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Solved
Angular Velocity of a Falling Rod Pivoted at One End (Energy + Rotation)
Engineers at Indian Institute of Technology Bombay are designing a rotating docking arm for a future space station. The arm is m...
8 hours ago
Solved
Angular Velocity Required to Create Artificial Gravity
Scientists at NASA and Indian Space Research Organisation are designing a rotating space station ring to simulate Earth-like gra...
8 hours ago
Solved
Moment of Inertia Using Parallel Axis Theorem
Engineers at Indian Space Research Organisation are designing a satellite with extendable robotic arms. When the arms extend out...
8 hours ago
Solved
Acceleration in a Symmetric Double-Pulley Constraint System
Engineers at Indian Institute of Technology Kanpur are designing a precision counterweight system for high-speed elevators. The ...
11 hours ago
Solved
Tension in String for Circular Motion (Advanced Rotational Dynamics)
At the astronaut training facility of Indian Space Research Organisation, astronauts are trained using a rotating centrifuge. Th...
11 hours ago
Solved
Angular Velocity of a Falling Rod Pivoted at One End (Energy + Rotation)
Engineers at Indian Institute of Technology Bombay are designing a rotating docking arm for a future space station. The arm is m...
12 hours ago
Solved
Motion of a Bead Sliding on a Rotating Rod (Non-Inertial Frame Dynamics)
Scientists at Indian Space Research Organisation are testing artificial gravity inside a rotating space station module. Inside ...
12 hours ago
Solved
Acceleration of Block Relative to Ground
Researchers at Indian Space Research Organisation test cargo motion inside accelerating spacecraft ramps. Find acceleration.
12 hours ago
Solved
Acceleration in an Atwood Machine with Massive Pulley
Engineers at Indian Institute of Technology Delhi are designing a precision elevator calibration system using two masses connect...
12 hours ago
Solved
Velocity of a Particle Under Constant Acceleration Using Energy Methods
Scientists at CERN are testing a linear accelerator that uses electromagnetic force to accelerate charged particles along a stra...
12 hours ago
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Euler primes
Historical context The great swiss mathematician Leonhard Euler found the formula to give some prime numbers. Problem...
5 days ago
Solved
Rotating 2d curve around a vertical axis
Let p be an even-degree polynomial such that has a unique vertex (single global extremum). Consider the counterclockwise rotatio...
6 days ago
Solved
Rotating the plane region bounded by two polynomials
Let p and q be n-degree and m-degree polynomials with n >= m >= 1. Consider clockwise rotate the plane region bounded by these t...
6 days ago
Solved
Odd Run Sums
Given a row vector x of integers, find every maximal run of consecutive odd numbers and return a row vector containing the sum o...
10 days ago
Solved
Comparing to scale all terms versus one term of even-degree polynomial by the same scale factor
Let p be an even-degree polynomial with positive leading coefficient. Consider the scale factor, k, that vertically transforms ...
10 days ago
Solved
Scaling vertically parabola by evaluating its area over an interval
Let p be a quadratic polynomial, with its axis of symmetry being the y-axis. Considering the vertical shift of its vertex to the...
10 days ago
Solved
Scaling vertically functions
Given a real function by the 1×n array, x, of inputs and the 1×n array, y, of outputs, consider shifting vertically its graph by...
10 days ago
Solved
Shifting vertically even-degree polynomial's graph by its mean over an interval
Let p be an even-degree polynomial with positive leading coefficient. Consider its vertical translation by shifting its graph by...
10 days ago
Solved
Translating even-degree polynomial by its vertex to the origin
Let p be an even-degree polynomial such that has a unique vertex (single global extremum). Consider its translation by shifting ...
10 days ago
Solved
Translating parabola by its vertex to the origin
Given a quadratic polynomial, p(x) = ax^2 + bx + c (a ~= 0), represented by the vector [a b c], consider the translation of the ...
10 days ago
Solved
Shifting vertically a function's graph
Given a real function, f, by n input-output pairs, consider a translation in the up-down direction given by an amount k. For a ...
10 days ago
Solved
Is it Possible? ( Easy )
In the first part of series, we simplify the problem. Given two jugs with capacities A and B, and a target amount T, determine i...
13 days ago
Solved
Power of Moving Vehicle
Engineers at Tesla calculate how much power is required to maintain vehicle motion.
13 days ago
Solved
Spring Energy Storage
Engineers at Bosch design suspension systems using springs. They calculate the energy stored when the spring compresses.
13 days ago
Solved
Machine Efficiency Test
Engineers at Siemens test how efficiently a motor converts electrical energy into mechanical work.
13 days ago
Solved
Falling Object Velocity
Scientists at ISRO drop test equipment from a height to study motion under gravity. They must calculate the velocity just befor...
13 days ago
Solved
Pushing a Heavy Machine
At a factory operated by Bharat Heavy Electricals Limited in Haridwar, engineers must move a heavy generator across the floor. ...
13 days ago
Solved
Roller Coaster Height Energy
At Imagicaa Theme Park, engineers calculate potential energy at the top of a roller coaster.
13 days ago
