A block with mass m = 7.3 kg is attached to two springs with spring constants k
ID: 1301515 • Letter: A
Question
A block with mass m = 7.3 kg is attached to two springs with spring constants kleft = 30 N/m and kright = 52 N/m. The block is pulled a distance x = 0.25 m to the left of its equilibrium position and released from rest.
1)
What is the magnitude of the net force on the block (the moment it is released)?
N
2)
What is the effective spring constant of the two springs?
N/m
3)
What is the period of oscillation of the block?
s
4)
How long does it take the block to return to equilibrium for the first time?
s
5)
What is the speed of the block as it passes through the equilibrium position?
m/s
6)
What is the magnitude of the acceleration of the block as it passes through equilibrium?
m/s2
7)
Where is the block located, relative to equilibrium, at a time 1.03 s after it is released? (if the block is left of equilibrium give the answer as a negative value; if the block is right of equilibrium give the answer as a positive value)
m
8)
What is the net force on the block at this time 1.03 s? (a negative force is to the left; a positive force is to the right)
N
9)
What is the total energy stored in the system?
J
10)
If the block had been given an initial push, how would the period of oscillation change?
the period would increase
the period would decrease
the period would not change
Explanation / Answer
a)
Force = spring force from left + spring force from right
= 30*0.25 + 52*0.25
= 20.5 N
b)
Effective k = 20.5 / 0.25
= 82 N/m
3)
T = 2*pi*sqrt (m/k)
= 2*3.14*sqrt(7.3 / 82)
= 1.875 s
4)
Time = T/4
= 1.875 / 4
= 0.467 s
5)
At equilbrium, KE = PE_at extreme
1/2*mv^2 = 1/2*ka^2
7.3*v^2 = 82*0.25^2
v = 0.838 m/s
6)
acceleration = 0
7)
w = sqrt (k/m) = sqrt (82 / 7.3) = 3.351 rad/s
x = a*cos (wt)
x = -0.25*cos (3.351*t)
At t = 1.03 s, we get
x = -0.25*cos(3.351*1.03)
= 0.238 m
8)
Spring force from left + spring force from right
= -30*0.238 - 52*0.238
= -19.52 N
9)
Total energy = 1/2*ka^2
= 1/2*82*0.25^2
= 2.5625 J
10)
the period would not change. It only depends upon m and k.
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.