What is the work done by friction on an object
The reason for calculating the average friction is that the positive pressure of the board on the rubber belt is variable. For example, half of the board is on the rubber belt and half on the smooth slope. At this time, the pressure of the board on the rubber belt is half of the pressure on the whole slope. In other words, the minimum pressure of the board on the rubber belt is 0, and the maximum pressure is mgcos37 °, Moreover, since the displacement of the friction force relative to the object changes linearly, it can be replaced by the average force. At this time, the total friction is the work done by friction. This is also a way to do work with variable forces. I'll draw you an image to illustrate this. The area of the F-X image is the work done by the force F
how to calculate the heat generated by friction
1 how to calculate the heat generated by friction
friction does negative work on the block and positive work on the trolley
the heat generated by friction q = FS relative
the relative displacement s relative = l
the heat generated by friction q = FS relative = FL
the process of molecules colliding on the surface of objects that rub each other. Suppose that one body is stationary and the other moves relative to it. In this process, the molecules in the stationary body are impacted and some or all of the directional kinetic energy of the molecules in the moving body is obtained
the molecules that obtain this directional kinetic energy will collide with other molecules around them. Because the collisions between molecules are very frequent and the direction of collision is random, the original directional kinetic energy will eventually change into irregular kinetic energy, that is, the thermal kinetic energy will increase
as a result, the internal energy and temperature of the surface of the object rubbing against each other increase macroscopically. On the other hand, the molecules near the surface that obtain the additional kinetic energy of heat transport from the directional kinetic energy may run to the interior of the object or collide with the interior molecules, thus intensifying the thermal motion of the interior molecules. This causes the entire object to become "hot.".
when two objects are in direct contact, elastic force appears on the contact surface, and the contact surface is not smooth. When there is relative motion on the contact surface, the two objects exert sliding friction to each other to hinder the relative motion
1. Does sliding friction do work
from the above description of sliding friction, it is easy to draw a conclusion: sliding friction must do work. In fact, this conclusion is wrong. Although there must be relative motion between two objects with sliding friction, s in the formula for calculating work is the displacement of the stressed object relative to the ground, and there is relative motion between the two objects, but not all the two objects have displacement relative to the ground
as shown in Figure 1, objects a and B are stacked on the horizontal ground, and object a is tied to the vertical wall with a string. The contact between the two objects is not smooth, so object B is pulled out with horizontal tension. In the process of pulling out object B, the sliding friction between B and a is horizontal to the right, while the displacement of object a relative to the ground is zero, so the sliding friction between B and a does no work for a
to judge whether sliding friction does work, we must first find out which force does work on that object. The key is to see whether the displacement of the object relative to the ground in the direction of friction is zero
2. Must sliding friction do negative work
since the direction of friction is always opposite to the direction of relative motion, for example, the direction of sliding friction between a and B is always opposite to the direction of motion between B and a, it is easy to draw the wrong conclusion that the sliding friction must do negative work
to judge whether the sliding friction is doing negative work or positive work, we must first make clear which force is doing work on which object. The key is to judge whether the angle between the direction of sliding friction and its displacement direction relative to the ground is greater than, equal to or less than 90o, which corresponds to doing negative work, not doing work and doing positive work respectively
as shown in Figure 2, a long board B with unsmooth surface is placed on the smooth horizontal ground, and a small object a can be regarded as a particle slides from the left end of the board to the right end at the horizontal initial velocity vo. As shown in Fig. 3 and Fig. 4, before a leaves B, the sliding friction Fab of object a is horizontally to the left, and the displacement SA direction of a relative to the ground is to the right, so the sliding friction Fab does negative work on a; The direction of the sliding friction FBA on B is right, and the direction of the displacement sb on the ground is right. The sliding friction FBA does positive work on B
3. Is the algebraic sum of the work of a pair of sliding friction forces not zero
the forces between objects always interact with each other, and the sliding friction between two objects is no exception. For example, in Figure 2, when a applies sliding friction FBA to B, it is also affected by the sliding friction FBA of B to a, which is the reaction force of this force. According to Newton's third law, these two forces are equal in size. If their size is f, then in the above process, The work of these two forces is: respectively,. Because | SA | & gt| So wa + WB ≠ 0
there is sliding friction between two objects, and the two objects must slide relative to each other. In a period of time, their respective displacements relative to the ground must not be equal, and the algebraic sum of the work of a pair of friction forces as force and reaction force must not be equal to zero
4. Is the algebraic sum of a pair of sliding friction work equal to the increment of their mechanical energy
in the "slider model" as shown in Figure 2, let the masses of a and B be m and m respectively, and their velocities when a leaves B be VA and VB respectively. The theorem of kinetic energy is used for a and B respectively. Thus, it can be seen that the algebraic sum of this pair of friction work is equal to the increment of mechanical energy of a and B systems. At the same time, it is not difficult to see. It can also be seen that the mechanical energy lost by the system. Therefore, the loss of mechanical energy or the increase of internal energy can also be calculated by the model
because the sliding friction does negative work on a, that is to say, a does work against the sliding friction, the amount of work is equal to the reced mechanical energy of A. It can be seen from the above discussion that part of the reced mechanical energy of a is transferred to the kinetic energy of B, and part of it is converted to the internal energy of the system
therefore, in the "slider model", the algebraic sum of the work of a pair of sliding friction forces acting as force and reaction force must be equal to the increment of their mechanical energy
5. Is the amount of work done by sliding friction only related to displacement
in the problem of work done by sliding friction discussed above, the size and direction of the sliding friction involved are constant, that is, in the process of discussion, the friction is a constant force. When calculating the work of friction, the displacement of the object in the process of study is taken to calculate the work. But if the sliding friction is variable in the process of research, the situation is different. For example:
pull the slider with horizontal tension to move along the horizontal circular track with radius r for one circle, as shown in Figure 5, the known mass of the slider is m, and the dynamic friction coefficient between the block and the track is μ Find the work done by friction in this process
in the process of an object moving along a circle, the direction of friction is always opposite to the direction of motion, and the circle is tangent, which belongs to variable force, but the size remains unchanged. As shown in Figure 6, if the circular orbit is divided into infinitely many infinitesimal segments, and the friction force on each segment can be regarded as a constant force, then the work done by the friction force on each segment is respectively,,,..., and the work done by the friction force in a week
therefore, if the friction involved in the problem is not constant, when calculating the work of sliding friction, the actual path of the object motion should be considered, not just the displacement. We can not only use the formula to calculate, but also use the "micro element division" or functional relationship, energy conservation and other physical relationships used above
2. Static friction
when there is static friction between two objects, the two objects are relatively static, but they may move relative to other reference frames, and the speed is the same
6. Does static friction do work
to answer this question, we have to start from the calculation formula of work. F in the formula is the force to calculate the work. S is the displacement of the stressed object. Its size and direction are related to the selection of reference system. When calculating the work of a certain force, the reference system is the object that is stationary on the ground or relative to the ground. In specific problems, if the forced object can be simplified as a particle, then the displacement is the displacement of the particle; if it cannot be simplified as a particle, then the displacement is the displacement of the point of action of the force. In the formula is the angle between the direction of displacement and the direction of force. Force F, displacement s, cos in the formula α, As long as one of the three quantities is zero, the work will be zero, that is, no work will be done. When we talk about whether static friction does work, the premise is that static friction must exist, and then we look at s and COS α If s is zero, that is to say, the object under the action of static friction is stationary relative to the ground, the work of static friction is zero, that is, static friction does not do work. If s is not zero, but α= When the static friction is perpendicular to the moving direction of the object, the static friction does not do work. In addition, the work of static friction will not be zero, that is to say, static friction will do work
for example, we use our fingers to hold up the pen and balance the force of gravity to make the pen stationary relative to our fingers, which is the static friction force between our fingers and the pen. Its direction is vertical and upward. When the pen moves horizontally in the air, the static friction force between our fingers and the pen does not work; When the pen moves in a non horizontal direction, the static friction between the finger and the pen does work on the pen
under the premise of static friction, whether it does work depends on s or cos α Is zero
7. Does static friction do positive work or negative work
after discussing whether static friction does work, it is relatively simple to discuss this problem. It can be seen from the formula that when the angle between the direction of static friction and the direction of displacement is less than 90o, that is α& lt; At 90o, the static friction does positive work; When the angle between the direction of static friction and the direction of displacement is greater than 90o, i.e α& gt; At 90o, the static friction does negative work. As mentioned above, the work of static friction is positive if the pen is moved upward with the finger in the air; If it moves downward, the work of static friction is negative
whether static friction does positive work or negative work depends on the angle between the direction of static friction and the direction of displacement
8. Is the algebraic sum of a pair of static friction work zero
the interaction of forces between objects is mutual, that is, force and reaction, which always act on two objects equivalently, reversely and collinear, and static friction is no exception. So, is the algebraic sum of the work done by a pair of static friction forces acting on each other and reacting on each other zero? Since the static friction force is relatively static, the displacement relative to the ground is the same. The answer is yes, that is, the algebraic sum of the work of a pair of static friction forces as the acting force and reaction force must be zero
for example, if an object is placed on a horizontal ground and pulled by a horizontal pull F, the object is still stationary. At this time, the static friction between the ground and the object and the ground is F. because the displacement of the object (particle) relative to the ground is zero, the displacement of the point of action of the static friction between the object and the ground relative to the ground is also zero, of course, The work of these two forces on each other is naturally zero, and the algebraic sum of the work of the static friction of these two forces is naturally zero. For another example, place two objects a and B on the horizontal ground, and pull object a with horizontal tension F, so that the two objects a and B remain relatively static and move in a straight line together, as shown in Figure 7. In the process of motion, the displacement of two objects is the same, the static friction of a to B is equal to that of B to a, and the current direction is opposite
9
at first glance, this problem seems to be doing positive work. In fact, the static friction of the ground against people does not do work. In the process of walking, only when people's feet touch the ground can they be affected by the static friction of the ground to the feet. When the feet are lifted and moved forward, they are not affected by the static friction of the ground. From the foot touching to the ground, the action point of static friction does not move relative to the ground, that is, the displacement of the foot relative to the ground is zero, so the static friction of the ground does no work to the human. In the same way, the static friction between human and the ground does not work on the ground
since people don't do work, how can they get kinetic energy when they walk? When walking, people's feet are inclined backward to the ground. When landing, the lower limbs of the human body exert an oblique forward and upward force on the trunk, and the trunk moves forward. Therefore, this force does positive work on the human body and enables people to obtain kinetic energy. When people land and lift their feet forward, they need the contraction and relaxation of lower limb muscles, which naturally consumes the biochemical energy of the human body. Therefore, the kinetic energy that people get ring walking actually comes from the chemical energy of human body. The existence of the static friction between the ground and the human body ensures the implementation of the force of the lower limbs on the trunk when walking, and provides conditions for human muscles to exert force and work
10. Does the friction between the ground and the driving wheel do work on the car in motion
in the movement of the car, the engine is driven by the transmission