When a spring is stretched, the force exerted is proportional to the increase in length from the equilibrium length, according to Hooke’s Law. The spring constant can be calculated using the following formula: k = -F/x, where k is the spring constant. F denotes the force, and x denotes the change in spring length.
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How do you solve a spring problem in physics?
What is the equilibrium position of a horizontal spring?
Horizontal Spring The position where the spring is not stretched or compressed is the equilibrium position (x=0 in Figure 1) and it corresponds to the natural length of the spring, L0 . If you attach the mass to the spring in this position, the mass will stay at rest and not move – if left unperturbed.
How do you solve SHM problems?
The velocity of the mass on a spring, oscillating in SHM, can be found by taking the derivative of the position equation: v ( t ) = d x d t = d d t ( A cos ( ฯ t + ฯ ) ) = โ A ฯ sin ( ฯ t + ฯ ) = โ v max sin ( ฯ t + ฯ ) .
What is the formula for spring force?
F = -kx. The proportional constant k is called the spring constant. It is a measure of the spring’s stiffness. When a spring is stretched or compressed, so that its length changes by an amount x from its equilibrium length, then it exerts a force F = -kx in a direction towards its equilibrium position.
What is the spring constant k value?
The letter k represents the “spring constant,” a number which essentially tells us how “stiff” a spring is. If you have a large value of k, that means more force is required to stretch it a certain length than you would need to stretch a less stiff spring the same length.
What is the spring constant k?
The spring constant, k, is a measure of the stiffness of the spring. It is different for different springs and materials. The larger the spring constant, the stiffer the spring and the more difficult it is to stretch.
How do you find slope in Hooke’s Law?
W = kx. W is the weight of the added mass. Therefore, the spring constant k is the slope of the straight line W versus x plot. Weight is mass times the acceleration of gravity or W = mg where g is about 980 cm/sec2.
What force causes the periodic motion of a spring on a horizontal surface?
Explanation: Once the mass attached to the spring is set to oscillate, the spring is being stretched or compressed periodically. When the spring it stretched, it exerts a force on the mass, pulling it toward the spring.
How do you calculate the period of a spring?
Mass on a spring – Where a mass m attached to a spring with spring constant k, will oscillate with a period (T). Described by: T = 2ฯโ(m/k). By timing the duration of one complete oscillation we can determine the period and hence the frequency.
How do you find the total energy of a spring?
The total energy of the system of a block and a spring is equal to the sum of the potential energy stored in the spring plus the kinetic energy of the block and is proportional to the square of the amplitude ETotal=(1/2)kA2. E Total = ( 1 / 2 ) k A 2 .
What is SHM in physics class 11?
Simple Harmonic Motion or SHM is defined as a motion in which the restoring force is directly proportional to the displacement of the body from its mean position.
What is the formula for velocity in SHM?
Now, we know that velocity is maximum when y=0, i.e., displacement is zero and acceleration is zero, which means the system is in equilibrium. Therefore, at a point in simple harmonic motion, the maximum velocity can be calculated using the formula v=Aฯ.
What is the formula for oscillation?
The angular frequency ฯ, period T, and frequency f of a simple harmonic oscillator are given by ฯ=โkm, T = 2ฯโmk, and f = 12ฯโkm, where m is the mass of the system and k is the force constant.
What does F =- KX stand for?
Mathematically, Hooke’s law states that the applied force F equals a constant k times the displacement or change in length x, or F = kx.
Is it f Kx or F =- KX?
Hooke’s law is formulated as either F = -kx with a minus symbol or as F = kx without the minus symbol. If the minus is present, F indicates a restoring force, that is, the force that allows the object to return to its original shape and position.
How do you calculate how far a spring will stretch?
We can find the spring constant of the spring from the given data for the 4 kg mass. Then we use x = F/k to find the displacement of a 1.5 kg mass. The work that must be done to stretch spring a distance x from its equilibrium position is W = ยฝkx2.
What is Hooke’s Law example?
A balloon is elastic in nature. When the air molecules are blown in it, it expands. Similarly, when it is evacuated, it shrinks in size. The expansion and compression of the balloon depend on the force with which the air is pressed into it; therefore, it works on the basis of Hooke’s law.
Why is Hooke’s Law negative?
Explanation: Hooke’s law, as we know, expresses an object’s restoring force when subjected to an external force. Because it acts in the opposite direction as the applied force, the restoring force is considered negative in the calculations.
What is dimension of Hooke’s Law?
M1L2Tโ1.
Does spring constant depend on length?
As from the spring constant equation, the spring constant and length are inversely proportional. Therefore if the length of the spring is increased spring constant decreases and If the spring is cut to half of its original length then the spring constant increases to twice that of the original value.
What is the SI unit of spring?
The unit of the spring constant is N/m.
Is spring constant negative?
The spring constant , is always positive to support the fact that it will oppose the applied external force.
What is Hooke’s Law BBC?
When an object, such as a spring, is stretched, the increased length is called its extension. Hooke’s law: The extension of a spring is directly proportional to the force applied, provided that the limit of proportionality is not exceeded.
What factor does spring constant depend on?
The spring constant will depend on the stiffness of the spring material, the thickness of the wire from which the spring is wound and, the diameter of the turns of the coil, the number of turns per unit length and the overall length of the spring.