# mcq on generalized hooke's law

For the object on the spring, the units of amplitude and displacement are meters. Have questions or comments? When a spring is hung vertically and a block is attached and set in motion, the block oscillates in SHM. The period is the time for one oscillation. In position (A) the spring is at rest and no external force acts on the block. We first find the angular frequency. The stress at which extension of a material takes place more quickly as compared to the increase in load is called ____________ When the position is plotted versus time, it is clear that the data can be modeled by a cosine function with an amplitude $$A$$ and a period $$T$$. We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. For example, a heavy person on a diving board bounces up and down more slowly than a light one. Stress is inversely proportional to strain. d) Yielding point Work is done on the block to pull it out to a position of x = + A, and it is then released from rest. For more information contact us at info@libretexts.org or check out our status page at https://status.libretexts.org. The angular frequency can be found and used to find the maximum velocity and maximum acceleration: $\begin{split} \omega & = \frac{2 \pi}{1.57\; s} = 4.00\; s^{-1}; \\ v_{max} & = A \omega = (0.02\; m)(4.00\; s^{-1}) = 0.08\; m/s; \\ a_{max} & = A \omega^{2} = (0.02; m)(4.00\; s^{-1})^{2} = 0.32\; m/s^{2} \ldotp \end{split}$. View Answer, 6. "Up to proportional limit, stress strain graph is", hooke's law Multiple Choice Questions (MCQ) with choices straight line, curved, parabola, and ellipse for questions to ask during an interview. A 2.00-kg block is placed on a frictionless surface. Eventually, Hooke’s law helps you relate stresses (which are based on loads) to strains (which are based on deformations). Quiz questions and answers on Hooke's law quiz answers PDF 15 to learn online mechanics of materials course. The stiffness constant describes the stiffness of a material, and is measured in $$Nm^{-1}$$ (or $$Kgs^{-2}$$). This is the currently selected item. This force obeys Hooke’s law Fs = −kx, as discussed in a previous chapter. 1.6 newton ? 0. Khan Academy is a 501(c)(3) nonprofit organization. The object oscillates around the equilibrium position, and the net force on the object is equal to the force provided by the spring. - question 2746 c) 9 View Answer, 4. All rights reserved. The maximum acceleration is amax = A$$\omega^{2}$$. View Answer, 8. Answer: b Explanation: Hooke’s law states that strain is directly proportional to strain produced by the stress when a material is loaded within the elastic limit. Get Free Current Affairs and Govt Jobs Alerts in your mailbox. here is complete set of 1000+ Multiple Choice Questions and Answers, Prev - Strength of Materials Questions and Answers – Elasticity, Next - Strength of Materials Questions and Answers – Stress & Strain Curve, Strength of Materials Questions and Answers – Elasticity, Strength of Materials Questions and Answers – Stress & Strain Curve, Corrosion Engineering Questions and Answers, Polymer Engineering Questions and Answers, Design of Steel Structures Questions and Answers, Finite Element Method Questions and Answers, Structural Analysis Questions and Answers, Engineering Physics I Questions and Answers, Geotechnical Engineering I Questions and Answers, Construction & Building Materials Questions and Answers, Engineering Materials and Metallurgy Questions and Answers, Mechanical Metallurgy Questions and Answers, Prestressed Concrete Structures Questions and Answers, Aerospace Materials and Processes Questions and Answers, Mechanical Behaviour & Testing of Materials Questions and Answers, Strength of Materials Questions and Answers, Strength of Materials Questions and Answers – Stress due to Materials Used and Their Applications, Strength of Materials Questions and Answers – Bending Equation, Strength of Materials Questions and Answers – Bending Stress in Unsymmetrical Sections. Metallurgy One shot with MCQ ... Generalized Hookes Law … If we require a 3D analysis of materials, we must use a more advanced matrix relationship between stress and strain, known as Generalized Hooke’s Law. Edit. The position, velocity, and acceleration can be found for any time. The equation of the position as a function of time for a block on a spring becomes, $x(t) = A \cos (\omega t + \phi) \ldotp$. Missed the LibreFest? The string vibrates around an equilibrium position, and one oscillation is completed when the string starts from the initial position, travels to one of the extreme positions, then to the other extreme position, and returns to its initial position. We can use the equations of motion and Newton’s second law ($$\vec{F}_{net} = m \vec{a}$$) to find equations for the angular frequency, frequency, and period. Potential energy stored in a spring. The stiffer the spring, the shorter the period. This is just what we found previously for a horizontally sliding mass on a spring. Free hooke's law MCQs, ultimate and allowable stress; factor of safety, forces and stress, repeated loadings; fatigue, stresses in elastic range, hooke's law test prep for top engineering universities. If the block is displaced to a position y, the net force becomes Fnet = k(y − y0) − mg = 0. If two springs are used in series, the effective stiffness constant of both of them is less than either of them. It is important to remember that when using these equations, your calculator must be in radians mode. In mechanics of materials, Hooke‘s law is the relationship that connects stresses to strains. c) Stress law Our mission is to provide a free, world-class education to anyone, anywhere. To derive an equation for the period and the frequency, we must first define and analyze the equations of motion. d) 1 Spring potential energy example (mistake in math) LOL diagrams. (adsbygoogle = window.adsbygoogle || []).push({}); Before the elastic limit is reached, the sample is experiencing Elastic Deformation, where it will return to its original shape when the load (force) has been removed. a) 2 The cosine function cos$$\theta$$ repeats every multiple of 2$$\pi$$, whereas the motion of the block repeats every period T. However, the function $$\cos \left(\dfrac{2 \pi}{T} t \right)$$ repeats every integer multiple of the period. Participate in the Sanfoundry Certification contest to get free Certificate of Merit. For an isotropic, homogeneous and elastic material obeying Hooke’s law, the number of independent elastic constants is ____________ Transponder - is used to receive a signal and transmit a reply immediately. Frequency (f) is defined to be the number of events per unit time. 9th - 12th grade. If F is force, k is spring constant and x is extension, Hooke's Law tells us that: Preview this quiz on Quizizz. Estimate, from your graph, the weight after the addition of which the law seems no longer to apply. Alfred Nobel if Sweden invented Dynamite in 1867, When you pluck a guitar string, the resulting sound has a steady tone and lasts a long time (Figure $$\PageIndex{1}$$). The equilibrium position (the position where the spring is neither stretched nor compressed) is marked as x = 0 . a) Stress limit Note that the force constant is sometimes referred to as the spring constant. The angular frequency depends only on the force constant and the mass, and not the amplitude. $x(t) = A \cos \left(\dfrac{2 \pi}{T} t \right) = A \cos (\omega t) \ldotp \label{15.2}$. Consider a block attached to a spring on a frictionless table (Figure $$\PageIndex{3}$$). But we found that at the equilibrium position, mg = k$$\Delta$$y = ky0 − ky1. 1.5 newtons ? 25:59. Where in the stress-strain curve, the hooke’s law is valid? The SI unit for frequency is the hertz (Hz) and is defined as one cycle per second: $1\; Hz = 1\; cycle/sec\; or\; 1\; Hz = \frac{1}{s} = 1\; s^{-1} \ldotp$, Example $$\PageIndex{1}$$: Determining the Frequency of Medical Ultrasound. Hooke's law Multiple Choice Questions and Answers (MCQs), hooke's law MCQs with answers, stresses in elastic range MCQs, repeated loadings fatigue MCQs, forces and stress MCQs, ultimate and allowable stress factor of safety MCQs for questions to ask during an interview. For periodic motion, frequency is the number of oscillations per unit time. Diesel Engine was invented by Rudolf Diesel of Germany 1892, In summary, the oscillatory motion of a block on a spring can be modeled with the following equations of motion: \begin{align} x(t) &= A \cos (\omega t + \phi) \label{15.3} \\[4pt] v(t) &= -v_{max} \sin (\omega t + \phi) \label{15.4} \\[4pt] a(t) &= -a_{max} \cos (\omega t + \phi) \label{15.5} \end{align}, \begin{align} x_{max} &= A \label{15.6} \\[4pt] v_{max} &= A \omega \label{15.7} \\[4pt] a_{max} &= A \omega^{2} \ldotp \label{15.8} \end{align}. The generalized Hooke’s law for a material is given as σij ijkl kl==Cijklε,,, 1,2,3 (1) where, σijis a second order tensor known as stress tensor and its individual elements are the stress components. View Answer, 2. The units for amplitude and displacement are the same but depend on the type of oscillation. A good example of SHM is an object with mass $$m$$ attached to a spring on a frictionless surface, as shown in Figure $$\PageIndex{2}$$. The only two forces that act perpendicular to the surface are the weight and the normal force, which have equal magnitudes and opposite directions, and thus sum to zero. Consider the block on a spring on a frictionless surface. Hooke’s Law. In this case, there is no normal force, and the net effect of the force of gravity is to change the equilibrium position. Audiometer - Measures intensity of sound. The relationship between frequency and period is. Mechanics Channel by Mark Barkey 15,359 views. ? Figure $$\PageIndex{4}$$ shows a plot of the position of the block versus time. Physics. Highest value of stress for which Hooke’s law is applicable for a given material is called ____________ This set of Strength of Materials Multiple Choice Questions & Answers (MCQs) focuses on “Hooke’s Law”. b) Necking region Next lesson. At the equilibrium position, the net force is zero. The word ‘period’ refers to the time for some event whether repetitive or not, but in this chapter, we shall deal primarily in periodic motion, which is by definition repetitive. X ray was invented by Wilhelm Roentgen of Germany in 1895, c) The ratio of ultimate stress to the permissible stress The period is related to how stiff the system is. A concept closely related to period is the frequency of an event. Cross multiply x × 20 = 5 × x + 5 × 60 20x = 5x + 300 15x = 300 Since 15 × 20 = 300, the original weight is 20 N Problem #5: The elastic limit of a spring is reached with a weight of 90 kg.In this situation, the final stretch is 20 more the original. In position (C), a force F is used to stretch the spring by a length Δ x by pulling the block to the right. A system that oscillates with SHM is called a simple harmonic oscillator. The string of a guitar, for example, oscillates with the same frequency whether plucked gently or hard. advertisement. Vertical springs and energy conservation. The block begins to oscillate in SHM between x = + A and x = −A, where A is the amplitude of the motion and T is the period of the oscillation. d) All of the mentioned If the net force can be described by Hooke’s law and there is no damping (slowing down due to friction or other nonconservative forces), then a simple harmonic oscillator oscillates with equal displacement on either side of the equilibrium position, as shown for an object on a spring in Figure $$\PageIndex{2}$$. Stress and strain are dependent on each other. Quiz questions and answers on Hooke's law quiz answers PDF 15 to learn online mechanics of materials course.

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