Instruction

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Case 1. The formula for force of friction: Fтр = MP, where m is the coefficient of sliding friction, N is the reaction force bearing, N. Body sliding on a horizontal plane, N = G = mg, where G is the weight of the body, N; m – body mass, kg; g – free fall acceleration, m/S2. Values of the dimensionless ratio m for a given pair of materials is given in reference literature. Knowing the body weight and a few materials. moving relative to each other, find the force of friction.

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Case 2. Consider a body sliding on a horizontal surface and moving uniformly accelerated. It is subject to four forces: the force that causes a body in motion, the force of gravity, the reaction force bearing, the sliding friction force. Since the surface is horizontal, the reaction force bearing and the force of gravity is directed along the same straight line and balance each other. The displacement equation: Fdv - Fтр = ma; where Fdv – power module, causing the body to move, N; Fтр module of the friction force, N; m – body mass, kg; a is the acceleration, m/S2. Knowing the mass of the acceleration and forces acting on it, find the force of friction. If these values are not specified directly, see if the condition data from which it is possible to find these values.

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Example problem 1: a block of mass 5 kg, lying on the surface, the impact force of 10 N. As a result, the bar is moving uniformly accelerated and passes 10 meters in 10 seconds. Find the force of sliding friction.

The equation for the motion of the bar:Fdv - Fтр = ma. The path of the body for uniformly accelerated motion is given by the equation: S = 1/2at^2. From here you can determine the acceleration: a = 2S/t^2. Substitute these terms: a = 2*10/10^2 = 0.2 m/S2. Now find the resultant of two forces: ma = 5*0,2 = 1 N. Calculate the friction force: Fтр = 10-1 = 9 N.

The equation for the motion of the bar:Fdv - Fтр = ma. The path of the body for uniformly accelerated motion is given by the equation: S = 1/2at^2. From here you can determine the acceleration: a = 2S/t^2. Substitute these terms: a = 2*10/10^2 = 0.2 m/S2. Now find the resultant of two forces: ma = 5*0,2 = 1 N. Calculate the friction force: Fтр = 10-1 = 9 N.

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Case 3. If the body on a horizontal surface is at rest, or moves uniformly according to the second Newton's law the forces are in balance : Fтр = Fdv.

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Example problem 2: block of mass 1 kg, are on a flat surface, said impulse, in which he traveled 10 meters in 5 seconds and stopped. Determine the force of sliding friction.

As in the first example, the slide bars affect the strength of the movement and the friction force. As a result, the impact of the body stops, i.e. comes to equilibrium. The equation of motion of the bar: Fтр = Fdv. Or: N*m = ma. The bar glides uniformly accelerated. Calculate its acceleration like a objective 1: a = 2S/t^2. Substitute the values: a = 2*10/5^2 = 0.8 m/S2. Now find the friction force: Fтр = ma = 0,8*1 = 0.8 N.

As in the first example, the slide bars affect the strength of the movement and the friction force. As a result, the impact of the body stops, i.e. comes to equilibrium. The equation of motion of the bar: Fтр = Fdv. Or: N*m = ma. The bar glides uniformly accelerated. Calculate its acceleration like a objective 1: a = 2S/t^2. Substitute the values: a = 2*10/5^2 = 0.8 m/S2. Now find the friction force: Fтр = ma = 0,8*1 = 0.8 N.

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Case 4. The body spontaneously moving up an inclined plane has three forces: the force of gravity (G) force of support reaction (N) and friction force (Fтр). The force of gravity can be written in the following form: G = mg, N, where m is body mass, kg; g – free fall acceleration, m/S2. Since these forces are not directed along the same line, write the equation of motion in vector form.

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Folded according to the rule of the parallelogram of forces N and mg, you will get a resulting force F’. From the figure we can conclude: N = mg*cosα; F’ = mg*sinα. Where α is the angle of the plane. The friction force can be recorded by the formula: Fтр = m*N = m*mg*cosα. The equation of motion takes the form: F’-Fтр = ma. Or: Fтр = mg*sinα-ma.

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Case 5. If applied to the body an additional force F, directed along an inclined plane, the friction force is expressed by: Fтр = mg*sinα+F-ma, if the direction of motion and the force F are the same. Or: Fтр = mg*sinα-F-ma, if the force F opposes the motion.

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Example problem 3: a block of mass 1 kg slipped from the top of an inclined plane in 5 seconds, having risen 10 meters. Determine the force of friction if the angle of inclination of plane is 45°. Consider also the case where the bar is exposed to an additional force of 2 N is applied along the angle of inclination in the direction of movement.

Find the acceleration of a body is similar to examples 1 and 2: a = 2*10/5^2 = 0.8 m/S2. Calculate the force of friction in the first case: Fтр = 1*9,8*sin(45o)-1*0,8 = N 7,53. Determine the friction force in the second case: Fтр = 1*9,8*sin(45o)+2-1*0,8= N at 9.53.

Find the acceleration of a body is similar to examples 1 and 2: a = 2*10/5^2 = 0.8 m/S2. Calculate the force of friction in the first case: Fтр = 1*9,8*sin(45o)-1*0,8 = N 7,53. Determine the friction force in the second case: Fтр = 1*9,8*sin(45o)+2-1*0,8= N at 9.53.

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Case 6. The body moves on the inclined surface evenly. So, according to Newton's second law, the system is in equilibrium. If slipping of the spontaneous motion of a body obeys the equation: mg*sinα = Fтр.

If applied to the body an additional force (F), which prevents a uniformly accelerated movement, the expression of motion has the form: mg*sinα–Fтр-F = 0. Hence, find the force of friction: Fтр = mg*sinα.

If applied to the body an additional force (F), which prevents a uniformly accelerated movement, the expression of motion has the form: mg*sinα–Fтр-F = 0. Hence, find the force of friction: Fтр = mg*sinα.

# Advice 2: How to find force of support reaction

The force

**of reaction****of support**refers to the elastic forces, and is always directed perpendicular to the surface. She resists any force that causes a body to move perpendicular to the support. In order to calculate it is necessary to identify and to know the numeric value of all the forces that act on the body, standing on a pedestal.You will need

- - scales;
- speedometer or the radar;
- - inclinometer.

Instruction

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Determine the body weight using a scale, or in any other way. If the body is on a horizontal surface (no matter it moves or remains at rest), the force of support reaction equal to the force of gravity acting on the body. To calculate it multiply the body weight in free fall acceleration equal to 9.81 m/S2 N=m•g.

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When the body moves along an inclined plane directed at an angle to the horizontal, the reaction force bearing is at an angle to gravity. However, she compensates only the component of gravity that acts perpendicular to the inclined plane. To calculate the reaction forces of the supports, using the protractor, measure the angle at which the plane is to the horizon. Calculate the

*force*of support reaction, multiplying body weight in free fall acceleration and the cosine of the angle at which the plane is to the horizon N=m•g•Cos(α).3

In that case, if the body moves over the surface, which is a part of a circle of radius R, for example, a bridge, a hill, the force of reaction of support takes into account the force acting in the direction from the center of the circle, with acceleration equal to the centripetal acting on the body. To calculate the reaction force bearing at the top, from the gravitational acceleration, subtract the ratio of the square of the velocity to the radius of curvature of the trajectory.

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The number you multiply by the mass of the moving body N=m•(g-v2/R). Speed should be measured in meters per second, and the radius in meters. At a certain speed, the value of the acceleration directed from the center of the circle can equal and even exceed the acceleration of free fall, in this moment, the clutch body with the surface will disappear, so, for example, motorists need to clearly control the speed on such sections of the road.

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If the curvature is directed downwards, and the trajectory of the body is concave, then calculate the reaction force bearing, adding to the acceleration of gravity the ratio of the square of the velocity and the radius of curvature of the trajectory, and the resulting multiply the result by body weight N=m•(g+v2/R).

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If you know the friction force and coefficient of friction, the reaction force bearing, calculate by dividing the friction force by this factor N=Fтр/μ.

# Advice 3: How to find work of friction force

The movement in real conditions can't continue indefinitely. The reason for this is the force

**of friction**. It occurs upon contact of a body with other bodies, and always directed opposite to the direction of movement. This means that the force**of friction**always does negative**work**, what to consider in the calculations.You will need

- - tape measure or rangefinder;
- - table for determining the coefficient of friction;
- - the concept of kinetic energy;
- - scales;
- calculator.

Instruction

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If the body is moving uniformly and rectilinearly, find the force which sets it in motion. It compensates for the force

**of friction**, therefore, numerically equal but pointing in the direction of motion. Measure with tape or rangefinder distance S, at which the force F moved the body. Then the work*of force***of friction**is equal to the product*of force*into distance with the sign "minus" A=-F∙S.2

Example. Car moving on the road uniformly. What

**work**does the force**of friction**on the distance of 200 m, if the thrust of the engine is equal to 800 N? With uniform rectilinear motion, the thrust of the engine is equal in magnitude to the force**of friction**. Then her work will be equal to A=F∙S =-800∙200=-160 -160000 j or kJ.3

The property of surfaces to hold on to each other shows the coefficient

**of friction**μ. For each pair of contacting surfaces it different. It is possible to calculate or learn the special table. There is a coefficient**of friction**of rest and the coefficient**of friction**of sliding. When calculating work*, the force***of friction**take the ratio for slides, because without the movement the work is not done. For example, the coefficient**of friction**of sliding of wood on metal is equal to 0.4.4

Determine

**the work***the force***of friction**acting on a body resting on a horizontal surface. To do this, determine its mass m to kilograms using the scales. Multiply the weight by the coefficient**of friction**of sliding of these surfaces μ, the acceleration of gravity (g≈10 m/S2) and the distance that moved the body, Before S. formula put a sign "a minus" because the body moves in the direction opposite to the direction*of force***of friction**(A=-μ∙m∙g∙S).5

The work of

*forces***of friction**, is only valid when it is equal to change in kinetic energy of the body. To find the definition of initial v0 and final velocity v of a body on the examined section of the route. Multiply the mass m of a body on the difference of the squares of the initial and final speed of the body, and the result divide by the number 2 (A=m∙(v2-v02)/2). For example, if the vehicle weight of 900 kg, traveling at a speed of 20 m/s stops, the work*of force***of friction**is equal And=900∙(02-202)/2=-180000 j or -180 kJ.# Advice 4: How to find frictional force

Friction – the process of interaction of two bodies, causing deceleration at offset relative to each other. Find

**force****friction**means to determine the magnitude of the impact is directed in the direction opposite to the movement, because of which the body loses energy and eventually stops.Instruction

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The force

**of friction**is a vector quantity, which depends on many factors: the pressure of bodies upon each other, the materials from which they were made, speed. Surface area in this case is irrelevant, because the bigger it is, the more reciprocal pressure (reaction force bearing N), which is already involved in finding the force**of friction**.2

These quantities are proportional to each other and connected with a coefficient

**of friction**μ, which can be considered constant, if greater accuracy of calculations is not required. So to find the**force****of friction**, you need to calculate the product:Fтр = μ•N.3

Given the physical formula refers to the friction caused by sliding. It can be dry and wet, if between the bodies is present in the liquid layer. The force

**of friction**must always be taken into account in determining the totality of the forces acting on the body in solving problems.4

Rolling friction occurs during rotation of a body on the surface of another. It is present on the boundary of contact bodies that is constantly changing. However, the force

**of friction**constantly opposes the motion. On this basis, it is equal to the ratio of the product of the coefficient**of friction**of the rolling and pressing forces to the radius of a rotating body:Fтркач = f•N/r.5

We must distinguish between the coefficient

**of friction**of sliding and rolling. In the first case is the value with no dimension, in the second it represents the distance between the straight lines that characterize the direction of clamping forces and the reaction forces of the supports. Therefore, it is measured in mm.6

The coefficient

**of friction**of rolling is usually a known value for common materials. For example, for iron for iron it is equal to 0.51 mm for iron on wood – 5,6, wood on wood – 0,8-1,5, etc. it can be Found by the formula the ratio of the moment**of friction**by the pressing force.7

The force

**of friction**of rest you receive at the minimum displacement or deformation. This force is always present in the dry slide. Its maximum value equals μ•N. There is also internal friction within the body between its layers or parts.Note

Uniform motion of a body is characterized by the balance between the external force and the frictional force.