High School (easy)

Challenge 6 – Bell

If a doorbell is ringing inside a bell jar and we extract the air, the bell will be heard but not seen.

What different property do light and sound have so that the bell is seen, but not heard?

Challenge 5 – Calculating the weight of an automobile

Cars usually have four wheels, so if you know how much weight can bear a tire, you know how much the car weights. In any shop or gas station they can tell you the pressure of each tire.

The challenge is to:

a) measure the contact surface of the tire with the ground and
b) with this data and the data of the pressure of the tire, calculate the mass of the car.

If you don’t have a car to do your experiment, suppose the wheel of an automobile has a pressure of 35 pounds / inch ² and the contact surface is 125cm ².
What is the weight of the car?
How would you measure the surface of contact?

Challenge 4 – Gravity on the Moon

The mass of the moon is 7.36 x 10²² kg, with a diameter of 3476 km. The moon has no atmosphere, i.e., no air. How long does it take for a 2kg object to get to the ground, if dropped from a height of 10m?

Does it depend on the mass?

Challenge 3 –  Shot put competition

In a competition we want to know who throws the highest metal ball whose mass is 2kg. Suppose the air friction is negligible and answer:

How high does the winner’s ball reaches, if  4.5s pass since when he throws it until it falls down?

How much energy the winner burns when throwing that ball  (assuming he is a perfect machine)?

Does the height reached by the ball depends on the distance that it falls from the launcher?

Challenge 2 – Microscopic Calculations

In science, knowing the size of tiny objects has always been a big challenge. Measuring the height of a person does not seem complicated, but how would you measure the size of a molecule? Be aware that molecules can’t be seen under the microscope, like cells. Perhaps a molecule is too difficult to measure. Let’s measure something easier, like the thickness of a sheet of paper.

The challenge consists in measuring with a ruler the thickness of a sheet of paper. If you can do it, you’ll have a method to measure even smaller things, such as cells or molecules.

Hint: Think that, in a package of sheets, the thickness of each one of them is exactly the same.

What is the measure of the thickness of a sheet of paper?

Special challenge: How would you measure the size of an onion cell, for example? Ask your Biology teacher for any ideas.

Challenge 1 – Astronomical Calculations

How do you know what mass is the Sun? What is the Earth’s mass or any other star’s?.

The magnitude of the centrifugal force of a body of mass    that rotates at an angular velocity     at a distance   from an axis of rotation is

We know that the Earth’s mass is 5.9736 × 1024 kg, its mean distance from the Sun is 149 598 261 km and its translation period is 365.256 days.

1. What is the mass of the Sun, approximately?
2. If you do not know the mass of Earth or the Sun, how would you calculate their masses? In particular, how to calculate the mass of the Earth?
3. What is the tangential velocity of the Earth in its motion around the Sun?

Note: the universal gravitational constant G is 6.674 × 10-11 N · m ²/kg².