(Originais Teachy 2023) - Question Medium of Physics

João is helping his father fill the home pool, which is rectangular and has the following dimensions: 8 meters in length, 4 meters in width, and 1.5 meters in depth. They are using a hose with a constant flow rate of 20 liters per minute. Considering that the pool was completely empty and there was no water wastage in the process, answer: (a) What is the total volume of the pool in liters? (b) How long, in hours, will it take to completely fill the pool with the hose? (c) If the water in the pool had the mentioned constant flow rate, but drained through an opening of the same size as the hose, how long would it take for the pool to completely empty?

A student is observing an object through a converging lens with a focal length of 10 cm. The object is located 40 cm away from the lens. (Consider that the thin lens approximation is valid). Based on this information: 1) Calculate the position of the image formed by the lens. 2) Determine the size of the image relative to the size of the object, knowing that the lens obeys the Gauss equation (1/f = 1/p + 1/p'), where f is the focal distance of the lens, p is the distance from the object to the lens, and p' is the distance from the image to the lens, all measured in cm. Consider that the coordinate system used has its origin at the lens's optical center, with the main axis oriented positively to the right, and that real images have a positive sign and virtual images have a negative sign.

The city of Salvador, famous for its hills and elevators, is a perfect example to demonstrate the force of traction. The Lacerda Elevator, one of the main postcards of the city, transports thousands of people daily between the Upper Town and the Lower Town. Suppose one day, a group of 15 people with an average mass of 70kg decide to use the elevator at the same time. Considering the elevator's mass as 500kg and the acceleration due to gravity equal to 10 m/s², what would be the traction force on the elevator cable when it is at rest or moving at a constant speed?