Pulleys
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Pulleys Example Whiteboards - Atwood’s Machine Whiteboards - Inclined Plane M 1 M 2
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Pulleys. Example Whiteboards - Atwood’s Machine Whiteboards - Inclined Plane. M 1. M 2. Step 1 - guess direction of + acceleration (This becomes the + direction for each mass). +a. For the 5.0 kg mass, the tension T is up (-). T (-). The weight of 5*9.8 = 49 N is down (+):. +a. - PowerPoint PPT Presentation
Transcript of Pulleys
PulleysExampleWhiteboards - Atwood’s Machine
Whiteboards - Inclined PlaneM1
M2
Example - Find Tension, and acceleration if k = .11:
32.0 kg
5.0 kg
Step 2 - Calculate or express <F> = ma for every mass object
For the 5.0 kg mass, the tension T is up (-)
T (-)
+49 N
The weight of 5*9.8 = 49 N is down (+):
And our formula becomes:49 N - T = (5.0 kg)a
Step 1 - guess direction of + acceleration (This becomes the + direction for each mass)
+a
+a
Example - Find Tension, and acceleration if k = .11:
32.0 kg
5.0 kg
Step 1 - guess direction of + acceleration (This becomes the + direction for each mass)
+a
+a
Step 2 - Calculate or express <F> = ma for every mass object
49 N - T = (5.0 kg)a
The 32.0 kg mass has the tension T to the right (+)
T
And, assuming it is moving to the right, a frictional force of .11*32*9.8 = 34.496 N to the left (-)
-34.496 N
So our equation becomes:T - 34.496 N = (32.0 kg)a
And now it’s math time!!!!
Two equations, two unknowns! 49 N - T = (5.0 kg)a T - 34.496 N = (32.0 kg)a
49 N - T + T - 34.496 N = (5.0 kg)a + (32.0 kg)a 49 N - 34.496 N = (37 kg)aa = (49 N - 34.496 N)/37 kg = .392 m/s/sAnd plug into an equation to find T:T - 34.496 N = (32.0 kg)aT = (32.0 kg)(.392 m/s/s) + 34.496 N = 47.04 N
+
Add them Together!
Whiteboards: Atwood’s Machine
1 | 2 | 3 | 4 | 5
TOC
Find acceleration and tension
Green, Bananas never do W
5.0 kg3.0 kg
Massless frictionless pulley
Step 1 - Guess the direction of acceleration - This becomes the positive direction for each mass.
Uhh well um. the 5.0 kg is heavier.
+a
+a
Find acceleration and tension
T - 29.4 N = (3.0 kg)a W
5.0 kg3.0 kg
Massless frictionless pulley
Step 2 - Set up the <F>=ma for the 3.0 kg mass: T is up , and the weight is down. Down is - and up is +
weight = (3.0 kg)(9.8 N/kg) = 29.4 N down (- in this case)T is up, -29.4 is down: T - 29.4 N = (3.0 kg)a
+a
+a
Find acceleration and tension
49 N - T = (5.0 kg)a W
5.0 kg3.0 kg
Massless frictionless pulley
Step 3 - Set up the <F>=ma for the 5.0 kg mass: T is up , and the weight is down, but now down is + and up is -
weight = (5.0 kg)(9.8 N/kg) = 49 N down (+ in this case)T is up (-), 49 N is down (+): 49 N - T = (5.0 kg)a
+a
+a
Find acceleration and tension
2.45 m/s/s W
5.0 kg3.0 kg
Massless frictionless pulley
Step 4 - Solve for acceleration:49 N - T = (5.0 kg)aT - 29.4 N = (3.0 kg)a
49 N - T = (5.0 kg)a+T - 29.4 N = (3.0 kg)a
T - 29.4 N + 49 N - T = (8.0 kg)aa = 2.45 m/s/s
+a
+a
Find acceleration and tension
37 N W
5.0 kg3.0 kg
Massless frictionless pulley
Step 5- Solve for T:49 N - T = (5.0 kg)aT - 29.4 N = (3.0 kg)aa = 2.45 m/s/s
Pick one of the formulas, and plug the acceleration in:T - 29.4 N = (3.0 kg)aT = (3.0 kg)(2.45 m/s/s) + 29.4 N = 36.75 N = 37 N
+a
+a
Whiteboards: Pulleys on Inclined Planes
1 | 2 | 3 | 4 | 5
TOC
Find acceleration and tension
Hmmm. Coconuts? W
Step 1 - Guess the direction of acceleration. Let’s guess this way. (it’s wrong)
6.0 kg
11.0 kg
s = 0k = 0
30.0o
+a
+a
Find acceleration and tension
T - 58.8 N = (6.0 kg)a
Step 2 - Set up the equation for the 6.0 kg mass. T is positive (up), and the weight of the mass is down
6.0 kg
11.0 kg
s = 0k = 0
30.0o
+a
+a
Weight = (6.0 kg)(9.8 N/kg) = 58.8 N down (-)Tension T is up (+), so we haveT - 58.8 N = (6.0 kg)a
W
Find acceleration and tension
53.9 N - T = (11.0 kg)a
Step 3 - Set up the equation for the 11.0 kg mass. Remember, down the plane is now positive. You have the tension T up (-) the plane, and the parallel component of gravity down (+) the plane:
6.0 kg
11.0 kg
s = 0k = 0
30.0o
+a
+a
F|| = mgsin() = (11.0 kg)(9.8 N/kg)sin(30.0o) = 53.9 N down (+) the plane, Tension T is up the plane (-), so we have:53.9 N - T = (11.0 kg)a
W
Find acceleration and tension
a = -0.2882 m/s/s
Step 4 - Solve the math for the acceleration:53.9 N - T = (11.0 kg)aT - 58.8 N = (6.0 kg)a
6.0 kg
11.0 kg
s = 0k = 0
30.0o
+a
+a
53.9 N - T = (11.0 kg)a+T - 58.8 N = (6.0 kg)a
53.9 N - T + T - 58.8 N = (17.0 kg)a53.9 N - 58.8 N = (17.0 kg)aa = -0.2882 m/s/sWe guessed wrong!! it accelerates the other way!!!
W
Find acceleration and tension
57.1 N
Step 5 - Solve for the tension:53.9 N - T = (11.0 kg)aT - 58.8 N = (6.0 kg)aa = -0.2882 m/s/s
6.0 kg
11.0 kg
s = 0k = 0
30.0o
+a
+a
Plug into one of the equations:T - 58.8 N = (6.0 kg)aT = 58.8 N + (6.0 kg)(-0.2882 m/s/s) = 57.1 N
W
