# It is question about forces and equilibrium ?

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A block of mass 20 kg is at rest on a plane inclined at 10◦ to the horizontal. A force acts on the block

parallel to a line of greatest slope of the plane. The coefficient of friction between the block and the

plane is 0.32. Find the least magnitude of the force necessary to move the block,

(i) given that the force acts up the plane,

(ii) given instead that the force acts down the plane.

A block of mass 20 kg is at rest on a plane inclined at 10◦ to the horizontal. A force acts on the block

parallel to a line of greatest slope of the plane. The coefficient of friction between the block and the

plane is 0.32. Find the least magnitude of the force necessary to move the block,

(i) given that the force acts up the plane,

(ii) given instead that the force acts down the plane.

Up the slope -

Down the slope -

Draw a forces diagram for these situations.

X is the force we exert up the slope.

Begin by resolving perpendicular to the slope using Newton's First Law (it is not accelerating into the slope).

To find friction:

Using

Resolve up the slope using Newton's Second Law.

(I'll let the acceleration be

Since we're looking for the minimal force to move the block, we can let

We take a similar scenario for when the force is acting down the slope.

Again, from Newton's First Law,

The difference comes when we resolve parallel to the slope using Newton's Second Law.

Let's resolve down the slope.

let

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See below.

i).

Resolving perpendicular to the plane:

Parallel to the plane:

Limiting equilibrium:

Let

Plugging in these values:

This is for limiting equilibrium, so:

ii).

Resolving perpendicular to the plane:

Parallel to the plane:

Limiting equilibrium:

Plugging in values:

This is for limiting equilibrium, so:

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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- Can you use Newton's third law to explain why a blown up but untied balloon will fly around the room when you let it go?
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