Solution D2-76 (Figure D2.7 condition 6 S.M. Targ 1989)

In accordance with Solution D2-76 (Figure D2.7, condition 6, S.M. Targ, 1989), load 1 with mass m is fixed on a spring suspension in an elevator that moves vertically according to the law z = 0.5α1t2 + α2sin (ωt) + α3cos(ωt) (z axis is directed upward, z is expressed in meters, t in seconds). The load is acted upon by the resistance force of the medium R = μv, where v is the speed of the load relative to the elevator. It is necessary to find the law of motion of the load relative to the elevator, that is, x = f(t), where the origin of coordinates is at the point where the end of the spring attached to the load is not deformed. To avoid errors in signs, the x-axis is directed in the direction of extension of the spring, and the load is depicted in a position where x>0, which means that the spring is extended. When calculating, you can take g = 10 m/s2. The mass of the springs and connecting strip 2 can be neglected. The table indicates c1, c2, c3 - spring stiffness coefficients, λ0 - elongation of a spring with equivalent stiffness at the initial time t = 0, v0 - initial speed of the load relative to the elevator (directed vertically upward). A dash in columns c1, c2, c3 means that the corresponding spring is missing and should not be shown in the drawing. If the end of one of the remaining springs is loose, it should be attached in an appropriate place, either to the load or to the ceiling (floor) of the elevator. The same should be done if the ends of both remaining springs connected by strap 2 are free. The condition μ = 0 means that there is no resistance force R.

Solution D2-76 (Figure D2.7 condition 6 S.M. Targ 1989)

The D2-76 solution is a unique digital product that can be useful to students and professionals in the field of physics and engineering. The solution is based on the work of S.M. Targa 1989 and contains a detailed description of the movement of a load mounted on a spring suspension in an elevator, which moves vertically according to a certain law.

The solution presents formulas for calculating the resistance force of the medium and the law of movement of the load relative to the elevator. Tables with spring stiffness coefficients and other parameters necessary to perform calculations are also provided.

The D2-76 solution is highly accurate and allows you to get a detailed understanding of the movement of cargo in a spring-suspended elevator. The product is available in PDF format and can be downloaded immediately after payment.

Purchase Solution D2-76 and gain the necessary knowledge and skills for your professional activities!

Solution D2-76 is a digital product containing a detailed description of the movement of a load mounted on a spring suspension in an elevator, which moves vertically according to a certain law. The solution is based on the work of S.M. Targa 1989 and contains formulas for calculating the resistance force of the environment and the law of movement of cargo relative to the elevator.

The solution also contains tables with spring stiffness coefficients and other parameters necessary to perform calculations. The D2-76 solution allows you to get a detailed picture of the movement of cargo in a spring-suspended elevator and is highly accurate.

The product is available in PDF format and can be downloaded immediately after payment. Solution D2-76 can be useful for students and professionals in the field of physics and engineering to obtain the necessary knowledge and skills for their professional activities.

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Solution D2-76 is a problem about the movement of a load of mass m mounted on a spring suspension in a vertically moving elevator. The movement of the elevator is described by the equation z = 0.5α1t^2 + α2sin(ωt) + α3cos(ωt), where z is the elevator coordinate, t is time, α1, α2, α3 are coefficients, and ω is the oscillation frequency. The load is acted upon by the resistance force of the medium R = μv, where v is the speed of the load relative to the elevator, and μ is the drag coefficient.

It is necessary to find the law of movement of the load relative to the elevator, i.e. x = f(t), provided that the x axis is directed in the direction of elongation of the spring, the origin of coordinates is at the point where the end of the spring attached to the load is located when the spring is not deformed, and the load is depicted in a position in which x > 0. It is also necessary to take g = 10 m/s^2 and neglect the mass of the springs and connecting strip 2. The table gives the values ​​of the spring stiffness coefficients c1, c2, c3, spring elongation λ0 and the initial speed of the load relative to the elevator v0. If there is no spring, then the corresponding coefficient takes on the value of a dash. If the end of the spring or the bars connected to it is free, it should be attached in the appropriate place.

If the resistance coefficient μ is zero, then there is no resistance force R.

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