Answer :
Final answer:
The mass of the block is 0.800 kg.
Explanation:
To calculate the mass of the block, we can use the given information and the formulas for simple harmonic motion.
First, let's calculate the period of oscillation using the formula T = 2π√(m/k), where T is the period, m is the mass of the block, and k is the spring constant.
Since the block is halfway between its equilibrium position and the endpoint, its displacement is equal to half the amplitude, which is 5.5 cm / 2 = 2.75 cm.
The speed of the block at this point is given as 38.8 cm/s.
Using the formula v = ωA, where v is the speed, ω is the angular frequency, and A is the amplitude, we can calculate the angular frequency:
ω = v / A = 38.8 cm/s / 5.5 cm = 7.05 rad/s.
Now, we can calculate the period using the formula T = 2π/ω:
T = 2π / 7.05 rad/s = 0.895 s.
Finally, we can use the period and the spring constant to calculate the mass of the block:
T = 2π√(m/k)
0.895 s = 2π√(m/7.4 N/m)
Squaring both sides of the equation:
0.800 m^2/s^2 = 4π^2(m/7.4 N/m)
Simplifying the equation:
0.800 m^2/s^2 = (4π^2/7.4 N/m) * m
0.800 m^2/s^2 = (1.698 m^2/s^2) * m
Dividing both sides of the equation by 1.698 m^2/s^2:
0.800 = m
Therefore, the mass of the block is 0.800 kg.
Learn more about calculating the mass of a block attached to a spring here:
https://brainly.com/question/30266126
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Final answer:
The mass of the block is 0.800 kg.
Explanation:
To calculate the mass of the block, we can use the given information and the formulas for simple harmonic motion.
First, let's calculate the period of oscillation using the formula T = 2π√(m/k), where T is the period, m is the mass of the block, and k is the spring constant.
Since the block is halfway between its equilibrium position and the endpoint, its displacement is equal to half the amplitude, which is 5.5 cm / 2 = 2.75 cm.
The speed of the block at this point is given as 38.8 cm/s.
Using the formula v = ωA, where v is the speed, ω is the angular frequency, and A is the amplitude, we can calculate the angular frequency:
ω = v / A = 38.8 cm/s / 5.5 cm = 7.05 rad/s.
Now, we can calculate the period using the formula T = 2π/ω:
T = 2π / 7.05 rad/s = 0.895 s.
Finally, we can use the period and the spring constant to calculate the mass of the block:
T = 2π√(m/k)
0.895 s = 2π√(m/7.4 N/m)
Squaring both sides of the equation:
0.800 m^2/s^2 = 4π^2(m/7.4 N/m)
Simplifying the equation:
0.800 m^2/s^2 = (4π^2/7.4 N/m) * m
0.800 m^2/s^2 = (1.698 m^2/s^2) * m
Dividing both sides of the equation by 1.698 m^2/s^2:
0.800 = m
Therefore, the mass of the block is 0.800 kg.
Learn more about calculating the mass of a block attached to a spring here:
https://brainly.com/question/30266126
#SPJ14
