Question

A block with mass m = 5.7 kg is attached to two springs with spring constants...

A block with mass m = 5.7 kg is attached to two springs with spring constants kleft = 36 N/m and kright = 53 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

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 0.91 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 0.91 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

Homework Answers

Answer #1

spring constant K-left ( for spring on left) = 36 N/m
spring constant K-right ( for spring on right) = 53 N/m
mass of block, m = 5.7 kg
initial displacement, x = 0.22 m to the left

a. Initial net force = Force by right spring + Force by left spring (RIght one is pull and left one is push, so both add up in the right direction)
F = (K-right + K-left)*x = (36+53)0.22 = 19.58 N ( to the right)
b. Effective spring constant be k
kx = 19.58N = k*0.22
k = 89 N/m
c. Period of osscillation = T
angular frequency = w
frequency of osscilation = f
for spriong mass system , w = sqroot(k/m)
and T = 1/f
and w = 2*pif
so, T = 2pi*sqroot(m/k) = 2*pi*sqroot(5.7/89) = 0.66601 s
d. BLovck takes T/4 time to reachequilibrium position for the first time it is released from rest
so, time taken , t = T/4 = 0.16650 s

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
A block with mass m = 4.6 kg is attached to two springs with spring constants...
A block with mass m = 4.6 kg is attached to two springs with spring constants kleft = 37 N/m and kright = 51 N/m. The block is pulled a distance x = 0.27 m to the left of its equilibrium position and released from rest. What is the magnitude of the net force on the block (the moment it is released)? What is the effective spring constant of the two springs? What is the period of oscillation of the...
A block with mass m = 4.2 kg is attached to two springs with spring constants...
A block with mass m = 4.2 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. What is the magnitude of the net force on the block (the moment it is released)? What is the effective spring constant of the two springs? N/m What is the period of oscillation of...
A block with mass m = 4.9 kg is attached to two springs with spring constants...
A block with mass m = 4.9 kg is attached to two springs with spring constants kleft = 30 N/m and kright = 55 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)? 2) What is the effective spring constant of the two springs? 3) What is the period of...
A block with mass m = 6.3 kg is attached to two springs with spring constants...
A block with mass m = 6.3 kg is attached to two springs with spring constants kleft = 32 N/m and kright = 51 N/m. The block is pulled a distance x = 0.22 m to the left of its equilibrium position and released from rest. 1. Where is the block located, relative to equilibrium, at a time 1.07 s after it is released? (if the block is left of equilibrium give the answer as a negative value; if the...
A block with mass m = 7.4 kg is attached to two springs with spring constants...
A block with mass m = 7.4 kg is attached to two springs with spring constants kleft = 31 N/m and kright = 53 N/m. The block is pulled a distance x = 0.27 m to the left of its equilibrium position and released from rest. 7) Where is the block located, relative to equilibrium, at a time 1.06 s after it is released? (if the block is left of equilibrium give the answer as a negative value; if the...
A block with mass m = 4.3 kg is attached to two springs with spring constants...
A block with mass m = 4.3 kg is attached to two springs with spring constants klef t = 35 N/m and kright = 48 N/m. The block is pulled a distance x = 0.23 m to the left of its equilibrium position and released from rest. (a) What is the magnitude of the net force on the block at the moment it is released? (2pt) (b) What is the period of oscillation of the block? (1pt) (c) How long...
A block of mass m = 0.53 kg attached to a spring with force constant 119...
A block of mass m = 0.53 kg attached to a spring with force constant 119 N/m is free to move on a frictionless, horizontal surface as in the figure below. The block is released from rest after the spring is stretched a distance A = 0.13 m. (Indicate the direction with the sign of your answer. Assume that the positive direction is to the right.) The left end of a horizontal spring is attached to a vertical wall, and...
A block of mass m = 2.00 kg is attached to a spring of force constant...
A block of mass m = 2.00 kg is attached to a spring of force constant k = 600 N/m as shown in the figure below. The block is pulled to a position xi = 5.35 cm to the right of equilibrium and released from rest. (a) Find the speed the block has as it passes through equilibrium if the horizontal surface is frictionless. m/s (b) Find the speed the block has as it passes through equilibrium (for the first...
A 200.g block on a horizontal, frictionless surface is located between two unstrained springs. The spring...
A 200.g block on a horizontal, frictionless surface is located between two unstrained springs. The spring on the left of the block has a spring constant of 35N/m and the spring on the right has a constant of 85N/m. a) How much work must be done by an external force to displace the block 3.0cm to the left? b) If the block is released from the above position, how fast will the block be moving when it returns to the...
A block with mass m =7.3 kg is hung from a vertical spring. When the mass...
A block with mass m =7.3 kg is hung from a vertical spring. When the mass hangs in equilibrium, the spring stretches x = 0.29 m. While at this equilibrium position, the mass is then given an initial push downward at v = 5 m/s. The block oscillates on the spring without friction. 1) What is the spring constant of the spring? N/m Submit 2) What is the oscillation frequency? Hz Submit 3) After t = 0.45 s what is...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT