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nexus9112 [7]
2 years ago
12

Notice that all the initial spring potential energy was transformed into gravitational potential energy. If you compressed the s

pring to a distance of 0.200 m , how far up the slope will an identical ice cube travel before reversing directions? Note that the spring is compressed twice as much as in the original problem.
Physics
1 answer:
Nostrana [21]2 years ago
8 0

<u><em>The  question doesn't provide enough data to be solved, but I'm assuming some magnitudes to help you to solve your own problem</em></u>

Answer:

<em>The maximum height is 0.10 meters</em>

Explanation:

<u>Energy Transformation</u>

It's referred to as the change of one energy from one form to another or others. If we compress a spring and then release it with an object being launched on top of it, all the spring (elastic) potential energy is transformed into kinetic and gravitational energies. When the object stops in the air, all the initial energy is now gravitational potential energy.

If a spring of constant K is compressed a distance x, its potential energy is

\displaystyle P_E=\frac{Kx^2}{2}

When the launched object (mass m) reaches its max height h, all that energy is now gravitational, which is computed as

U=mgh

We have then,

U=P_E

\displaystyle mgh=\frac{Kx^2}{2}

Solving for h

\displaystyle h=\frac{Kx^2}{2mg}

We have little data to work on the problem, so we'll assume some values to answer the question and help to solve the problem at hand

Let's say: x=0.2 m (given), K=100 N/m, m=2 kg

Computing the maximum height

\displaystyle h=\frac{(100)0.2^2}{2(2)(9.8)}

\displaystyle h=\frac{4}{39.2}=0,10\ m

The maximum height is 0.10 meters

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A 25.0 kg box of textbooks rests on a loading ramp that makes an angle α with the horizontal. The coefficient of kinetic frictio
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Answer:

The minimum angle at which the box starts to slip (rounded to the next whole number) is α=19°

Explanation:

In order to solve this problem we must start by drawing a sketch of the problem and its corresponding fre body diagram (See picture attached).

So, when we are talking about friction, there are two types of friction coefficients. Static and kinetic. Static friction happens when the box is not moving no matter what force you apply to it. You get to a certain force that is greater than the static friction and the box starts moving, it is then when the kinetic friction comes into play (kinetic friction is generally smaller than static friction). So in order to solve this problem, we must find an angle such that the static friction is the same as the force applie by gravity on the box. For it to be easier to analyze, we must incline the axis of coordinates, just as shown on the picture attached.

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when solving for the static friction we get:

f_{s}=W_{x}

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we can substitute this on our sum of forces equation:

f_{s}=mg sin \alpha

the static friction will depend on the normal force applied by the plane on the box, static friction is found by using the following equation:

f_{s}=N\mu_{s}

so we can substitute this on our equation:

N\mu_{s}=mg sin \alpha

but we don't know what the normal force is, so we need to find it by doing a sum of forces in y.

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when solving for N we get:

N=W_{y}

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we can go ahead and substitute this equation in the sum of forces in x equation so we get:

mg cos \alpha \mu_{s}=mg sin \alpha

we can divide both sides of the equation into mg so we get:

cos \alpha \mu_{s}=sin \alpha

as you may see, the angle doesn't depend on the mass of the box, only on the static coefficient of friction. When solving for \mu_{s} we get:

\mu_{s}=\frac{sin \alpha}{cos \alpha}

when simplifying this we get that:

\mu_{s}=tan \alpha

now we can solve for the angle so we get:

\alpha= tan^{-1}(\mu_{s})

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\alpha= tan^{-1}(0.350)

which yields:

α=19.29°

which rounds to:

α=19°

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