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 ...

4 months 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...

4 months ago

Solved

Juggling
There is a notation system for <http://en.wikipedia.org/wiki/Juggling jugglers> called <http://en.wikipedia.org/wiki/Siteswap si...

4 months 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...

4 months 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...

4 months 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...

4 months 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...

4 months 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...

4 months ago

Solved

Specific Fuel Consumption
Brake-specific fuel consumption (BSFC) measures how efficiently an engine converts fuel mass into useful work. Lower is better...

4 months 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...

4 months ago

Solved

Engine Displacement
Engine displacement is the total swept volume of all cylinders. It is determined by bore (cylinder diameter), stroke (piston tra...

4 months 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 ...

4 months 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...

4 months 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...

4 months 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...

4 months 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...

4 months 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 + ...

4 months 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...

4 months 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...

4 months 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...

4 months 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...

4 months 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...

4 months 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...

4 months 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...

4 months 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...

4 months 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...

4 months 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...

4 months 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 ...

4 months 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...

4 months ago

Solved

Steering 101-Ackermann Steering Ratio
In a turning vehicle, inner and outer wheels follow different radii. Ackermann steering geometry ensures both wheels roll withou...

4 months ago