How much work would it take to horizontally accelerate an object with a mass of #2"kg"# to #9"m/s"# on a surface with a kinetic friction coefficient of #3#?
It can be anything greater than
According to the Work-Energy Theorem, the work completed is equal to the object's change in kinetic energy plus the energy lost as a result of friction.
It will be "81"J"# no matter how you push the object, so the work done will be at least that.
Conversely, the amount of work done against friction can range from infinitesimally small to infinitely big; let's consider the two extreme cases in an intuitive manner.
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The work done to horizontally accelerate an object can be calculated using the equation:
[ W = \frac{1}{2} m v^2 ]
where:
- ( W ) is the work done,
- ( m ) is the mass of the object (2 kg),
- ( v ) is the final velocity (9 m/s).
Substituting the given values:
[ W = \frac{1}{2} \times 2 \times (9)^2 ]
[ W = \frac{1}{2} \times 2 \times 81 ]
[ W = 81 ]
Therefore, it would take 81 joules of work to horizontally accelerate the object to 9 m/s.
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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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- The force applied against an object moving horizontally on a linear path is described by #F(x)=2x +2 #. By how much does the object's kinetic energy change as the object moves from # x in [ 1, 3 ]#?
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- What is the work energy theorem?

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