FORCES IN TWO DIMENSIONS · EQUILIBRIUM & THE EQUILIBRANT §An object is in equilibrium when the...
Transcript of FORCES IN TWO DIMENSIONS · EQUILIBRIUM & THE EQUILIBRANT §An object is in equilibrium when the...
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FORCES IN TWO DIMENSIONS
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EQUILIBRIUM & THE EQUILIBRANT
§ An object is in equilibrium when the net force on it is zero§ Object is motionless or moves with a
constant velocity§ Equilibrant: a single, additional force that is
exerted on an object to produce equilibrium§ To find the equilibrant: find the sum of the 2
forces exerted on the object
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What is the relationship between the equilibrant and the resultant vector?§ Equilibrant is the same magnitude
but opposite direction as the sum of all the forces acting on an object
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§ One way of determining the net force involves vector resolution (vector components)§ Recall:
§ Ax = Acosθ§ Ay = Asinθ§ R2 = Ax
2 + Ay2
§ θ = tan-1(y/x)
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ANALYZE A HANGING SIGN
§ Common example of object in static equilibrium are hanging signs
§ Ex: A sign is held up by two ropes with a tension of 50 N and the angle that each cable makes with the horizontal is known to be 30°. What is the weight of the sign?1. Determine the components of the
tensions2. Sum of the two Ay component is equal
to the weight (mg) of the sign
25 N + 25 N = 50 NWeight of sign = 50 N
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YOU TRY!
A picture frame hanging on a wall is held by two ropes each pulling with a force of 30 N with an angle of 45° with respect to the horizontal. What is the weight of the picture frame?
§ 42.4 NWhat is the picture frame’s mass?§ 4.33 kg
Two ropes pull on a ring. One exerts a 62 N force at 30.0°, the other a 62 N force at 60.0°. What is the resultant net force on the ring?*
§ 120 N
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How About This One?§ A sign is symmetrically hung by two ropes. The sign is known to have
a mass of 5 kg and the angle between the two ropes is 100°. What is the tension on each cable?§ 38.1 N
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MOTION ALONG AN INCLINED PLANE
Which direction does the gravitational force on the object point?§Toward the center of the Earth in a downward
direction; Fg = mg
In which direction is normal force?
§ Perpendicular to the surface
You can break up Fg into components (Fgx, Fgy)§ y-component = what is pushing the object into
the surface§ x-component = force that is trying the
accelerate the object along the incline
Fg
θ Fgy
Fgx
FN
Fgx
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§ If Fgy tells us what is pushing the object into the surface, what is the relationship between Fgy and FN?§ They are equal in magnitude
Fg
θ Fgy
Fgx
FN
Fgy = Fg cos θ Fgx = Fg sin θ
θ
It’s important to choose your coordinate plane (to indicate + and – axis)
+x
+y
These angles
are the same (aka F⟂ or Fperp)(aka FII or Fpara)
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SAMPLE PROBLEMA 562 N crate is resting on a plane inclined 30.0 above the horizontal. Find the components of the crate’s weight that are parallel and perpendicular to the plane.Given:§ Fg = 562 N§ θ = 30.0°Unknown:§ Fgx = ?§ Fgy = ?
Equation:§ Fgy = Fg cos θ § Fgx = Fg sin θSubstitute & Solve:§ Fgy = Fg cos θ = 562 cos 30° = 487 N
= - 487 N § Fgx = Fg sin θ = 562 sin 30° = 281 N
= - 281 N
Fgx and Fgy are negative because they point in directions opposite to the positive axes
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YOU TRY!
§ Scott and Becca are moving a folding table out of the sunlight. A cup of lemonade with a mass of 0.44 kg is on the table. Scott lifts his end of the table before Becca does, and as a result, the table makes an angle of 15.0° with the horizontal. Find the components of the cup's weight that are parallel and perpendicular to plane of table. § Fgx (parallel) = 1.1N ; Fgy (perpendicular) = 4.2 N
§ Fernando, who has a mass of 43.0 kg, slides down the banister at his grandparents’ house. If the banister makes an angle of 35.0° with the horizontal, what is the normal force between Fernando and the banister?§ 345 N
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Consider the crate in the incline in the Sample Problem.Calculate the magnitude of the acceleration.§ 4.90 m/s2
After 4.00 s, how fast would the trunk be moving?§ 19.6 m/s