Newton's laws --- Introduction ---

This module currently includes 19 simple exercices on Newton's laws :

Tension of a simple pendulum string

A pendulum, consisting of a mass m= kg that is suspended from a string l= m long, is set free from an initial position having an angle ° with respect to the vertical.
( )
  • What is the modulus, V, of the mass velocity when the pendulum passes through its vertical position?
    V (m/s)=
  • Deduce the string tension, T, at the same instant:
    T(N)=
  • Assume g=9.81 m.s-2 and give the answers with 2 significant digits.

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Will the package slip?

A box filled with books, having a mass kg, rests on the ground.
Let = and = respectively be the static and dynamic friction coefficients between the cardboard and the ground.
An horizontal force of F= Newton is applied on the box.
Determine the modulus of the friction force acting on the box (rounded to the nearest Newton).
(Assume g= 10 m/s2)

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It is assumed that in the conditions of the experiment, the equilibrium of the box can only be broken by slip (the box will not overturn).


( )

Sliding with friction on the horizontal plane

A block B of mass mB= g is suspended from a wire of negligible mass
which passes over an (ideal) pulley and is then connected to a block A of mass mA,
resting on a horizontal table.

Let = and = respectively be the static and dynamic friction coefficients of block A on the table surface and let us assume g=9.81 m/s2.

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The ensemble will slide if mA is at : g .
(The answer must be rounded to the gram).

Knowing that mA= g, determine with 2 significant digits,

Identical masses connected by a taut wire - QCM 1

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A block B of mass m is suspended from a wire of negligible mass which passes over an (ideal) pulley and is then connected to a block A having the same mass m, resting on a long horizontal table.
We neglect friction forces between the block A and the table.
As long as the block A does not get in contact with the pulley, we can deduce that :


Sliding at a constant velocity - QCM


A package slides along an inclined plane with a constant velocity.
It is known that the total force exerted by the inclined plane is the sum of the reaction force, normal to the incline, and the friction force parallel to the incline

It is possible to deduce :


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Frictionless sliding - QCM


You are skiing down a piste when all of the sudden one of your skiis, having a mass M, dettaches and slids downhill with almost no friction.
It is possible to deduce that:
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Blocks in contact - QCM1

Two carboard boxes full of books are in contact with each other and both of them rest on the ground.
The friction forces between the carboard and the ground are negligible.
The mass of the box B is equal to times the mass of the box A.
You push the box A by applying a horizontal force F to it.

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The resultant force on the box B is equal to... (tick your answer below)


Hanging object inside an elevator - QCM2

A decorative object of mass M is hanging from a string connected to the ceiling of an elevator cab.

Blocks in contact - QCM2

Two carboard boxes full of books are in contact with each other and both of them rest on the ground. Let be the dynamic friction coefficient between the cardboard and the ground. The mass of the box B is equal to times the mass, m, of the box A. You push the box A by applying to it a horizontal force F such that the boxes move with a constant velocity.

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The friction coefficient is equal to ( tick your answer below)?:

Stacked blocks - QCM1

Two cardboard boxes full of books are stacked one on the other.
Let be the static friction coefficient between the two cardboard surfaces and let us neglect friction between the bottom carboard and the ground.
The mass of the box A is times the mass, m, of the box B. You push the box A by applying a horizontal force F to it.

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N.B.: We assume the weak friction conditions where B will not tip over A.

The two boxes will not slide with respect to one another if...?

Tick your answer below .


Stacked blocks - QCM2

Two cardboard boxes full of books are stacked one on the other.
Let s be the static friction coefficient between the two cardboard surfaces and let us neglect friction between the bottom carboard and the ground. The mass of the box A is times the mass, m, of the box B. You push the box B by applying a horizontal force F to it.

N.B.: We assume the weak friction conditions where B will not tip over A.

The two boxes will not slide with respect to one another if (Tick your answer below ):
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Masses connected by a taut wire - QCM3

A block A of mass m is at rest on a horizontal table. It is connected by a wire (of negligible mass) which passes over an (ideal) pulley to a block B of mass m/. Lete be the static friction coefficient between the block A and the table.
We assume that under the conditions of the experiment the equilibrium of the system can only be broken by sliding (the block A cannot tip over)


The system will be in equilibrium if and only if (tick you answer below):
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Masses connected by a taut wire - QCM2

A block A of mass m is at rest on a horizontal table. It is connected by a wire (of negligible mass) which passes over an (ideal) pulley to a block B of mass . Let us neglect friction forces between the block A and the table.

The modulus of the acceleration of the block B is given by:



The tension of the wire is given by:


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Package in a train

A suitcase of mass 11 kg sits on the floor in the middle of the hallway of a car, of lengh 2L= m, which is moving horizontally at a constant velocity along the direction of the 0x axis.
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Let s= and d= respectively be the coefficients of static and dynamic friction between the suitcase and the floor, and let us assume g= 10 m/s2. At the initial instant t=0, the speed of the car with a constant of modulus A.

The block will not slide on the floor if A does not exceed the value A0 (m/s2)=

Let us assume that we actually have A=*A0.
The block will slip with respect to the floor and will hit one of the car vertical walls
after a time t (s)= (give 2 significant digits).

Pendulum in a train

A pendulum of mass g is suspended from the ceiling in the middle of a car that is moving horizontally at a constant velocity along the direction of the 0x axis.
The height of the car is equal to m and the vertical of the pendulum intersects the car floor at point H.
Let us assume g=10 m/s2

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At the initial instant, , the car speed begins to with a constant of modulus A = g.

The pendulum will therefore tilt with respect to the train,
defining an angle with respect to the vertical (give the answer rounded to the degree).

If at a given time we cut the pendulum string
the pendulum will hit the car floor at a distance d from point H, d = (give the answer in m and use 2 significant digits). ( )



Mass placed on a turntable

A block of mass m rests on an horizontal disk that is rotating anticlockwise with a constant angular velocity .
The block does not slide on the disk and it is placed at a distance L from the center of rotation O.
Let be the friction force exerted by the disk on the block, the static friction coefficient between the block and the disk, and we are going to use .

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It is possible to deduce (tick ALL of the correct answers) :

Significant digits

Rounding a numerical result to a given number of significant digits.
( )

Mass attached to a string - QCM

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A block of mass m is attached to a spring having a constant equal to k and a natural length (at rest) equal to b.
This block oscillates vertically around its equilibrium position, ze.

For a given position of the mass, represented by its abscissa, z, write an expression for the following quantities as a function of m, g, k, b and z :



Passenger at subway startup

A man falls backwards when the subway starts up.

If we work (we place ourselves) in the frame of reference , which one of the following three is a correct description of the horizontal forces acting on the passenger ?

 

 

 

Explain what is the nature of the represented forces :

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