Can someone tell me how to do half life or something because I am so confused and it is due in a couple of hours

A large crate with mass m rests on a horizontal floor. The static and kinetic coefficients of friction between the crate and the

rjkz [21]

Answer:

a) $F=\frac{\mu_{k}mg}{cos \theta-\mu_{k}sin \theta}$

b) $\mu_{s}=\frac{Fcos \theta}{Fsin \theta +mg}$

Explanation:

In order to solve this problem we must first do a drawing of the situation and a free body diagram. (Check attached picture).

After a close look at the diagram and the problem we can see that the crate will have a constant velocity. This means there will be no acceleration to the crate so the sum of the forces must be equal to zero according to Newton's third law. So we can build a sum of forces in both x and y-direction. Let's start with the analysis of the forces in the y-direction:

$\Sigma F_{y}=0$

We can see there are three forces acting in the y-direction, the weight of the crate, the normal force and the force in the y-direction, so our sum of forces is:

$-F_{y}-W+N=0$

When solving for the normal force we get:

$N=F_{y}+W$

we know that

W=mg

and

$F_{y}=Fsin \theta$

so after substituting we get that

N=F sin θ +mg

We also know that the kinetic friction is defined to be:

$f_{k}=\mu_{k}N$

so we can find the kinetic friction by substituting for N, so we get:

$f_{k}=\mu_{k}(F sin \theta +mg)$

Now we can find the sum of forces in x:

$\Sigma F_{x}=0$

so after analyzing the diagram we can build our sum of forces to be:

$-f+F_{x}=0$

we know that:

$F_{x}=Fcos \theta$

so we can substitute the equations we already have in the sum of forces on x so we get:

$-\mu_{k}(F sin \theta +mg)+Fcos \theta=0$

so now we can solve for the force, we start by distributing $\mu_{k}$ so we get:

$-\mu_{k}F sin \theta -\mu_{k}mg)+Fcos \theta=0$

we add $\mu_{k}mg$ to both sides so we get:

$-\mu_{k}F sin \theta +Fcos \theta=\mu_{k}mg$

Nos we factor F so we get:

$F(cos \theta-\mu_{k} sin \theta)=\mu_{k}mg$

and now we divide both sides of the equation into $(cos \theta-\mu_{k} sin \theta)$ so we get:

$F=\frac{\mu_{k}mg}{cos \theta-\mu_{k}sin \theta}$

which is our answer to part a.

Now, for part b, we will have the exact same free body diagram, with the difference that the friction coefficient we will use for this part will be the static friction coefficient, so by following the same procedure we followed on the previous problem we get the equations:

$f_{s}=\mu_{s}(F sin \theta +mg)$

and

F cos θ = f

when substituting one into the other we get:

$F cos \theta=\mu_{s}(F sin \theta +mg)$

which can be solved for the static friction coefficient so we get:

$\mu_{s}=\frac{Fcos \theta}{Fsin \theta +mg}$

which is the answer to part b.

3 0

3 years ago

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Use Hooke's Law to determine the work done by the variable force in the spring problem. Nine joules of work is required to stret

natima [27]

Answer:

29.16 J

Explanation:

From Hook's law,

W = 1/2(ke²)..................... Equation 1

Where W = work done, k = Spring constant, e = extension.

Given: W = 9 J, e = 0.5 m.

Substitute into equation 1

9 = 1/2(k×0.5²)

Solve for k

k = 18/0.5²

k = 72 N/m.

The work done required to stretch the spring by additional 0.4 m is

W = 1/2(72)(0.4+0.5)²

W = 36(0.9²)

W = 29.16 J.

6 0

3 years ago

A teacher discusses a scientific theory that has been in place for almost a century. which would present the greatest challenge

Umnica [9.8K]

Answer: The theory might have become Obsolete or Superseded

Explanation:

A theory becomes obsolete or superseded if it becomes inadequate, false or incomplete in how its describes reality. It does not matter if it was once accepted. There are some theories such as Lysenkoism that are currently described as being obsolete because it does not conform to current reality. Another example of a theory that was superseded is the phlogiston theory. It was replaced a different theory of energy.

3 0

3 years ago

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The width of a nuclear state is found to be 10^-2 ev. The corresponding lifetime of this state is?

Lelechka [254]

The width of a nuclear state is found to be 10^-2 ev. The corresponding lifetime are called Reconstruction debate that had federalism debate that had been an issue since the 1790s.

Reconstruction failed by most other measures: Radical Republican legislation ultimately nuclear to protect former slaves from white persecution and failed to engender fundamental changes to the social fabric of the South. When President Rutherford B. federalism debate that had been an issue since the 1790s almost mediately . Hayes removed federal troops from the South in 1877, former Confederate officials and slave returned to nuclear the support of a conservative Supreme Court, these newly empowered white southern politicians passed black codes, voter qualifications, and other anti-progressive legislation to reverse the rights that blacks had gained during Radical Reconstruction. The U.S. Supreme Court bolstered this federalism anti-progressive movement federalism with decisions in the Slaughterhouse Cases, the Civil Rights Cases, and United States v.

Learn more about Reconstruction on:

brainly.com/question/24761999

#SPJ4

7 0

2 years ago

Use the equation d = m/v [stack fraction), where d= density, m= mass, and v

sladkih [1.3K]

Answer:

54.

Explanation:

6 (v) x 9 (m) = 54.

54 (m) / 6 (v) = 9 (d)

5 0

4 years ago