A block with mass m = 4.3 kg is attached to two springs with spring constants k
ID: 1305808 • Letter: A
Question
A block with mass m = 4.3 kg is attached to two springs with spring constants kleft = 34 N/m and kright = 57 N/m. The block is pulled a distance x = 0.22 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
Your submissions:
Computed value:
20.02
Submitted:
Sunday, May 4 at 6:51 PM
Feedback:
Correct!
2)
What is the effective spring constant of the two springs?
N/m
Your submissions:
Computed value:
91
Submitted:
Sunday, May 4 at 6:51 PM
Feedback:
Correct!
3)
What is the period of oscillation of the block?
s
Your submissions:
Computed value:
1.36
Submitted:
Sunday, May 4 at 6:54 PM
Feedback:
Correct!
4)
How long does it take the block to return to equilibrium for the first time?
s
Your submissions:
Computed value:
.341
Submitted:
Sunday, May 4 at 6:54 PM
Feedback:
Correct!
5)
What is the speed of the block as it passes through the equilibrium position?
m/s
Your submissions:
Computed value:
1.01
Submitted:
Sunday, May 4 at 6:54 PM
Feedback:
Correct!
6)
What is the magnitude of the acceleration of the block as it passes through equilibrium?
m/s2
Your submissions:
Computed value:
1.01
Submitted:
Sunday, May 4 at 6:54 PM
Feedback:
7)
Where is the block located, relative to equilibrium, at a time 0.82 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
Your submissions:
Computed value:
.2199
Submitted:
Sunday, May 4 at 6:59 PM
Feedback:
This is where the block will be after exactly 1/2 a period has passed, but the time given is more than half the period, so it will have moved back to the left a little. You will need to set up an expression for the position as a function of time.
8)
What is the net force on the block at this time 0.82 s? (a negative force is to the left; a positive force is to the right)
N
Your submissions:
Computed value:
20.02
Submitted:
Sunday, May 4 at 6:58 PM
Feedback:
Feedback will be available after 11:59 PM on Wednesday, May 7
9)
What is the total energy stored in the system?
J
Your submissions:
Computed value:
2.2022
Submitted:
Sunday, May 4 at 6:58 PM
Feedback:
Feedback will be available after 11:59 PM on Wednesday, May 7
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
1) F = k1*x + k2x
= 34*0.22 + 57*0.22
= 20.02 N
2) Keff = k1+k2 = 91 N/m
3) w = sqrt(keff/m) = sqrt(91/4.3) = 4.6 rad/s
T = 2*pi/w
= 2*pi*sqrt(m/Keff)
= 2*pi*sqrt(4.3/91)
= 1.365 s
4) t = T/4 = 0.34128 s
5) 0.5*Keff*x^2 = 0.5*m*v^2
v = x*sqrt(Keff/m)
= 0.22*sqrt(91/4.3)
= 1.012 m/s
6) zero
7) x = A*cos(w*t)
x = 0.22*cos(4.6*0.82)
= -0.1776 m
8) Fnet = (k1+k2)*x
= (34+57)*0.1776
= +16.172 N
9) U = 0.5*Kef*A^2
= 0.5*91*0.22^2
= 2.2022 J
10) the period would not change
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