A force of 50N extends by a material by 0.05 m. Calculate the force constant. (a) 10.0 N/m (b) 100.0 N/m (C) 1000.0 N/m (d) 10,000.0 N/m
To calculate the force constant, we can use Hooke's Law equation:
Force = force constant × extension
Given:
Force = 50 N
Extension = 0.05 m
Using Hooke's Law equation:
50 N = force constant × 0.05 m
To find the force constant, divide both sides of the equation by 0.05 m:
Force constant = 50 N / 0.05 m
Simplifying the expression:
Force constant = 1000 N/m
Therefore, the correct answer is (c) 1000.0 N/m.
To calculate the force constant, we need to use Hooke's Law, which states that the force exerted by a spring is directly proportional to the displacement of the spring from its equilibrium position.
Hooke's Law can be written as:
F = kx
Where:
F = Force
k = Force constant (also known as spring constant)
x = Displacement
Given that the force is 50 N and the displacement is 0.05 m, we can plug these values into the formula and solve for the force constant.
50 N = k * 0.05 m
Next, we isolate k by dividing both sides of the equation by 0.05 m:
k = 50 N / 0.05 m
k = 1000 N/m
Therefore, the force constant is 1000.0 N/m, which corresponds to option (C).
F = kx
so,
50 = .05k