that is confusing.

It looks as though as Force is being applied to the car and the block from 0 to 500N, there is an associated acceleration applied to the car and block from 0 to 2m/s^2. The difference is, the car can be viewed as literally accelerating while the block remains stationary. So the "a" in the formula [μmg = ma] seems to be manifesting into the vehicles accelerating motion. However, although the same force is being applied to the block, you don't see the force having any affect on the blocks motion.

So, my question now is, what happens to the acceleration of an object upon breaking past the maximum static friction?

Would I measure the block accelerating at a rate of just over 2m/s^2 exactly at the instant it breaks from static friction? Would I measure the acceleration quickly increase from 0 to 2m/s^2? Will it immediately drop to the net acceleration of [itex]\frac{f_{s}-f_{k}}{m} = a_{net}[/itex]? Or will the acceleration at the instant of breaking free from the static friction automatically start at [itex]\frac{f_{s}-f_{k}}{m} = a_{net}[/itex]?

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