The maximum speed of a 3.1-{\rm kg} mass attached to a spring is 0.70 m/s, and the maximum force exerted on the mass is 12 N.
What is the amplitude of motion for this mass?
Express your answer using two significant figures.
Let A = the amplitude
k*A = 12 newtons
(1/2) kA^2 = (1/2)M*Vmax^2, with
Vmax = 0.70 m/s
M = 3.1 kg
You have two equations in two unknowns, k and A.
You should be able to take it from there
To find the amplitude of motion for the mass, we need to use the relationship between maximum speed, maximum force, and the amplitude of motion in a simple harmonic motion system.
The maximum speed of the mass is given as 0.70 m/s. This is the maximum speed of the mass as it oscillates back and forth.
The maximum force exerted on the mass is given as 12 N. This force occurs at the maximum displacement from equilibrium in the opposite direction of motion.
In simple harmonic motion, the maximum speed is related to the amplitude and frequency of the motion by the equation:
v_max = ω * A
where v_max is the maximum speed, A is the amplitude of motion, and ω is the angular frequency.
The maximum force is related to the amplitude and the spring constant (k) of the system by the equation:
F_max = k * A
where F_max is the maximum force and k is the spring constant.
We can rearrange the second equation to solve for the amplitude (A) in terms of the maximum force and the spring constant:
A = F_max / k
Now, we can substitute the given values into the equation to calculate the amplitude:
A = 12 N / k
However, the problem does not provide us with the value of the spring constant (k). Without this information, we cannot calculate the amplitude of motion.
To find the amplitude, we would need additional information such as the spring constant or the frequency of the motion.