Tension Problems

TENSION PROBLEMS

HOW TO SOLVE TENSION PROBLEMSFollow 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.



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.

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?



1) There is just one rope, so the tension on each side is equal.

2) The two blocks will have the same acceleration (because they are connected), but the direction of the acceleration will be different.

3) 90g block will move up. 110 g block will move down.

What’s our next step?



Draw free body diagrams for each mass.

What’s next?



Add the forces on each mass, and set = ma.

What’s next?

1st EquationFnet = ma T – mg = ma T – 0.9 = 0.09 a

2nd EquationFnet = ma mg – T= ma 1.1 – T = 0.11a



Set the two Ts equal to each other to solve a.

What’s next?


2nd EquationFnet = ma mg – T= ma 1.1 – T = 0.11a0.09a + 0.9 = 1.1 – 0.11a

a = 1 m/s2



Plug a into either equation to solve T.


2nd EquationFnet = ma mg – T= ma 1.1 – T = 0.11a0.09a + 0.9 = 1.1 – 0.11a

a = 1 m/s2T = 1.1 – 0.11a = 1.1 – 0.11(1) T = 0.99 N

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?


FIRST: Think about what is going on in the problem.

What do you know about the system and about how the blocks will move?




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)





Next: Draw free-body diagrams for each object





Add up the forces and set = ma


1st Equation 2nd EquationFnet = ma Fnet = maT = 10a 50 – T = 40a




Set the two T s equal to each other.



50 – T = 40a 50 – 10a = 40a




Solve for a then solve for t.


50 – T = 40a 50 – 10a = 40a

a = 1 m/s2 T = 10a = 10 N

CHECK YOUR UNDERSTANDING

CHECK YOUR UNDERSTANDING

Tension is equal in all parts of a rope.

1)Find the tension in each cable.

2) Find the tension in each cable and the acceleration of the blocks. M1 = 10 kg, and M2 = 5 kg

TENSION PRACTICE – YOU DO

1)Find the tension in each cable.


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 T3 = 200NandT1X + T2X – T3 = 0T1Y + T2Y – T3 = 0 (you will need to use trig)

Then, you’ll have to solve for one of the Ts and plug into the other equation.

T1 = 148.4 NT2 = 79.0 NT3 = 200 N

2) Find the tension in each cable and the acceleration of the blocks.


Strategy: Draw the free body diagrams for each weight. Add the forces and set = ma.

You will find M1a = TandM2a = M2g - T

Set the Ts equal.T = 30 Na = 3.3 m/s2

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Tension Problems