It is question about forces and equilibrium ?
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. 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.
(I'll let the acceleration be
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.
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.
- An object, previously at rest, slides #8 m# down a ramp, with an incline of #pi/12 #, and then slides horizontally on the floor for another #15 m#. If the ramp and floor are made of the same material, what is the material's kinetic friction coefficient?
- 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?
- If an object is moving at #16# #ms^-1# over a surface with a kinetic friction coefficient of #u_k=80/g#, how far will the object continue to move?
- A box with an initial speed of #2 m/s# is moving up a ramp. The ramp has a kinetic friction coefficient of #3/4 # and an incline of #(5 pi )/12 #. How far along the ramp will the box go?
- How fast will an object with a mass of #8 kg# accelerate if a force of #5 N# is constantly applied to it?

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