Physics Ball Simulator

Try the game: Physics Ball Simulator by dot-ammar

Overview

This game, I wrote in Python, is a physics-based simulation that provides an interactive and visual representation of key concepts from AP Physics 1. It allows users to control a ball's movement, observing real-time changes in velocity, acceleration, and distance traveled. The game's physics engine calculates the trajectory of the ball under the influence of gravity and user interactions, offering a practical understanding of kinematics and dynamics.

Game Physics, Mathematics, and Code

Gravity and Ball Movement

The Game simulates gravity and its effect on the ball's movement. Gravity is defined in terms of pixels per frame squared, scaled to the screen's dimensions:

PIXELS_PER_METER = 100
GRAVITY = 9.8 * PIXELS_PER_METER / (FPS**2)

Ball Trajectory Prediction

The function predict_path calculates the ball's trajectory based on its current position, velocity, gravity, and screen boundaries. It uses a loop to iteratively update the ball's position using its velocity, adjusting for gravity with each step:

for _ in range(max_steps):
    x += velocity_x
    y += velocity_y
    velocity_y += gravity
    path.append((x, y))

Velocity is calculated in a way that is essentially:

pos_x += vel_x * time_step
pos_y += vel_y * time_step + 0.5 * gravity * time_step ** 2
vel_y += gravity * time_step

Kinematic Equations

$$ x = x_o + v_{xo}t+\frac12at^2 $$

$$ y = y_o + v_{yo}t+\frac12at^2 $$

$$ v_y = v_o + at $$

Collision Detection and Response

The game handles collisions with the ground, ceiling, and walls. Upon collision, it modifies the ball's velocity to simulate a bounce, applying a dampening factor to simulate energy loss:

if ball_rect.bottom >= screen.get_height():
    ball_velocity[1] *= -0.7
    ball_velocity[0] *= friction

Real-time Metrics Calculation

The game calculates and displays real-time metrics like velocity, acceleration, and distance traveled. Velocity and acceleration are computed in meters per second, considering the frame rate for time measurement. The distance is calculated by including the velocity over time:

velocity_x = (ball_velocity[0] / PIXELS_PER_METER) * FPS
distance_traveled += velocity_magnitude * SECONDS_PER_FRAME

Dragging and Throwing Mechanism

Users can interact with the ball, dragging and throwing it. The game tracks mouse movement to determine the ball's new velocity when released:

if dragging:
    ball_velocity = weighted_velocity[:]

where weighted_velocity is defined by:

current_mouse_pos = pygame.mouse.get_pos()
ball_rect.center = current_mouse_pos

# Calculate the instantaneous velocity
movement_x = current_mouse_pos[0] - last_mouse_pos[0]
movement_y = current_mouse_pos[1] - last_mouse_pos[1]

if abs(movement_x) > MIN_MOVEMENT_THRESHOLD or abs(movement_y) > MIN_MOVEMENT_THRESHOLD:
    instant_velocity = [movement_x, movement_y]

    # Update the weighted velocity
    weighted_velocity[0] = alpha * instant_velocity[0] + (1 - alpha) * weighted_velocity[0]
    weighted_velocity[1] = alpha * instant_velocity[1] + (1 - alpha) * weighted_velocity[1]  
else:
    # Reset weighted_velocity if there's no significant movement
    weighted_velocity = [0, 0]
last_mouse_pos = current_mouse_pos

This works to create a smooth throwing simulation.

Relevance to AP Physics 1

The game demonstrates key concepts from the AP Physics 1 curriculum, including:

• Kinematics in one and two dimensions
• Newton's laws of motion
• Friction and collisions

Screen.Recording.2024-01-09.at.11.28.55.PM.mov

Key observation from metrics:

• Acceleration is constant 9.8m/s^2
• X Velocity is constant through the air.
• Y Velocity changes due to acceleration.