If a #"0.50 kg"# object moving at #"3.5 m/s"# slows to a halt after moving #"0.25 m"#, what is the coefficient of kinetic friction of the surface that the object was moving over?
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To find the coefficient of kinetic friction (( \mu_k )), you can use the equation:
[ F_{\text{friction}} = \mu_k \times N ]
where ( F_{\text{friction}} ) is the force of friction and ( N ) is the normal force. The normal force is equal to the weight of the object, which can be calculated as ( mg ), where ( m ) is the mass of the object and ( g ) is the acceleration due to gravity (approximately ( 9.8 , \text{m/s}^2 )).
The force of friction can be found using Newton's second law:
[ F_{\text{friction}} = ma ]
where ( m ) is the mass of the object and ( a ) is its acceleration.
First, calculate the initial velocity (( v_i )) of the object using the equation of motion:
[ v_f^2 = v_i^2 + 2a d ]
where ( v_f ) is the final velocity (0 m/s), ( v_i ) is the initial velocity, ( a ) is the acceleration (negative because it's decelerating), and ( d ) is the distance.
Next, calculate the acceleration (( a )) using the equation:
[ a = \frac{v_f - v_i}{t} ]
where ( t ) is the time it takes for the object to come to a stop (unknown, but can be found using ( v_f = v_i + at )).
Once you have ( a ), you can find ( F_{\text{friction}} ) and then ( \mu_k ).
Finally, use the equation:
[ \mu_k = \frac{F_{\text{friction}}}{mg} ]
Substitute the values you've found to calculate ( \mu_k ).
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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