How To Solve Tension Problems F ollow the same procedure as other force problems but keep in mind 1 Draw a free body diagram for EACH object or for each junction in a rope How To Solve Tension Problems ID: 216086
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Slide1
Tension ProblemsSlide2
How To Solve Tension Problems
F
ollow the same procedure as other force problems, but keep in mind:
1) Draw a free body diagram for EACH object or for each junction in a rope.Slide3
How To Solve Tension Problems
F
ollow the same procedure as other force problems, but keep in mind:
1) Draw a free body diagram for EACH object or for each junction in a rope.
2) Remember that the tension on opposite sides of a rope is equal and opposite.Slide4
How To Solve Tension Problems
F
ollow the same procedure as other force problems, but keep in mind:
1) Draw a free body diagram for EACH object or for each junction in a rope.
2) Remember that the tension on opposite sides of a rope is equal and opposite.3) Create a system of equations – write force equations for each object / rope and set them equal to each other.Slide5
Two blocks are connected by a string and pulley as shown. Assuming that the string and pulley are massless, find
a) the magnitude of the acceleration of each block
b) Tension force on the blocks
Tension Practice – We DoSlide6
Two blocks are connected by a string and pulley as shown. Assuming that the string and pulley are massless, find
a) the magnitude of the acceleration of each block
b) Tension force on the blocks
Tension Practice – We Do
FIRST: Think about what is going on in the problem.
What do you know about the system and about how the blocks will move?Slide7
Two blocks are connected by a string and pulley as shown. Assuming that the string and pulley are massless, find
a) the magnitude of the acceleration of each block
b) Tension force on the blocks
Tension Practice – We Do
There is just one rope, so the tension on each side is equal.The two blocks will have the same acceleration (because they are connected), but the direction of the acceleration will be different.
90g block will move up. 110 g block will move down.
What’s our next step?Slide8
Two blocks are connected by a string and pulley as shown. Assuming that the string and pulley are massless, find
a) the magnitude of the acceleration of each block
b) Tension force on the blocks
Tension Practice – We Do
Draw free body diagrams for each mass.
What’s next?Slide9
Two blocks are connected by a string and pulley as shown. Assuming that the string and pulley are massless, find
a) the magnitude of the acceleration of each block
b) Tension force on the blocks
Tension Practice – We Do
Add the forces on each mass, and set = ma.
What’s next?
1
st
Equation
F
net
= ma
T – mg = ma
T –
0.9
= 0.09 a
2
nd
Equation
F
net
= ma
mg
– T= ma
1.1 – T =
0.11aSlide10
Two blocks are connected by a string and pulley as shown. Assuming that the string and pulley are massless, find
a) the magnitude of the acceleration of each block
b) Tension force on the blocks
Tension Practice – We Do
Set the two Ts equal to each other to solve a.
What’s next?
1
st
Equation
F
net
= ma
T – mg = ma
T – 0.9 = 0.09 a
2
nd
Equation
F
net
= ma
mg
– T= ma
1.1 – T =
0.11a
0.09a + 0.9 = 1.1 – 0.11a
a
= 1
m/s
2Slide11
Two blocks are connected by a string and pulley as shown. Assuming that the string and pulley are massless, find
a) the magnitude of the acceleration of each block
b) Tension force on the blocks
Tension Practice – We Do
Plug a into either equation to solve T.
1
st
Equation
F
net
= ma
T – mg = ma
T – 0.9 = 0.09 a
2
nd
Equation
F
net
= ma
mg
– T= ma
1.1 – T =
0.11a
0.09a + 0.9 = 1.1 – 0.11a
a
= 1
m/s
2
T = 1.1 – 0.11a = 1.1 – 0.11(1)
T =
0.99 N Slide12
A 10-kg block is connected to a 40-kg block as shown in the figure. The surface on which the blocks slide is frictionless. A force of 50 N pulls the blocks to the right.
a) What is the magnitude of the acceleration of the 40-kg block?
b) What is the magnitude of the tension T in the rope that connects the two blocks?
Tension Practice – We Do
FIRST:
Think about what is going on in the problem.
What do you know about the system and about how the blocks will move?Slide13
A 10-kg block is connected to a 40-kg block as shown in the figure. The surface on which the blocks slide is frictionless. A force of 50 N pulls the blocks to the right.
a) What is the magnitude of the acceleration of the 40-kg block?
b) What is the magnitude of the tension T in the rope that connects the two blocks?
Tension Practice – We Do
FIRST:
Think about what is going on in the problem.
Tension is equal and opposite because they are connected by the same rope.
Acceleration is the same (b/c connected)
What’s our next step?Slide14
A 10-kg block is connected to a 40-kg block as shown in the figure. The surface on which the blocks slide is frictionless. A force of 50 N pulls the blocks to the right.
a) What is the magnitude of the acceleration of the 40-kg block?
b) What is the magnitude of the tension T in the rope that connects the two blocks?
Tension Practice – We Do
Next: Draw free-body diagrams for each object
What’s our next step?Slide15
A 10-kg block is connected to a 40-kg block as shown in the figure. The surface on which the blocks slide is frictionless. A force of 50 N pulls the blocks to the right.
a) What is the magnitude of the acceleration of the 40-kg block?
b) What is the magnitude of the tension T in the rope that connects the two blocks?
Tension Practice – We Do
Add up the forces and set = ma
What’s our next step?
1
st
Equation
2
nd
Equation
F
net
=
ma
F
net
=
ma
T =
10a
50
– T = 40a Slide16
A 10-kg block is connected to a 40-kg block as shown in the figure. The surface on which the blocks slide is frictionless. A force of 50 N pulls the blocks to the right.
a) What is the magnitude of the acceleration of the 40-kg block?
b) What is the magnitude of the tension T in the rope that connects the two blocks?
Tension Practice – We Do
Set the two T s equal to each other.
What’s our next step?
1
st
Equation
2
nd
Equation
F
net
=
ma
F
net
=
ma
T =
10a
50
– T =
40a
50 – T = 40a
50 – 10a = 40a
Slide17
A 10-kg block is connected to a 40-kg block as shown in the figure. The surface on which the blocks slide is frictionless. A force of 50 N pulls the blocks to the right.
a) What is the magnitude of the acceleration of the 40-kg block?
b) What is the magnitude of the tension T in the rope that connects the two blocks?
Tension Practice – We Do
Solve for a then solve for t.
1
st
Equation
2
nd
Equation
F
net
=
ma
F
net
=
ma
T =
10a
50
– T =
40a
50 – T = 40a
50 – 10a = 40a
a = 1 m/s
2
T = 10a = 10 NSlide18
Check your understandingSlide19
Check your understanding
Tension is equal in all parts of a rope.Slide20
Find the tension in each cable.
2) Find the tension in each cable and the acceleration of the blocks. M
1
= 10 kg, and M
2 = 5 kgTension Practice – You DoSlide21
Find the tension in each cable.
Tension Practice – You Do
Strategy: Draw the free body diagrams for the weight and for the middle junction. Add the forces and set = 0. (no a). You will find
T
3
= 200N
a
nd
T
1X
+ T
2X
– T
3
= 0
T
1Y
+ T
2Y
– T
3
= 0 (you will need to use trig)
Then, you’ll have to solve for one of the
Ts
and plug into the other equation.
T
1
= 148.4 N
T
2
= 79.0 N
T
3
= 200 NSlide22
2) Find the tension in each cable and the acceleration of the blocks.
Tension Practice – You Do
Strategy: Draw the free body diagrams for
each weight. Add
the forces and set =
ma.
You
will find
M
1
a = T
and
M
2
a = M
2
g - T
Set the
Ts
equal.
T = 30 N
a = 3.3 m/s
2