An exercise spring has a spring constant of 315 N/m. How much work is required to stretch the spring 30 cm? What force is needed to stretch the spring 30 cm?
Use meters for the displacement, X.
Force = k*X = 315*0.3 = 94.5 N
Work = (1/2)*k*X^2 = (1/2)(315)(.3)^2
= 14.2 J
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To find the amount of work required to stretch the spring, we can use the formula:
Work = (1/2) * k * x^2
where k is the spring constant and x is the displacement from the equilibrium position.
Given:
Spring constant (k) = 315 N/m
Displacement (x) = 30 cm = 0.3 m (converted from cm to meters)
1. Calculate the work required:
Work = (1/2) * k * x^2
Work = 0.5 * 315 N/m * (0.3 m)^2
Work = 0.5 * 315 N/m * 0.09 m^2
Work = 14.175 N * m
Therefore, the work required to stretch the spring 30 cm is 14.175 N * m.
2. To find the force needed to stretch the spring:
Force = k * x
Force = 315 N/m * 0.3 m
Force = 94.5 N
Therefore, the force needed to stretch the spring 30 cm is 94.5 N.
To determine the work required to stretch the spring and the force needed to do so, we can use Hooke's Law, which states that the force required to stretch or compress a spring is directly proportional to the displacement of the spring from its equilibrium position. The formula for Hooke's Law is:
F = -kx
Where:
F is the force applied to the spring (in newtons),
k is the spring constant (in newtons per meter),
and x is the displacement of the spring (in meters).
First, let's convert the displacement of the spring from centimeters to meters. Since 1 meter is equal to 100 centimeters, we divide the given displacement of 30 cm by 100:
x = 30 cm ÷ 100 cm/m = 0.3 m
Now we can calculate the force required to stretch the spring:
F = -kx
F = -(315 N/m)(0.3 m)
F = -94.5 N
The negative sign indicates that the force required is in the opposite direction of the displacement. In this case, the force will be directed towards the equilibrium position of the spring.
To calculate the work required to stretch the spring, we use the formula:
Work = (1/2)kx^2
Work = (1/2)(315 N/m)(0.3 m)^2
Work = (1/2)(315 N/m)(0.09 m^2)
Work = 14.175 J
Therefore, it requires 14.175 J of work to stretch the spring 30 cm, and a force of -94.5 N is needed to accomplish this.