In an electric shaver, the blade moves back and forth over a distance of 2.0 mm. The motion is simple harmonic, with frequency 118 Hz.
(a) Find the amplitude.
mm
(b) Find the maximum blade speed.
m/s
(c) Find the magnitude of the maximum blade acceleration.
m/s2
a) A= 2.0 mm /2 = 1.0 mm = 0.001 m
b) The time it takes the blade to go back AND forth (the period of the oscillation) can be found as follows:
T=1/f= 1/118Hz = 0.00847 s
So, for the blade to cross the distance of 0.002 m, it takes 0.00847/2 s = 0.00424 s.
v = x/t = 0.002 m / 0.00424 s = 0.472 m/s
So its maximum speed is 0.472 m/s
I will be happy to critique your thinking.
nope, we need to find w then find v= w*xm = 741.416*0.001= .741416
then a= w^2*xm = 549.697
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To find the answers to these questions, we need to use the formulas related to simple harmonic motion. The formulas we will use are:
(a) Amplitude (A) = maximum displacement from the equilibrium position
(b) Maximum speed (vmax) = maximum speed when the displacement is maximum
(c) Maximum acceleration (amax) = maximum acceleration when the displacement is maximum
Now let's solve the problems step by step:
(a) The amplitude (A) is equal to half the total distance traveled by the blade. In this case, the total distance is 2.0 mm. So, the amplitude is:
Amplitude (A) = 2.0 mm / 2 = 1.0 mm
Therefore, the amplitude is 1.0 mm.
(b) The maximum speed (vmax) can be found using the formula:
vmax = 2πfA
Where:
- π (pi) is a constant approximately equal to 3.14
- f is the frequency in hertz
- A is the amplitude
Substituting the given values, we have:
vmax = 2π(118 Hz)(1.0 mm)
Now we need to convert the amplitude from mm to meters because the speed is given in m/s:
1.0 mm = 1.0 mm / 1000 = 0.001 m
vmax = 2π(118 Hz)(0.001 m)
Solving this equation, we find the maximum speed (vmax).
(c) The maximum acceleration (amax) can be found using the formula:
amax = (2πf)^2A
Substituting the given values, we have:
amax = (2π(118 Hz))^2(1.0 mm)
Again, we need to convert the amplitude from mm to meters:
1.0 mm = 1.0 mm / 1000 = 0.001 m
amax = (2π(118 Hz))^2(0.001 m)
Now, we can solve this equation to find the magnitude of the maximum blade acceleration (amax).
Therefore, to find the amplitude, maximum blade speed, and magnitude of maximum blade acceleration, follow the steps outlined above using the given formulas and values.
Sorry, made an error in my reasoning.
Amplitude is correct, but speed and acceleration isn't.
For a body undergoing simple harmonic motion, the expression for the maximum speed is:
v(max) = A*f = 0.001 m * 118 Hz = 0.118 m/s
and the expression for the maximum acceleration is:
a(max) = A*f² = 0.001m * (118 Hz)² = 13.924 m/s²