If an object is moving at #7# #ms^-1# over a surface with a kinetic friction coefficient of #u_k=14 /g#, how far will the object continue to move?
Finding the frictional force and the acceleration due to it allows us to find the distance traveled,
The force accelerating (decelerating) the mass will be the frictional force, which is the frictional coefficient times the normal force:
In this case the normal force is the weight force of the object:
So
The acceleration (deceleration) of the object with this force acting on it is given by Newton's Second Law :
This should be given a minus sign, because it is an acceleration in the opposite direction to the object's velocity - a deceleration.
Rearranging:
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The object will continue to move for a distance determined by the equation: distance = (initial velocity^2) / (2 * friction coefficient * gravity). Plugging in the values, the distance can be calculated.
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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.
- An object with a mass of #7 kg# is hanging from a spring with a constant of #2 (kg)/s^2#. If the spring is stretched by # 2 m#, what is the net force on the object?
- If the length of a #58 cm# spring increases to #81 cm# when a #9 kg# weight is hanging from it, what is the spring's constant?
- If a #3/2 kg# object moving at #3/4# #ms^-1# slows to a halt after moving #5/8 m#, what is the coefficient of kinetic friction of the surface that the object was moving over?
- If a #2 kg# object moving at #12 m/s# slows to a halt after moving #144 m#, what is the coefficient of kinetic friction of the surface that the object was moving over?
- An object with a mass of #6 kg# is hanging from a spring with a constant of #4 (kg)/s^2#. If the spring is stretched by #18 m#, what is the net force on the object?

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