3. The Growing Ostrich
Ostriches go through a large change in body mass as they grow from
hatchlings to adults. Body
mass increases 25 fold as the bird develops from a four week
hatchling to a full grown adult. If
they grow isometrically, then by what proportion will their optimal
stride frequency during walking
change as they grow into adults? By what proportion will their
maximum walking speed change?
Answer
The optimal stride frequency changes by a factor of 1.72 from
hatchling to adult.
The maximum speed of the adult is 71% greater than the maximum
speed of the hatchling.
Homework Answers
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3. The Growing Ostrich
Ostriches go through a large change in body mass as they grow...
2. (35 points) A pendulum consists of a point mass (m) attached to the end of a spring (massless ...
2. (35 points) A pendulum consists of a point mass (m) attached to the end of a spring (massless spring, equilibrium length-Lo and spring constant- k). The other end of the spring is attached to the ceiling. Initially the spring is un-sketched but is making an angle θ° with the vertical, the mass is released from rest, see figure below. Let the instantaneous length of the spring be r. Let the acceleration due to gravity be g celing (a) (10...
An L-shaped rigid body ABC consists of two identical uniform slender rods, each of mass 40 kg and...
An L-shaped rigid body ABC consists
of two identical uniform slender rods, each of mass 40
kg and of length, L= 1.6
m welded together. The rigid body is pinned at its
vertex B as shown, with the
end C attached to a spring with a spring
constant, 6 N/cm .
PART A - Determine the natural cycle frequency of the
system.
PART B - If during the oscillatory motion the
end A is observed to move with a speed of 0.12
m/s when AB is vertical,
what...
A slender, uniform metal rod of mass M and length l is pivoted without friction about an axis through its midpoint and p...
A slender, uniform metal rod of mass M and length l is pivoted
without friction about an axis through its midpoint and
perpendicular to the rod. A horizontal spring, assumed massless and
with force constant k, is attached to the lower end of the rod,
with the other end of the spring attached to a rigid support.
(Figure 1)
2. Find the torque τ due to the spring. Assume that θ is small
enough that the spring remains effectively horizontal...
Problem 3-Under the ambient condiion, one can use the oscillation frequency of a spring-mass system to...
Problem 3-Under the ambient condiion, one can use the oscillation frequency of a spring-mass system to determine the mass suspended at the end of a spring using equation where f if the frequency of oscillation in the unit of s1, k is the spring constant in the unit of N/m, and m is the mass of the oscillating object in the unit of kg. The spring constant k is obtained by suspending an object of known mass mo under the...
A pendulum of length L and mass M has a spring of force constant k connected to it at a distance h bel...
A pendulum of length
L
and mass
M
has a spring of force constant
k
connected to it at a distance
h
below its point of suspension (as shown in the following figure).
Find the frequency of vibration of the system for small values of
the amplitude (small
?).
Assume that the vertical suspension of length
L
is rigid, but ignore its mass. (Use any variable or symbol stated
above along with the following as necessary:
g
and
?.)
f...
A pendulum of length L and mass M has a spring of force constant k connected to it at a distance h bel...
A pendulum of length
L
and mass
M
has a spring of force constant
k
connected to it at a distance
h
below its point of suspension (as shown in the following figure).
Find the frequency of vibration of the system for small values of
the amplitude (small
?).
Assume that the vertical suspension of length
L
is rigid, but ignore its mass. (Use any variable or symbol stated
above along with the following as necessary:
g
and
?.)
f...
Consider a bicycle wheel of mass M and radius R that sits on a flat, level...
Consider a bicycle wheel of mass M and radius R that sits on a flat, level surface, such that the surface is tangent to the wheel. One end of a spring (spring constant, k) is attached to bicycle wheel’s hub, and the other end is fixed to a vertical wall. The spring is horizontal. There is sufficient friction to prevent the wheel from sliding at the point of contact with the surface. When the center of the wheel is directly...
Consider a bicycle wheel of mass M and radius R that sits on a flat, level...
Consider a bicycle wheel of mass M and radius R that sits on a flat, level surface, such that the surface is tangent to the wheel. One end of a spring (spring constant, k) is attached to bicycle wheel's hub, and the other end is fixed to a vertical wall. The spring is horizontal. There is sufficient friction to prevent the wheel from sliding at the point of contact with the surface. When the center of the wheel is directly...
Learning Goal: To study the undamped vibration of a rigid body. A slender, uniform metal rod...
Learning Goal:
To study the undamped vibration of a rigid body.
A slender, uniform metal rod of mass m and length
l is pivoted without friction about an axis through its
midpoint and in a direction that is perpendicular to the rod. A
massless horizontal spring, with spring constant k, is
attached to the lower end of the rod; the other end of the spring
is attached to a rigid support. (Figure 1)
Part C) What is ωn, the angular...
An object of mass M = 5.00 kg is attached to a spring with spring constant...
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2. (35 points) A pendulum consists of a point mass (m) attached to the end of a spring (massless spring, equilibrium length-Lo and spring constant- k). The other end of the spring is attached to the ceiling. Initially the spring is un-sketched but is making an angle θ° with the vertical, the mass is released from rest, see figure below. Let the instantaneous length of the spring be r. Let the acceleration due to gravity be g celing (a) (10...
An L-shaped rigid body ABC consists
of two identical uniform slender rods, each of mass 40
kg and of length, L= 1.6
m welded together. The rigid body is pinned at its
vertex B as shown, with the
end C attached to a spring with a spring
constant, 6 N/cm .
PART A - Determine the natural cycle frequency of the
system.
PART B - If during the oscillatory motion the
end A is observed to move with a speed of 0.12
m/s when AB is vertical,
what...
A slender, uniform metal rod of mass M and length l is pivoted
without friction about an axis through its midpoint and
perpendicular to the rod. A horizontal spring, assumed massless and
with force constant k, is attached to the lower end of the rod,
with the other end of the spring attached to a rigid support.
(Figure 1)
2. Find the torque τ due to the spring. Assume that θ is small
enough that the spring remains effectively horizontal...
Problem 3-Under the ambient condiion, one can use the oscillation frequency of a spring-mass system to determine the mass suspended at the end of a spring using equation where f if the frequency of oscillation in the unit of s1, k is the spring constant in the unit of N/m, and m is the mass of the oscillating object in the unit of kg. The spring constant k is obtained by suspending an object of known mass mo under the...
A pendulum of length
L
and mass
M
has a spring of force constant
k
connected to it at a distance
h
below its point of suspension (as shown in the following figure).
Find the frequency of vibration of the system for small values of
the amplitude (small
?).
Assume that the vertical suspension of length
L
is rigid, but ignore its mass. (Use any variable or symbol stated
above along with the following as necessary:
g
and
?.)
f...
A pendulum of length
L
and mass
M
has a spring of force constant
k
connected to it at a distance
h
below its point of suspension (as shown in the following figure).
Find the frequency of vibration of the system for small values of
the amplitude (small
?).
Assume that the vertical suspension of length
L
is rigid, but ignore its mass. (Use any variable or symbol stated
above along with the following as necessary:
g
and
?.)
f...
Consider a bicycle wheel of mass M and radius R that sits on a flat, level surface, such that the surface is tangent to the wheel. One end of a spring (spring constant, k) is attached to bicycle wheel's hub, and the other end is fixed to a vertical wall. The spring is horizontal. There is sufficient friction to prevent the wheel from sliding at the point of contact with the surface. When the center of the wheel is directly...
Learning Goal:
To study the undamped vibration of a rigid body.
A slender, uniform metal rod of mass m and length
l is pivoted without friction about an axis through its
midpoint and in a direction that is perpendicular to the rod. A
massless horizontal spring, with spring constant k, is
attached to the lower end of the rod; the other end of the spring
is attached to a rigid support. (Figure 1)
Part C) What is ωn, the angular...
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