If a car's has a suspension system with a force constant of 5.00×10^4N/m, how much energy must the car's shocks remove to dampen an oscillation starting with maximum displacement of 0.0750m?
The energy stored in a spring is given by:
E = (1/2)kx^2
where E is the energy, k is the force constant, and x is the displacement from the equilibrium position.
In this case, the maximum displacement is 0.0750m, so the energy stored in the suspension system is:
E = (1/2)(5.00×10^4 N/m)(0.0750m)^2
E = 211.9 J
To dampen the oscillation, the shocks must remove all of this energy, so the answer is:
211.9 J
To calculate the energy that the car's shocks must remove to dampen the oscillation, we can use the formula for the potential energy stored in a spring:
Potential Energy = (1/2) * k * x^2
Where:
k is the force constant of the suspension system (5.00 × 10^4 N/m)
x is the maximum displacement (0.0750 m)
Plugging in the given values into the formula, we get:
Potential Energy = (1/2) * (5.00 × 10^4 N/m) * (0.0750 m)^2
Potential Energy = 0.5 * 5.00 × 10^4 * (0.005625) N*m
Potential Energy = 1406.25 J
Therefore, the car's shocks must remove approximately 1406.25 Joules of energy to dampen the oscillation.