Download Product Instructions: Inclined Plane

Product Instructions: Inclined Plane
TI58760
www.timstar.co.uk [email protected]
01270 250459 01270 250601
Product Instructions: Inclined Plane
Assembly
Attaching the Pulley
Begin by screwing the boss into the hole on the front of the apparatus. Do NOT tighten this fully.
Slide the collar over the boss. If you cannot place the collar on without partially covering the hole
for the pulley, loosen the boss further.
Hole should not be blocked by collar
Do not fully tighten
Insert the pulley into the hole on the boss, and then tighten the boss so that the collar secures the
pulley firmly.
Fully tighten
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01270 250459 01270 250601
Product Instructions: Inclined Plane
Attaching the Protractor
The protractor has two slots on the bottom which align with two securing screws on the base of
the inclined plane.
On the inclined plane itself is a third screw that goes into the slot that runs along the curved edge
of the protractor.
Unscrew the nut and remove one of the washes from the side of the inclined plane.
Loosen the two screws on the side of the metal base, and rest the protractor on them, with the
scale on the protractor facing outwards. To do this, you’ll need to raise the inclined plane by
approximately 30°, and tilt the protractor away from the apparatus.
The screw on the side of the inclined plane should fit into the slot on the side of the protractor,
so the inclined plane can swing freely up and down, and the angle now read off the protractor.
Tighten the nuts on the base of the apparatus to hold the protractor securely upright.
Replace the washer and nut onto the screw on the side of the inclined plane, and this can be
tightened to secure the plane at the desired angle.
www.timstar.co.uk [email protected]
01270 250459 01270 250601
Product Instructions: Inclined Plane
Theory
Mass on an Incline
Consider a mass on an incline.
N
F
θ
θ
mg
There are three forces acting upon it:
Gravity:
Normal reaction:
=
cos
Friction:=
The force due to gravity is simply the mass of the object, multiplied by the acceleration due to
gravity, as per Newton’s second law.
The normal reaction is so-called because it is normal to the inclination of the surface. It varies
with the angle of the incline.
Finally, the friction is proportional to the normal reaction, with a proportionality constant µ which
is called the coefficient of friction.
If down the incline is considered the positive direction, the net force is therefore:
sin – = sin – =sin – cos
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01270 250459 01270 250601
Product Instructions: Inclined Plane
External Force
Now consider a cord attached to the mass on the incline, running over a frictionless pulley, with
another mass hanging free off the other end.
N
T
m2g
θ
F
m1g
The forces acting on the mass are now:
Gravity:
1
Normal reaction:
= 1 cos
Friction:
=
Tension:
= 2
If the tension in the cord is equal and opposite to the action of the weight along the incline:
1 cos – 2 =0
Then the friction will be zero. However:
If
1 cos – 2 <0 then >0
If
1 cos – 2 >0 then <0
This is because friction acts to oppose the motion along the surface.
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01270 250459 01270 250601
Product Instructions: Inclined Plane
Experiments
Frictionless Mass
Consider a mass on an incline, which has a zero coefficient of friction with the surface
(i.e. no friction). The mass is attached to a cord which runs over a frictionless pulley at the top of
the incline, and on the other end of the cord is a free-hanging mass.
N
T
m2g
θ
m1g
For a normal balance, the two masses would need to be the same in order for the system to be
in equilibrium.
However, only a component of the weight of 1 is acting to pull it down the incline, so the mass
of 2 only need be equal and opposite to the component of 1 acting along the incline.
2 = 1 sin
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01270 250459 01270 250601
Product Instructions: Inclined Plane
Record the weight of the roller, and setup the apparatus as illustrated.
Assume that the pulley and roller are frictionless.
Try to balance the rolling mass at different angles. Use the protractor to measure the angle, and
work out what mass you’ll require at the end of the cord to balance the two.
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01270 250459 01270 250601
Product Instructions: Inclined Plane
Determining the coefficient of Static Friction
Consider the following system:
N
T
F
m1g
m2g
If the mass 1 on the flat surface is not moving, despite the fact that on one side there is a cord
pulling the mass, then it means that the friction with the surface is acting in the opposite direction
and therefore keeping the mass stationary.
Because the mass is not moving, this is called static friction, and is given by the formula:
=
Because the surface is flat, the normal reaction is equal and opposite to the weight of 1, so:
=1
If 1 is stationary, then:
1 =1
So we can easily find the coefficient of static friction:
= 1 2
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01270 250459 01270 250601
Product Instructions: Inclined Plane
Use a block of material such as wood, and set up the apparatus as pictured below.
The protractor is not necessary for this experiment so it can be removed if desired.
Gradually add masses to the end of the cord until the block just starts to move, then remove the
last mass so the static friction is just stopping the mass from moving.
Record the amount of mass on the end of the cord 2, and the mass of the block of material 1.
The coefficient of static friction between this wooden block and the surface of the plane is
therefore:
= 1 2
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01270 250459 01270 250601
Product Instructions: Inclined Plane
Indirect Measurement of the Normal Reaction
Consider the following system:
T
N
m2g
θ
F
m1g
If the mass 1 is stationary, then:
1 sin + = 2
And we know
1 sin +
=
, so:
= 2
Or:
= 2 – 1 sin
If the mass is stationary, the net force acting upon it must be zero (Newton’s first law).
Therefore we can say that:
= 1 cos
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01270 250459 01270 250601
Product Instructions: Inclined Plane
Using the same setup as before, raise the inclined plane to an angle, and adjust the mass 2 so
that the mass 1 is just stationary.
At different angles, record the normal reaction, given by the equation derived on the previous
page. Use the value for static friction obtained in the previous experiment.
You will need to adjust the mass 2 when changing angle, to prevent the block from sliding.
10°
20°
If the mass is stationary, the net force acting upon it must be zero (Newton’s first law).
Therefore we can say that:
N = m1 g cos θ
Check that your measurements agree with this.
www.timstar.co.uk [email protected]
01270 250459 01270 250601