Answer:
Explanation:
x = 2 cos wt = 2 cos 10t ; w = 10
velocity = dx/dt = -2 x 10 sin 10 t.=- 20 sin 10t
t = .4
velocity = -20 sin 10 x .4 = -20 sin 4 = -20 x -0.7568 = 15.136 cm /s
w = √ k / m = 10 = √ k / .05
k = 15.136 N/m
A. the velocity at t = 0.40 s is about 15 cm/s
B. the spring constant k is about 5.0 N/m
[tex]\texttt{ }[/tex]
Let's recall Elastic Potential Energy formula as follows:
[tex]\boxed{E_p = \frac{1}{2}k x^2}[/tex]
where:
Ep = elastic potential energy ( J )
k = spring constant ( N/m )
x = spring extension ( compression ) ( m )
Let us now tackle the problem!
[tex]\texttt{ }[/tex]
Given:
oscillating mass = m = 50 g = 0.05 kg
amplitude = A = 2.0 cm
angular frequency = ω = 10 rad/s
time taken = t = 0.40 s
Asked:
A. velocity = v = ?
B. spring constant = k = ?
Solution:
[tex]v = \frac{dx}{dt}[/tex]
[tex]v = \frac{d}{dt} (2.0 \cos 10t)[/tex]
[tex]v = -20 \sin 10t[/tex]
[tex]v = -20 \sin 10(0.40)[/tex]
[tex]v = -20 \sin (4.0)[/tex]
[tex]\boxed{v \approx 15 \texttt { cm/s}}[/tex]
[tex]\texttt{ }[/tex]
[tex]k = m \omega^2[/tex]
[tex]k = 0.05 \times 10^2[/tex]
[tex]\boxed{k = 5.0 \texttt{ N/m}}[/tex]
[tex]\texttt{ }[/tex]
[tex]\texttt{ }[/tex]
Grade: High School
Subject: Physics
Chapter: Elasticity
