Question
In: Math
a. A force of 40 lb is necessary to hold a spring that has been stretched...
a. A force of 40 lb is necessary to hold a spring that has
been stretched from its natural
length of 10 ft to a length of 15 ft. How much work is done in
stretching the spring from 15 ft to a length of 18 ft? (Hint: Use
Hook’s Law F = kx, where x represents distance that the spring is
stretched or compressed past its natural length)
b. A tank full of water has the shape of an inverted circular
cone with height 12 ft and base radius 5 ft. Find the work required
to empty the tank by pumping all of the water to the top of the
tank. (The density of water is 62.5 ??/??3)
c. A heavy rope, 30 ft long, weighs 0.2 lb/ft and hangs over
the edge of a building. Find the work done required in pulling the
rope to the top of the building
Solutions
milcah answered 2 years agoRelated Solutions
1) A force of 2 pounds is required to hold a spring stretched 0.2 feet beyond...
1) A force of 2 pounds is required to hold a spring stretched
0.2 feet beyond its natural length. How much work (in foot-pounds)
is done in stretching the spring from its natural length to 0.9
feet beyond its natural length?
2) Work of 3 Joules is done in stretching a spring from its
natural length to 19 cm beyond its natural length. What is the
force (in Newtons) that holds the spring stretched at the same
distance (19 cm)?...
DIfferential Equation Class Problem: A spring is stretched 0.10 m by a force of 3 newtons....
DIfferential Equation Class Problem: A spring is stretched 0.10
m by a force of 3 newtons. A mass of 2 kg is hung from the spring
and is also attached to a viscous damper that exerts a force of 3
newtons when the velocity of the mass is 5 m/sec. If the mass is
pulled down 0.05 m below its equilibrium position and given an
initial downward velocity of 0.10 m/sec, determine its position U
at any time T.
A spring with a spring rate of 75 lb/in has a working deflection of 1 in....
A spring with a spring rate of 75 lb/in has a working deflection
of 1 in. It provides a minimum of 150 lb at installation. The
spring is formed from 0.25 in diameter unpeened music wire. The
coil has squared and ground ends, and it fits in a 2.1 in diameter
hole with 0.1 in clearance.
Assuming a 15% clash allowance, find:
a) Safety factor for infinite life in fatigue
b) Shut height
c) Safety factor at shut height
d)...
A 128-lb weight is attached to a spring having a spring constant of 64 lb/ft. The...
A 128-lb weight is attached to a spring having a spring constant
of 64 lb/ft. The weight is started in motion with no initial
velocity by displacing it 6 in below the equilibrium position and
by simultaneously applying an external force F(t) = 8sin(4t). a.
Assuming no air resistance, find the equation of motion. b. What is
the long term behavior of the motion? Please use differential
equations to solve this
7) A spring has is stretched horizontally to the right from a wall 0.5 meters by...
7) A spring has is stretched horizontally to the right from a
wall 0.5 meters by a force of 40 newtons. This spring has a mass of
10 kg. The mass is pulled to the right (from the equilibrium
position) 1 meter and released (at t = 0) with an initial velocity
to the right of 2 meters per second.
I) Write down the differential equation that governs the motion
of the mass. Include the initial conditions. (assume no
damping)....
A force of 640 newtons stretches a spring 4 meters. A mass of 40 kilograms is...
A force of 640 newtons stretches a spring 4 meters. A mass of 40
kilograms is attached to the end of the spring and is initially
released from the equilibrium position with an upward velocity of
10 m/s. Find the equation of motion.
An unstretched spring is 30 cm long. When the spring is stretched to a total length...
An
unstretched spring is 30 cm long. When the spring is stretched to a
total length of 60cm, it supports transverse waves moving at 4.5
m/s. How fast will waves travel in this spring if it is stretched
to 90cm?
An unstretched spring is 30 cm long. When the spring is stretched to a total length...
An
unstretched spring is 30 cm long. When the spring is stretched to a
total length of 60cm, it supports transverse waves moving at 4.5
m/s. How fast will waves travel in this spring if it is stretched
to 90cm?
A single spring with a 0.75 kg mass on it is stretched out and then released....
A single spring with a 0.75 kg mass on it is stretched out and
then released. Then the velocity of the mass is measured as the
spring passes through its equilibrium position. This experiment is
repeated 18 times; pulling the spring to a different distance each
time. The amplitudes and speeds are listed below.
Amplitude (m.)
Speed at Equilibrium (m/s)
0.05
0.23
0.10
0.38
0.15
0.60
0.20
0.84
0.25
0.98
0.30
1.14
0.35
1.49
0.40
1.63
0.45
1.82
0.50
2.30...
A spring contains a weight of 32 lbs. It is stretched to a distance of 1.6...
A spring contains a weight of 32 lbs. It is stretched to a
distance of 1.6 ft and is
currently at rest. The damping force is 9 ˙x and an external force
of 2 cos 4t
applied. Set up the differential equation,
including the initial conditions, but
you do not need to solve.
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