Spring Physics: Energy and Force Calculation
This problem involves calculating the force required to extend a spring based on its stored energy during compression. We will use the formulas for potential energy stored in a spring and Hooke's Law.
Calculating the Spring Constant
First, we determine the spring constant (\(k\)) using the energy stored (\(E\)) when compressed by a distance (\(\Delta x_1\)).
- Given Energy: \(E = 2\) J
- Given Compression: \(\Delta x_1 = 4\) cm \(= 0.04\) m
- Potential Energy Formula: \(E = \frac{1}{2} k (\Delta x_1)^2\)
- Rearranging for \(k\): \(k = \frac{2E}{(\Delta x_1)^2}\)
- Calculation: \(k = \frac{2 \times 2 \text{ J}}{(0.04 \text{ m})^2} = \frac{4}{0.0016} \text{ N/m} = 2500 \text{ N/m}\)
Calculating the Extension Force
Next, we calculate the force (\(F\)) needed to extend the spring by a different distance (\(\Delta x_2\)), using the calculated spring constant (\(k\)).
- Spring Constant: \(k = 2500\) N/m
- Given Extension: \(\Delta x_2 = 8\) cm \(= 0.08\) m
- Force Formula (Hooke's Law): \(F = k (\Delta x_2)\)
- Calculation: \(F = (2500 \text{ N/m}) \times (0.08 \text{ m}) = 200 \text{ N}\)
The force required to extend the spring by 8 cm is 200 N.
Similar Questions
If a force ‘F’ acts on a body such that body gets displaced through the distance ‘x’ in the direction of the force, then the work done by the force is ____________.
The kinetic energy of a moving object is dependent on which of the following quantities:
i) Mass of the body
ii) Square of the velocity
iii) PressureWhich of the following statements refer/s to the law of conservation of energy?
Statements:
I) Energy can be converted from one form to another form of energy.
II) Energy can neither be created nor destroyed.
The work done in moving 10 coulomb charges across the potential difference of 5 volts is______.
- Mechanical energy is the sum of _______.
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Important Questions from Work and Energy
If a force ‘F’ acts on a body such that body gets displaced through the distance ‘x’ in the direction of the force, then the work done by the force is ____________.
The kinetic energy of a moving object is dependent on which of the following quantities:
i) Mass of the body
ii) Square of the velocity
iii) PressureWhich of the following statements refer/s to the law of conservation of energy?
Statements:
I) Energy can be converted from one form to another form of energy.
II) Energy can neither be created nor destroyed.
The work done in moving 10 coulomb charges across the potential difference of 5 volts is______.
- Mechanical energy is the sum of _______.
