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3 years ago

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A group of physics students hypothesize that for an experiment they are performing, the speed of an object sliding down an incli

ned plane will be given by the expression v=2gd(sin(θ)−μkcos(θ))−−−−−−−−−−−−−−−−−−√. For their experiment, d=0.725meter, θ=45.0∘, μk=0.120, and g=9.80meter/second2. Use your calculator to obtain the value that their hypothesis predicts for v.

2 answers:

goblinko [34]3 years ago

6 0

Answer:

v = 2.974

Explanation:

Perhaps the formula should be

v = √(2*g*d (sin(θ) - uk*cos(θ) ) This is a bit easier to read.

v = √(2* 9.80*0.725(0.707 - 0.12*0.707) ) Substitute values. Find 2*g*d

v = √14.21 * (0.707 - 0.0849) Figure out Sin(θ) - uk cos(θ)

v = √14.21 * (0.6222)

v = √8.8422 Take the square root of the value

v = 2.974

Tju [1.3M]3 years ago

6 0

Answer:

$v = 2.97 m/s$

Explanation:

As we know that the velocity expression for the given experiment is

$v = \sqrt{2gd(sin\theta - \mu_kcos\theta)}$

now we know that

d = 0.725 m

$\theta = 45 ^o$

$\mu_k = 0.120$

$g = 9.80$

now we have

$v = \sqrt{2(9.80)(0.725)(sin45 - 0.120cos45)}$

$v = 2.97 m/s$

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This is a problem easily solve using energy conservation. As there are no non-conservative forces, we know that the energy is conserved.

When the spring is compressed downward, the spring has elastic potential energy. When the spring is relaxed, there is no elastic potential energy, but the pellet will have gained gravitational potential energy and kinetic energy. Lets see what are the terms for each of this.

<h3>Elastic potential energy</h3>

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So, the elastic energy of the compressed spring is:

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<h3>Gravitational potential energy</h3>

To see how much gravitational potential energy will the pellet win, we can use

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where m is the mass of the pellet, g is the acceleration due to gravity and \Delta h is the difference in height.

Taking all this together, the gravitational potential energy when the spring is relaxed will be:

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We know that the kinetic energy for a mass m moving at speed v is:

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