[sr2123]

A parcel of mass 5kg lies or a rough plane inclined at an angle (alpha) to the horizontal, where tan (alpha) = 3/4. The parcel is held in equilibrium by the action of a horizontal force of magnitude 20N. The force acts in a vertical plane through a line of greatest slope of the plane. The parcel is on the point of sliding down the plane.

a) Find the coefficient of friction between the parcel and the plane.

[Mr M]

So what have you done so far?

[TenOfThem]

(Original post by Mr M)
So what have you done so far?

Joined TSR and asked for help

[TenOfThem]

(Original post by sr2123)
A parcel of mass 5kg lies or a rough plane inclined at an angle (alpha) to the horizontal, where tan (alpha) = 3/4. The parcel is held in equilibrium by the action of a horizontal force of magnitude 20N. The force acts in a vertical plane through a line of greatest slope of the plane. The parcel is on the point of sliding down the plane.

a) Find the coefficient of friction between the parcel and the plane.

Have you drawn a diagram and written in all the forces

[sr2123]

(Original post by Mr M)
So what have you done so far?

Nothing

[bhogs001]

(Original post by Mr M)
So what have you done so far?

Can I just say, your help on the GCSE thread was greatly appreciated.

[Claree]

(Original post by sr2123)
A parcel of mass 5kg lies or a rough plane inclined at an angle (alpha) to the horizontal, where tan (alpha) = 3/4. The parcel is held in equilibrium by the action of a horizontal force of magnitude 20N. The force acts in a vertical plane through a line of greatest slope of the plane. The parcel is on the point of sliding down the plane.

a) Find the coefficient of friction between the parcel and the plane.

Draw a diagram with everything you know so far. (include friction)

Hints:

Spoiler:

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To label the angles, work out what cos(alpha) and sin(alpha) are using the value of tan(alpha). If you're stuck, try drawing a right angled triangle with opposite side=3 and adjacent side=4.

Spoiler:

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Resolve the forces parallel and perpendicular to the surface to get an equation for R (the normal reaction).

As the particle is in equilibrium, what does this tell you about f=ma=?

Spoiler:

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0

Spoiler:

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What does the fact that the particle is on the point of sliding down the plane tell you about the frictional force F?

Spoiler:

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Use the equation F(max)=coefficient of friction*R

[raheem94]

(Original post by sr2123)
Nothing

Use this below diagram:


As the question says that the particle is on the point of moving down the plane, hence the friction will be upwards because friction always opposes motion.

You know that tantheta = 3/4 so you can easily find the values for costheta and sintheta, by making a triangle.

Next, resolve the force perpendicular to the plane to find the normal reaction.

Now, resolve the forces parallel to the plane to find friction. Remember that the particle is in equilibrium hence acceleration is zero.

Next, use to find the the coefficient of friction.

[sr2123]

How can I work out the values of cos and sin (alpha) using tan (alpha)...sorry, im not understanding this

[TenOfThem]

Well, you can use a calculator if you need to


However, as has already been explained, you can draw a right angled triangle and write in the OPPOSITE and ADJACENT from your Tan ratio

Pythagoras will furnish you with the HYPOTENUSE and, therefore Sin and Cos

[raheem94]

(Original post by sr2123)
How can I work out the values of cos and sin (alpha) using tan (alpha)...sorry, im not understanding this

See the diagram below:



From the above diagram you can easily find the values of sin and cos. But first find the hypotenuse of the triangle.

[Claree]

(Original post by raheem94)
See the diagram below:



From the above diagram you can easily find the values of sin and cos. But first find the hypotenuse of the triangle.

Just wondering, how do you draw your diagrams on the computer and get them onto a TSR post?

[sr2123]

(Original post by raheem94)
See the diagram below:



From the above diagram you can easily find the values of sin and cos. But first find the hypotenuse of the triangle.

What would the hypotenuse be?

+ where did u get the numbers 3 & 4?

[sr2123]

What would the hypotenuse be?

+ where did you get the numbers 3 & 4?

[TenOfThem]

(Original post by sr2123)
What would the hypotenuse be?

+ where did you get the numbers 3 & 4?

Do you not know how to use Pythagoras?

You were given Tan = 3/4

[raheem94]

(Original post by sr2123)
What would the hypotenuse be?

+ where did you get the numbers 3 & 4?

Tantheta equal 3/4. It means that the opposite is 3 and base is 4.
Now use phythagoras theorem to find hypotenuse.

[TenOfThem]

(Original post by Claree)
Just wondering, how do you draw your diagrams on the computer and get them onto a TSR post?

You can use any drawing tool (paint is one) and then save as an image ... then use the insert image link above

[TenOfThem]

(Original post by raheem94)
Tantheta equal 3/4. It means that the opposite is 3 and base is 4.

Adjacent rather than base

[raheem94]

(Original post by Claree)
Just wondering, how do you draw your diagrams on the computer and get them onto a TSR post?

I use adobe photoshop to draw the diagrams. I upload them on imageshack to post here.

[sr2123]

Im not familiar with there being an unknown angle, could someone please go through the question step by step....it's really important that I understand this.