1. Tension Problems

2. How To Solve Tension Problems
Follow 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.

3. How To Solve Tension Problems
Follow 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.

4. How To Solve Tension Problems
Follow 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.

5. Tension Practice – We Do
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

6. Tension Practice – We Do
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
FIRST:
Think about what is going on in the problem.
What do you know about the system and about how the blocks will move?

7. Tension Practice – We Do
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
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 g block will move down.
What’s our next step?

8. Tension Practice – We Do
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
Draw free body diagrams for each mass.
What’s next?

9. Tension Practice – We Do
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
Start your equation with the forces that are in the same direction as acceleration, and minus the forces that are in opposite direction.
Note: Order is important!
Add the forces on each mass, and set = ma.
1st Equation
Fnet = ma
T – mg = ma
T – 0.9 = 0.09 a
2nd Equation
Fnet = ma
mg – T= ma
1.1 – T = 0.11a
What’s next?

10. Tension Practice – We Do
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
Set the two Ts equal to each other to solve a.
1st Equation
Fnet = ma
T – mg = ma
T – 0.9 = 0.09 a
2nd Equation
Fnet = ma
mg – T= ma
1.1 – T = 0.11a
What’s next?
0.09a = 1.1 – 0.11a
a = 1 m/s2

11. Tension Practice – We Do
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
Plug a into either equation to solve T.
1st Equation
Fnet = ma
T – mg = ma
T – 0.9 = 0.09 a
2nd Equation
Fnet = ma
mg – T= ma
1.1 – T = 0.11a
0.09a = 1.1 – 0.11a
a = 1 m/s2
T = 1.1 – 0.11a = 1.1 – 0.11(1) T = 0.99 N

12. Tension Practice – We Do
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?

13. Tension Practice – We Do
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.
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?

14. Tension Practice – We Do
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?
Next: Draw free-body diagrams for each object
What’s our next step?

15. Tension Practice – We Do
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?
Add up the forces and set = ma
1st Equation 2nd Equation
Fnet = ma Fnet = ma
T = 10a – T = 40a
What’s our next step?

16. Tension Practice – We Do
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?
Set the two T s equal to each other.
1st Equation 2nd Equation
Fnet = ma Fnet = ma
T = 10a – T = 40a
50 – T = 40a
50 – 10a = 40a
What’s our next step?

17. Tension Practice – We Do
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?
Solve for a then solve for t.
1st Equation 2nd Equation
Fnet = ma Fnet = ma
T = 10a – T = 40a
50 – T = 40a
50 – 10a = 40a
a = 1 m/s T = 10a = 10 N

18. Check your understanding

19. Check your understanding
Tension is equal in all parts of a rope.

20. Tension Practice – You Do
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

21. Tension Practice – You Do
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 = 200N
and
T1X + T2X – T3 = 0
T1Y + 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 = N
T2 = 79.0 N
T3 = 200 N

22. Tension Practice – You Do
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 = T
and
M2a = M2g - T
Set the Ts equal.
T = 30 N
a = 3.3 m/s2