To investigate the tension in cables at various angles

• 500 hook mass
• string
• 2 10 N scales
• protractor or angle card

• Hang your mass from one of the spring scales.  Record the reading on the scale.  How does this reading compare to the weight of your mass?
• Hang the string from the two spring scales.  Hang the hook mass from the string.  Hold the two spring scales vertically and record the reading on each.  How do the readings compare to the weight of the mass?
• Hang your mass from one of the spring scales.  Record the reading on the scale.  How does this reading compare to the weight of your mass?
• Hang the string from the two spring scales.  Hang the hook mass from the string.  Hold the two spring scales vertically and record the reading on each.  How do the readings compare to the weight of the mass?
• Gradually increase the angle between the two sides of the string while noting the readings on the spring scales.  What happens to the tension in the string as you increase the angle?
• Tape your angle card, or protractor, to the wall.  Use it to hold the string at the following angles by lining the strings up with the lines on your card: 30 degrees, 60 degrees, 90 degrees, 120 degrees, and 150 degrees.  Be sure to line up the mass as well as the strings with the lines on your card.  (HINT: When your strings are correctly aligned, the readings on the spring scales should be the same.)  Record the readings on the scales in a data table.
• Draw a vector diagram for each set of data.  Break the tension in each half of the string into perpendicular components—one that is horizontal and one that is vertical.  Solve for the magnitude of each component.  Be sure to show and label your work neatly.
• Record the sum of your vertical components for each angle in your data table.  

1. How does the sum of the vertical components compare to the weight of the mass?
2. Is your mass in equilibrium?  Give evidence to support your answer.
3. What happens to the horizontal component as the angle increases?
4. Explain in terms of tension why high-voltage wires are allowed to sag between towers.

• I usually do the first 3 steps as a demonstration and have students work along with me using their own equipment.
• I make “angle cards” by hand as I think copying them will change the dimensions. (See below)
• I also demonstrate how to hang these on the wall with the arrow pointing straight down. I use the string and weight as a plumb bob.
• Finally, I demonstrate how to align the string with the angle card and to adjust the spring scales until they have the same reading.
• Really, this activity is about breaking force vectors into components. (Students have to draw the vector diagrams and show work for each angle.) My students really benefit from this. They understand better how to sum forces for an object in equilibrium.
• You could definitely add a conclusion or application.