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10TH GRADE · DYNAMICS

Strength and Balance

Gravity, elasticity, friction, inclined plane and moment of force.

28 minutes33 theory cards
Open interactive lesson

LESSON MATERIAL

Basic Concepts

4

Universal gravity

Mutual attraction of any bodies with mass.

The attraction is mutual: bodies act on each other with forces equal in magnitude, and the force quickly decreases with distance.

Elastic force

The force that arises during deformation and is aimed at restoring the original shape of the body.

It counteracts deformation. For small tensions and compressions, its modulus is usually found using Hooke's law.

Friction force

A force that resists the relative motion of contacting surfaces.

Friction is directed along the surface and interferes with relative sliding or its initiation; its value depends on the state of the contact.

Mechanical balance

A condition in which a body does not receive translational and rotational acceleration.

For balance, a zero sum of forces and a zero total moment are simultaneously required. In this case, the body can be at rest or move uniformly.

LESSON MATERIAL

Physical quantities

15

Gravitational constant

GG

Coefficient in the law of universal gravitation.

Unit: newton square meter per square kilogram · Nm2kg2\frac{\mathrm{N}\cdot\mathrm{m}^2}{\mathrm{kg}^2}

Planet mass

MM

The mass of a celestial body creating a gravitational field.

Unit: kilogram · kg\mathrm{kg}

Mass of the first body

m1m_1

Mass of the first interacting body.

Unit: kilogram · kg\mathrm{kg}

Mass of the second body

m2m_2

Mass of the second interacting body.

Unit: kilogram · kg\mathrm{kg}

Distance between bodies

rr

The distance between the centers of interacting bodies.

Unit: meter · m\mathrm{m}

Spring stiffness

kk

Spring deformation resistance coefficient.

Unit: newton per meter · Nm\frac{\mathrm{N}}{\mathrm{m}}

Elongation

Δl\Delta l

Change in the length of a deformed body.

Unit: meter · m\mathrm{m}

Ground reaction force

NN

The force of support on the body.

Unit: newton · N\mathrm{N}

Body weight

PP

The force exerted by a body on a support or suspension.

Unit: newton · N\mathrm{N}

Friction force

FfrF_{\text{fr}}

A force that resists the relative motion of surfaces.

Unit: newton · N\mathrm{N}

Friction coefficient

μ\mu

Dimensionless characteristic of friction of a pair of surfaces.

Unit: dimensionless quantity

Tilt angle

α\alpha

The angle of the inclined plane to the horizon.

Unit: radian · rad\mathrm{rad}

Longitudinal component of gravity

FF_{\parallel}

Component of gravity along an inclined plane.

Unit: newton · N\mathrm{N}

moment of force

MM

Rotational action of a force relative to an axis.

Unit: newton meter · Nm\mathrm{N}\cdot\mathrm{m}

Shoulder of power

ll

The shortest distance from the axis to the line of action of the force.

Unit: meter · m\mathrm{m}

LESSON MATERIAL

Lesson formulas

14

Law of Gravity

F=Gm1m2r2F=G\frac{m_1m_2}{r^2}

The force of attraction is proportional to the product of masses and inversely proportional to the square of the distance.

Hooke's law

Felastic=kΔlF_{\text{elastic}}=k\lvert\Delta l\rvert

The elastic force is proportional to the deformation modulus.

Weight on horizontal support

P=NP=N

In the absence of vertical acceleration, the weight is equal to the ground reaction force.

Sliding friction force

Ffr=μNF_{\text{fr}}=\mu N

The friction force is equal to the coefficient of friction multiplied by the reaction of the support.

Friction on a horizontal surface

Ffr=μmgF_{\text{fr}}=\mu mg

On a horizontal surface without vertical acceleration, the reaction of the support is equal to the force of gravity.

Component of gravity along the inclined

F=mgsinαF_{\parallel}=mg\sin\alpha

The longitudinal component of gravity is directed along the inclined plane.

Inclined support reaction

N=mgcosαN=mg\cos\alpha

The normal reaction is equal to the perpendicular component of gravity.

Friction on an inclined plane

Ffr=μmgcosαF_{\text{fr}}=\mu mg\cos\alpha

The frictional force on an inclined plane takes into account the reduced reaction of the support.

Acceleration near the surface of the planet

g=GMR2g=G\frac{M}{R^2}

The acceleration of gravity is determined by the mass and radius of the planet.

The value of the gravitational constant

G=6,671011Nm2kg2G=6{,}67\cdot10^{-11}\,\frac{\mathrm{N}\cdot\mathrm{m}^2}{\mathrm{kg}^2}

The gravitational constant sets the scale of gravitational interaction.

Translational equilibrium condition

F=0\sum\vec{F}=0

The vector sum of forces in translational equilibrium is zero.

Rotational equilibrium condition

M=0\sum M=0

The algebraic sum of the moments of forces in rotational equilibrium is equal to zero.

moment of force

M=FlM=Fl

The moment of force is equal to the product of force and its arm.

Unit of moment of force

[M]=1Nm[M]=1\,\mathrm{N}\cdot\mathrm{m}

The moment of force is measured in newton meters.

DIRECTORY

Related formulas

PRACTICE

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