Question

A thin plastic strip is stretched by hanging 100g masses on its end. When the total hanging mass of the strip is less than 0.800 kg, the elongation of the strip is proportional to the stretching force. When the hanging mass is exactly 0.800 kg, the elongation of the strip is 14 cm. As more mass is hung from it, the plastic becomes more flexible but ends up breaking when the total mass hanging from it is 1.2 kg and it has lengthened up to 30 cm, without recovering its original shape.

a. Sketch a force-distance curve that represents the behavior of the plastic strip.
b. Estimate the total work done to stretch the plastic: i. 14cm ii. 30cm.
c. Suggest what happens to the energy transferred during the stretch of the plastic.

Answer 1

The force-distance curve representing the behavior of the plastic strip will increase up to a certain point, and then decrease as the strip breaks. The total work done to stretch the plastic can be estimated using the formula Work = Force * Distance. The energy transferred during the stretch of the plastic is converted into potential energy stored in the strip.

Step-by-step explanation:

To sketch a force-distance curve that represents the behavior of the plastic strip, you can plot the elongation of the strip on the y-axis and the hanging mass on the x-axis. As the mass increases, the elongation of the strip will also increase. However, at a hanging mass of 0.800 kg, the elongation is 14 cm, indicating a point of maximum elongation. After this point, the plastic strip starts to break and does not recover its original shape. Therefore, the force-distance curve will show an increase in elongation up to a certain point, and then a decrease as the plastic strip breaks.

To estimate the total work done to stretch the plastic, you can use the formula:

• Work = Force * Distance

i. For an elongation of 14 cm, the work done can be calculated as:

• Work = Force * Distance = (0.8 kg * 9.8 m/s^2) * 0.14 m = 1.1136 J

ii. For an elongation of 30 cm, the work done can be calculated as:

• Work = Force * Distance = (1.2 kg * 9.8 m/s^2) * 0.3 m = 3.528 J

The energy transferred during the stretch of the plastic is converted into work done to stretch the plastic. This energy is stored in the plastic strip as potential energy. As the plastic strip breaks, this potential energy is released in the form of kinetic energy and sound energy.