Question

A cylindrical cardboard tube 15 cm long contains 500 g of lead shots. When the tube is held vertical, the shots occupy 6 cm length of the tube. The tube is suddenly inverted so that the end which was above is now below and the shots fall to the other end of the tube. The process is repeated 200 times. Calculate the heat generated.

Answer 1

Hint: In this question we have been asked to calculate the heat generated in the given system. The system contains lead shots for 6 cm in a tube of 15 cm. The weight of the shots is 500 grams. We know that when the tube is suddenly inverted the shots from a height of 6 cm will drop to 15 cm. if this process is repeated 200 times, heat will be generated due to change in potential energy.
Formula Used: \[H=mgh\]
H is heat generated
M is the mass of the system
G is gravitational acceleration
H is the height \[(15-6)\]cm

Complete answer:
The lead shots are filled in the tube as shown in the figure below. Suddenly, the tube is inverted. The balls now go to the top point because of that. This process when repeated generates heat. This heat is generated because of the potential energy of the shots which increases 200 times.
             

Therefore, the heat generated can be given by the formula,
\[H=200\times mgh\]
After substituting the value
 We get,
\[H=200\times 0.5\times 9.8\times 9\times {{10}^{-2}}\] …………….. ( \[\because (15-6)cm=\times {{10}^{-2}}m\])
Therefore,
\[H=88.2J\]
Therefore, the heat generated will be 88.2 Joules.

Note:
The potential energy is the energy that is stored in an object and has the potential to do work. The energy stored is due to the displacement of the object in vertical direction is known as gravitational potential energy. Mechanical heat is the heat generated due to the mechanical process. In this case, the heat generated is due to the process of inverting the tube and increasing the potential energy.