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Solved
Distance of the centroids of the balls
Given *n* balls of radius *r* and the vector *p (nx3)* with all position *(x,y,z)* of the balls, return the symmetric matrix *A ...
14 hours ago
Solved
center of mass
R is a given matrix with size [n,2]. R(i,:) is interpreted as the 2D-position of a mass point with mass i. Calculate the center ...
15 hours ago
Solved
Find the jerk
No, it's not the author of this problem... Jerk is the rate of change in acceleration over time of an object. So, if given t...
15 hours ago
Solved
Juggling
There is a notation system for <http://en.wikipedia.org/wiki/Juggling jugglers> called <http://en.wikipedia.org/wiki/Siteswap si...
15 hours ago
Solved
The Case of the Missing Prototype – Decode the Secret Note Found on the Desk to Reveal a Hidden Message
On the lab desk, you discover a short note filled with strange letters. After examining it, you realize it’s written in a Caesa...
15 hours ago
Solved
The Case of the Missing Prototype – Check the Lab’s Logbook for Suspicious Late-Night Entries
After counting the fingerprints, you turn your attention to the security logbook.It records the entry hours (from 0 to 23) of ev...
15 hours ago
Solved
The Case of the Missing Prototype - Count the Fingerprints Found at the Lab Door to Begin Your Investigation
You arrive at the Innovation Lab where the secret prototype was stolen. The door has been dusted for fingerprints, and a technic...
15 hours ago
Solved
Geometric Compression Ratio
The geometric compression ratio CR is the ratio of the total cylinder volume at BDC to the clearance volume at TDC. It is one of...
16 hours ago
Solved
Swept Volume and Clearance Volume
The swept volume (V_s) is the volume displaced by the piston as it travels from BDC (Bottom Dead Centre) to TDC (Top Dead Centre...
16 hours ago
Solved
Specific Fuel Consumption
Brake-specific fuel consumption (BSFC) measures how efficiently an engine converts fuel mass into useful work. Lower is better...
16 hours ago
Solved
Piston Mean Speed
Mean piston speed is a critical mechanical stress indicator — it sets limits on valve timing, bearing loads, and material fatigu...
17 hours ago
Solved
Engine Displacement
Engine displacement is the total swept volume of all cylinders. It is determined by bore (cylinder diameter), stroke (piston tra...
17 hours ago
Solved
Fuel-Air Equivalence Ratio (Lambda)
Lambda (λ) is the ratio of actual air-fuel ratio to the stoichiometric air-fuel ratio. λ = 1 is perfect stoichiometry, λ < 1 is ...
17 hours ago
Solved
Volumetric efficiency
Volumetric efficiency measures how well an engine breathes. The ratio of the actual air mass drawn in per cycle to the theoreti...
17 hours ago
Solved
Brake Mean Effective Pressure (BMEP)
BMEP is a normalised measure of engine work output per cycle per unit displacement. It lets you compare engines of different siz...
18 hours ago
Solved
Engine torque and RPM
Torque and power are related through rotational speed. Knowing brake power and engine RPM, you can back-calculate the torque del...
18 hours ago
Solved
Engine Thermal Efficiency
The thermal efficiency of an ideal Otto cycle engine depends only on the compression ratio. A higher compression ratio yields gr...
18 hours ago
Solved
Bernoulli's Equation
Bernoulli's equation states that for an incompressible fluid the following summation is constant across the flow: v^2/2 + g*z + ...
15 days ago
Solved
Kepler's Equation
Solve <http://en.wikipedia.org/wiki/Kepler's_equation Kepler's Equation>. Note that the solution is rounded down to 5 decima...
15 days ago
Solved
Bouncing disk
A disk is placed in a rectangular room with dimensions a and b in a point with coordinates x0 and y0. The disk is given a startu...
15 days ago
Solved
Mechanics 1
I thought I would make a mechanics problem for all those physics lovers out there. Imagine two solid, rigid spheres B1 and B...
15 days ago
Solved
Electric Power Steering (EPS) Motor Torque with Efficiency
In EPS systems, the motor must generate additional torque to compensate for system losses. Given Required assist torque at rack...
15 days ago
Solved
EPS Assist Map with respect to the Vehicle Speed
In Electric Power Steering (EPS), assist torque reduces as vehicle speed increases to improve stability at high speeds. Given S...
15 days ago
Solved
Electric Power Steering (EPS) Assist Curve Calculation
Electric Power Steering (EPS) provides assist torque proportional to driver input. Given Steering torque Ts and Gain k, Compute...
15 days ago
Solved
Steering Torque Estimation
Steering torque is generated due to lateral tire forces acting through the steering mechanism. Given Lateral force Fy and Lever...
15 days ago
Solved
Understeer or Oversteer Gradient Calculation
This gradient determines whether a vehicle tends to understeer or oversteer. Given Mass m, Wheelbase L, Front cornering stiffne...
15 days ago
Solved
Steering Ratio Calculation
The steering ratio defines the relationship between steering wheel angle and road wheel angle. Given wheel angle δ and Steering...
15 days ago
Solved
Tire Slip Angle Calculation
Slip angle represents the angle between the direction a tire is pointing and the direction it is moving. Given Lateral velocity...
15 days ago
Solved
Yaw rate of the vehicle
Yaw rate defines how quickly a vehicle rotates about its vertical axis during motion. Given Vehicle speed v and Turning radius ...
15 days ago
Solved
Turning radius of a vehicle
The turning radius represents the radius of the circular path followed by a vehicle. Given Wheelbase L and Steering angle δ, Co...
15 days ago
