A 2.0 kg mass is attached to the end of horizontal spring (k = 50 N/m) and set into simple harmonic motion with an amplitude of 0.10 m. What is the maximum speed of the mass?
(Assume there is no friction.)
A. 0.25 m/s
B. 0.5 m/s
C. 1.0 m/s
D. 2.5 m/s
E. 5.0 m/s
To find the maximum speed of the mass in simple harmonic motion, we need to use the equation for the maximum speed of an object in simple harmonic motion.
The maximum speed (v_max) of an object in simple harmonic motion can be calculated using the formula:
v_max = A * ω
where A is the amplitude of the motion and ω is the angular frequency, which can be calculated using the formula:
ω = √(k / m)
where k is the spring constant and m is the mass.
Given:
Amplitude (A) = 0.10 m
Spring constant (k) = 50 N/m
Mass (m) = 2.0 kg
Step 1: Calculate the angular frequency (ω)
ω = √(k / m)
ω = √(50 N/m / 2.0 kg)
ω = √(25 N.kg^(-1))
ω = 5 rad/s
Step 2: Calculate the maximum speed (v_max)
v_max = A * ω
v_max = 0.10 m * 5 rad/s
v_max = 0.50 m/s
Therefore, the maximum speed of the mass is 0.50 m/s.
The correct answer is B. 0.5 m/s.
To find the maximum speed of the mass in simple harmonic motion, you can use the relationship between amplitude and maximum speed in simple harmonic motion.
The maximum speed (Vmax) of an object in simple harmonic motion is given by the equation:
Vmax = ω A
Where ω is the angular frequency and A is the amplitude of the motion.
The angular frequency (ω) can be calculated using the formula:
ω = √(k / m)
Where k is the spring constant and m is the mass attached to the spring.
Let's substitute the given values into the formula:
k = 50 N/m
m = 2.0 kg
A = 0.10 m
First, find ω:
ω = √(k / m)
= √(50 N/m / 2.0 kg)
= √(25 N/kg)
= 5 N/kg
Now, find Vmax using the formula:
Vmax = ω A
= (5 N/kg) × (0.10 m)
= 0.50 N/kg·m
So, the maximum speed of the mass is 0.50 m/s.
Thus, the correct answer is B. 0.5 m/s.
Since the period T = 2π√(m/k)
y = 0.1 sin(√(k/m) t) = 0.1 sin(5t)
the speed
v = 0.5 cos(5t) which has a maximum value of 0.5