Write the numbers 8, 4, 2, and 1 in descending order. Binary numbers are formed by choosing numbers from this sequence and adding them together to form a number that is desired. The number 1 is used to choose numbers out of the ( 8, 4, 2, 1 ) sequence that are needed, and aContinue reading “MATHEMATICS: A Review of Binary Mathematics and the Hexadecimal Counting System:”
Author Archives: George Walker
ENERGY AND MOMENTUM: Conservation of Linear and Angular Momentum ( Part 1 )
Q: A ( 1kg ) ball of clay moving with a velocity ( vbi ) collides and sticks to the end of a ( 120cm ) rod of uniform mass ( 2kg ). Assuming that the ball and rod are at rest upon a frictionless surface: ( a ) Where is the new center ofContinue reading “ENERGY AND MOMENTUM: Conservation of Linear and Angular Momentum ( Part 1 )”
ENERGY AND MOMENTUM: Elastic Collision Determination ( Part 2 )
Q: An elastic collision occurs between two objects of mass ( m1 ) and ( m2 ). Prior to the collision, mass ( m2 ) is stationary and approached by ( m1 ) with a velocity ( v1 ). If only the values of ( m1 ), ( m2 ), and ( v1 ) areContinue reading “ENERGY AND MOMENTUM: Elastic Collision Determination ( Part 2 )”
ENERGY AND MOMENTUM: Elastic Collisions and the Center of Mass Velocity ( Part 3 )
Q: Consider a system in which a mass ( m1 = 6kg ) moves in the +x-direction at ( 2 m/s ) as a mass ( m2 = 2kg ) moves in the -x-direction at ( – 4 m/s ): How may we use the center of mass ( c.o.m. ) of this system toContinue reading “ENERGY AND MOMENTUM: Elastic Collisions and the Center of Mass Velocity ( Part 3 )”
ENERGY AND MOMENTUM: Elastic Collisions and the Center of Mass Velocity ( Part 2 )
In Part 1 of this entry, it was determined that the center of mass between objects moving with constant velocities is also constant ( vcm ): We will now use mass ( kg ) and instantaneous-distance coordinates along ( x ) to determine the system’s center of mass. Let’s begin using the x-coordinates of (Continue reading “ENERGY AND MOMENTUM: Elastic Collisions and the Center of Mass Velocity ( Part 2 )”
ENERGY AND MOMENTUM: Elastic Collisions and the Center of Mass Velocity ( Part 1 )
A system’s center of mass is the location where the average mass distribution of the system is located. Consider a system in which two equal masses rest at the ends of a balance: The sum of torques acting upon the system is zero, and it will remain in static equilibrium until acted upon by anContinue reading “ENERGY AND MOMENTUM: Elastic Collisions and the Center of Mass Velocity ( Part 1 ) “
ENERGY AND MOMENTUM: Final Velocity of Target and Projection After Elastic Collision ( Part 1 )
Q: Within a given system, a projectile moves with a constant velocity ( v1 ) prior to colliding with a stationary target of equal mass ( m1 = m2 ). Since the system is isolated from outside forces, momentum ( p ) and kinetic energy ( KE ) both are conserved during the collision. (Continue reading “ENERGY AND MOMENTUM: Final Velocity of Target and Projection After Elastic Collision ( Part 1 )”
FORCE AND ACCELERATION: Net Force Exerted on a Ring
Q: How may we determine the net force ( F ) exerted on the ring below? A: We must first reduce the F1 and F2 vectors into their x/y-components: The F1y and F2y components of F1 and F2 oppose the motion of F3. The net force in the y-direction is as follows: Fnety = F2yContinue reading “FORCE AND ACCELERATION: Net Force Exerted on a Ring”
ELECTRONICS: Kirchhoff’s Laws
Q: What are the values of the currents ( I ) and unknown voltage drops ( V ) across the resistors ( R ) pictured below? A: The first problem-solving step involves assigning labels to the junctions ( j ) in the circuit: We must now sketch the currents flowing in the circuit: The currentContinue reading “ELECTRONICS: Kirchhoff’s Laws”
FORCE AND ACCELERATION: 3-4-5 Right-Triangle Mathematics
Q: Two men attempt to pull a box in the diagram below: What is the resultant force in Newtons ( N ) exerted on the box? A: This is a classic question involving a 3-4-5 right triangle. Trigonometry and the Pythagorean Theorem enable us to solve the problem using the numbers 3, 4, and 5.Continue reading “FORCE AND ACCELERATION: 3-4-5 Right-Triangle Mathematics”
