Question

In: Math

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)?

3) How much work is done lifting a 40-pound object from the ground to the top of a 30-foot building if the cable used weighs 0.5 pounds per foot?
foot-pounds.

Solutions

Expert Solution


Related Solutions

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...
will rate :-) A mass weighing 8 pounds stretches a spring 2 feet. At t=0 the...
will rate :-) A mass weighing 8 pounds stretches a spring 2 feet. At t=0 the mass is released from a point 2 feet above the equilibrium position with a downward velocity of 4 (ft/s), determine the motion of the mass.
In a spring-mass-dashpot system, a force of 1 Newtons is required to stretch the spring for...
In a spring-mass-dashpot system, a force of 1 Newtons is required to stretch the spring for .05 meters. A mass of 4 kg is hung from the spring and also attached to a viscous damper that has a damping constant 8 Newton-sec/m. The mass is suddenly set in motion from its equilibrium location at t = 0 by an external force of 8 cost Newtons with initial velocity 0 m/sec. Find the transient solution and the steady state solution of...
A mass weighing 12 pounds stretches a spring 2 feet. The mass is initially released from...
A mass weighing 12 pounds stretches a spring 2 feet. The mass is initially released from a point 1 foot below equilibrium with an upward velocity of 4 ft/s. (a) Find the equation of motion (b) In correct units, what are the amplitude, period, and frequency of this simple harmonic motion? (c) What is the velocity of the mass at ? = 3? 16 seconds? (d) Find the first three times that the velocity is zero, expressed both in exact...
A mass of 35 pounds of weight causes a spring to stretch 10 feet, if the...
A mass of 35 pounds of weight causes a spring to stretch 10 feet, if the medium surrounding the system has a damping coefficient, that is, it is equivalent to 5 times the instantaneous speed and the weight is released from a point located at 15 inches below the equilibrium position with an initial velocity of 1 foot per second downwards. A) Derive the differential equation that models the mass-spring system. b) Calculate the displacements (t) at all times “t”...
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.
undamped spring-mass system with mass 6 kg and a spring which is stretched 2 meter by...
undamped spring-mass system with mass 6 kg and a spring which is stretched 2 meter by 10 Newtons. Suppose an oscillating force 3 cos(ωt) is acting on the system. What value of ω causes resonance? For this value of ω, find a formula for x, the distance between the weight and equilibrium t seconds after the weight starts at x = 0 at rest.
A mass of 1 slug, when attached to a spring, stretches it 2 feet. It is...
A mass of 1 slug, when attached to a spring, stretches it 2 feet. It is released from a point 1 foot above the equilibrium position with a downward velocity of 2 ft/s. 1) Find the equation of motion if the surrounding medium offers a damping force that is numerically equal to 4 times the instantaneous velocity. 2) Classify the motion as underdamped, overdamped, or critically damped.
A mass of 1 slug, when attached to a spring, stretches it 2 feet and then...
A mass of 1 slug, when attached to a spring, stretches it 2 feet and then comes to rest in the equilibrium position. Starting at t = 0, an external force equal to f(t) = 10 sin(4t) is applied to the system. Find the equation of motion if the surrounding medium offers a damping force that is numerically equal to 8 times the instantaneous velocity. (Use g = 32 ft/s2 for the acceleration due to gravity.) x(t) = ____________ft
A certain spring is compressed 0.2 metres from its natural length by a force of 0.02...
A certain spring is compressed 0.2 metres from its natural length by a force of 0.02 newtons. A 0.1 kilogram mass is attached to this spring. There is no damping, and the mass is acted on by an external force of 0.05 cos(0.8 t) newtons, where t is measured in seconds. At t = 0, the mass is released, at rest, from its rest (equilibrium) position. (a) Set up and solve the initial value problem for the displacement x(t) of...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT