Kinetic energy of an object is equal to

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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Which statement is true of a mechanical wave?

svet-max [94.6K]

It must have a medium. It must travel in empty space. Mechanical waves are waves which needs medium of propogation.

7 0

1 year ago

Which takes place as water cycles from the bottom of the pot toward the top?

Elenna [48]

The option that takes place as water cycles from the bottom of the pot toward the top is that A. thermal energy is transferred.
As the pot gets warmer and warmer, the heat flows everywhere inside the pot, ultimately reaching the top, and heating the water at the top as well. There is no chemical energy here, and molecules don't gain thermal energy, it is just transferred to the top of the pot.

8 0

3 years ago

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Why smartphone and computer are called modern technology?

topjm [15]

Answer:

Hey

I am sure from what i know that your answer should be the following:

Modern technology is deeply tied to efficiancy and speed. Think of the knew 5G network it gives us very fast internet, or perhaps our very nessisitys such as our phone or cumputer. On a phone you have so much (thats to say you can acces alot easly); pictures videos dictionarys video games etc etc.

6 0

2 years ago

If Abdul pedals his 20 kg bike with a force of 100 N, what will the bike’s acceleration be? The formulas above may be helpful in

Scorpion4ik [409]

Answer:

5 m/s/s

Explanation:

F = ma

100 = 20a

100/20 = a

a = 5 m/s/s

4 0

3 years ago