Fundamentals of statics --- Introduction ---

This module currently includes 4 exercices on .....

Acceleration of a sprinter

A sprinter runs 100 meters in seconds (starting from rest). Assuming a constant acceleration throughout the whole effort, calculate the magnitude of this acceleration, , as well as the magnitude of her velocity, , in , the moment she crosses the finish line.

Physical quantities and instructions :

Give 3 significant digits (write the significant 0's).

Do not forget to include the units in the answer (for exemple, m/s^2).

g = 9.81 m.s


Acceleration of a locomotive

In this exercise we analyze the acceleration phase of a locomotive. To simplify the problem, we will assume that the solid friction, , is the only force opposing motion; that is, the viscous friction force due to the air is negligible as long as the speed of the train is low. We will also assume that the rails are perfectly straight.

A locomotive of mass M= T, initially at rest, departs from a station. The engine generates a constant force, , that sets the locomotive in motion. The locomotive is then also subject to a solid friction force, , having a constant magnitude equal to N. Therefore the acceleration of the locomotive is

Calculate the magnitude, , of the driving force in Newton :

Calculate the time T, in seconds, that will take the locomotive to reach a speed of 60 km/h :

What distance, L, will the locomotive have travelled at time T ?

Physical quantities and instructions :

Give 3 significant digits.

Give the answer in S.I. units. (include the units in the answer).

g = 9.81 m.s


Hovering helicopter

A helicopter of mass m= kg hovering at point M is subject to a horizontal force, , exerted by the wind, of N. In order to keep hovering the rotor blades must produce a force .

Calculate the intensity of the force and the angle, , of this force with respect to the (O,x) axis.

xrange -11, 11 yrange -11, 11 arrow -10,-10,11,-10,10,black arrow -10,-10,-10,10,10,black text black,9.5,-9.,large,x text black,-9.5,9.,large,y text black,-9.5,-9,large,O fcircle 0,0,10,black text black,0.5,-0.5,large,M arrow 0,0,0,-/100,10,red arrow 0,0,/1000,0,10,blue arrow 0,0,-/1000,/100,10,green text blue,/1000,0,large,f text red,0.5,-/100,large,P text green,-/1000+0.5,/100+0.5,large,F text pink,1,1.5,large,d arc 0,0,2,2,0,, pink linewidth 2

Instructions and parameters :

Write the significant 0's.

Do not forget to include the units in the answer.


Spring in equilibrium

A spring is suspended from the ceiling. Its natural length, , is cm. When mass m= g is then attached to its free end the spring elongates and it eventually attains an equilibrium length, , of cm.

The magnitude of the elastic force of a spring, , is given by : where is the spring elastic constant and is the spring lengthening/shortening.

ressort

Calculate the value of the elastic constant in units of the International System (S.I.) and give also its dimensions.

Instructions :

Give the results with 5 significant digits (write the significant 0's).

Include the units in the answer.

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Description: exercises on fundamentals of statics in mechanics. interactive exercises, online calculators and plotters, mathematical recreation and games

Keywords: interactive mathematics, interactive math, server side interactivity, mechanics, Statics Force Principle Fundamentals Inertia