Proposal-1

Problem 1: Determining the Mass of an Object

Objective

Determine the mass of an object without using pre-made sensors for measuring different types of mass.

Methodology Explanation

There are many methods for determining the mass of an object, but since the competition organizers will provide a spring with a known spring constant, we have chosen to use the following formula for calculations to align with the resources provided by the competition organizers.

Hooke’s Law

Solving for mass m:

Schematic Diagram

Problem 2: Projectile Launching

Objective

Shooting a ball to collide with an object falling freely to the ground from a different position.

Methodology Explanation

Concept-1: Shoot the Monkey

The "Shoot the Monkey" experiment is a classic physics demonstration used to illustrate projectile motion and the effect of gravity on two objects in free fall.

The speed of the ball, the weight of the ball, the distance between the launcher and the monkey, and the weight of the monkey do not affect whether the ball will hit the monkey, as long as:

1. Aim directly at the monkey (before it starts falling).
   


2. Shoot the ball at the exact moment the monkey starts to fall.
   

From this concept, we don't need to calculate anything complicated in real time during the experiment.

Concept-2: Use a Formula

This formula is similar to the concept of "Shoot the Monkey." It shows how different variables are related to each other in a projectile motion problem.

Formula

• The motion of an object falling freely under the influence of gravity
  
  




• To ensure a collision between the ball and the freely falling object, we must establish the following equation
  
  




• Solve the Equation for t
  
  
  

The tangent function relates an angle in a triangle to a specific ratio of side lengths, specifically the ratio of the opposite side (height) to the adjacent side (horizontal distance). This means that the formula "tangent of θ = height / distance" tells us how angles and side lengths in right-angled triangles interact. In practical terms, it describes how the angle of elevation (or depression) is related to the height of an object and the horizontal distance from it.

Project Design