Question

To use Newton's 2nd law as well as energy conservation for a vertical mass-spring

A proud deep-sea fisherman hangs a 65.0-kgkg fish from an ideal spring having negligible mass. The fish stretches the spring from its initial equilibrium position until it comes to a new equilibrium position, which is 0.120 mm below the initial equilibrium position.

a)Draw a force diagram of the fish at its new equilibrium position. Then use Newton's 2nd law to solve for the spring constant of the spring

b)The fish is now pulled down 5.00 cmcm from the new equilibrium position and released. Solve for the period of the oscillation of the fish.

c)Use energy conservation to solve for the maximum speed of the fish during its oscillation. (Remember that once we account for the “new” equilibrium position, we no longer have to include gravitational potential energy!)

Answer #1

A proud deep-sea fisherman hangs a 64.0-kg fish from an ideal
spring having negligible mass. The fish stretches the spring 0.135
m.
(a) Find the force constant of the spring.
N/m
The fish is now pulled down 5.75 cm and released.
(b) What is the period of oscillation of the fish?
s
(c) What is the maximum speed it will reach?
m/s

A block with mass m =7.5 kg is hung from a vertical spring. When
the mass hangs in equilibrium, the spring stretches x = 0.25 m.
While at this equilibrium position, the mass is then given an
initial push downward at v = 4.1 m/s. The block oscillates on the
spring without friction.
After t = 0.3 s what is the speed of the block?
What is the magnitude of the maximum acceleration of the
block?
At t = 0.3...

A block with mass m =6.2 kg is hung from a vertical spring. When
the mass hangs in equilibrium, the spring stretches x = 0.22 m.
While at this equilibrium position, the mass is then given an
initial push downward at v = 4.6 m/s. The block oscillates on the
spring without friction.
What is the spring constant of the spring?
2)
What is the oscillation frequency?
After t = 0.32 s what is the speed of the block?
What...

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...

A block with mass m =7.1 kg is hung from a vertical spring. When
the mass hangs in equilibrium, the spring stretches x = 0.24 m.
While at this equilibrium position, the mass is then given an
initial push downward at v = 4.5 m/s. The block oscillates on the
spring without friction.
1) What is the spring constant of the spring?
2) What is the oscillation frequency?
3) After t = 0.38 s what is the speed of the...

A block with mass m =6.7 kg is hung from a vertical spring. When
the mass hangs in equilibrium, the spring stretches x = 0.27 m.
While at this equilibrium position, the mass is then given an
initial push downward at v = 4.5 m/s. The block oscillates on the
spring without friction.
1. What is the spring constant of the spring?
2. What is the oscillation frequency?
3. After t = 0.46 s what is the speed of the...

We consider a spring mass system. We use standard international
system of units, the mass is 1kg and the change of magnitude of
force |∆Fs| (in unit of Newton, 1N = 1kg ∗ m/s2) from the spring is
9 times the change of length of the spring |∆x|(in meter), i.e
|∆Fs| = |9∆x|, the spring is a linear spring with spring constant
equal to 3 in Hook’s law. The equilibrium position is at x = 0.
When the external forcing...

(a) Use energy ideas to set up an equation that describes the
motion of a mass moving horizontally under the influence of a
linear spring force. Neglect air resistance and friction. Solve
your equation to obtain expressions for the object’s position,
velocity and acceleration as functions of time. Obtain an
expression for the angular frequency of the oscillation. Clearly
define all quantities you need to do this. Show and explain each
step, and be clear about what your answers are...

Problem 2: (a) In this exercise a massless spring with a spring
constant k = 6 N/m is stretched from its equilibrium position with
a mass m attached on the end. The distance the spring is stretched
is x = 0.3 m. What is the force exerted by the spring on the mass?
(5 points)
(b) If we were to stretch the spring-mass system as in part (a)
and hold it there, there will be some initial potential energy
associated...

A block with mass 3.10 kgkg is attached
to a vertical spring that has negligible mass and force constant
895 N/mN/m . The spring initially is relaxed and in equilibrium.
The block is released from rest.
a) What is its speed after it has descended 0.0500 mm from its
initial position?
Express your answer with the appropriate units.
b) What is the maximum speed of the block as it descends?
Express your answer with the appropriate units.

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