A force of 35 N is required to hold a spring that has been stretched from its natural EXAMPLE 3 length of 5 cm to a length of 10 cm. How much work is done in stretching the spring from 10 cm to 14 cm? According to Hooke's Law, the force required to hold the spring stretched x meters SOLUTION beyond its natural length is f(x) = kx. When the spring is stretched from 5 cm to 10 cm, the m. This means that f(0.05) = amount stretched is 5 cm = so 35 0.05k = 35 0.05 Thus f(x) 700x and the work done in stre ching the spring from 10 cm to 14 cm is ]0.09 r0.09 700 x2 2 Jo.05 700х dx 3D 350( ) - co.05)2 : J. = 350

Q: a crane lifts a 1000 lb science desk to a height of 20 ft using a chain that weighs 2 lb/ft. If the…

A:

Q: 5) Given h(x) = √√√8+x (a) Find the linearization of h at a = 0. (b) Use the linearization from…

A:

Q: The equation for the parachutist's velocity is given by: gm (1-e-c/m)t) where t is the time, g is…

A: We will solve this question using fixed-point iteration scheme.

Q: An object weighing 1000 pounds sinks in water starting from rest. Two forces act on it, a buoyant…

A:

Q: Suppose it takes 4 pounds of force to keep a spring stretched 3 inches longer than its equilibrium…

A: We have to find work done to stretch spring one foot from its equilibrium..

Q: The value v (in dollars) of a fir tree used for lumber in a plantation changes with the age of the…

A: The value of the fir tree is given by the function: vt=50t1+0.1t Given that the trees harvested are…

Q: The plate, bounded by the parabola y = x² and y = 16, is submerged vertically in water (distance in…

A:

Q: battery. It was found that the time (t) is proportional to different powers of acceleration (a) ,…

A: Homogeneity Principle : Principle of Homogeneity states that dimensions of each of the terms of a…

Q: A 4-foot spring measures 8 feet long after a mass weighing 8 pounds is attached to it. The medium…

A: Given that,A 4-foot spring measures 8 feet long after a mass weighing 8 pounds is attached to it.…

Q: If the brakes on a car can give the car a constant negative acceleration of 2k m/s2 , where k is a…

A: Here is the solution

Q: Consider the two tanks shown in the figure below. Each has a capacity of 300 gallons. At time t = 0,…

A:

Q: A spring has natural length 0.75 m and a 5 kg mass. A force of 25 N is needed to keep the spring…

A: Mass of spring,m=5kg Natural length of spring,l=0.75m Force keep spring at 1m is F=25 N Intial…

Q: A 800-lb object is released from rest 600 ft above the ground and allowed to fall under the…

A: According to the given information, it is required to determine the equation of motion of object…

Q: A spring with a 5-kg mass and a damping constant 15 can be held stretched 2 meters beyond its…

A: The objective is to find the position of the mass, after t seconds.

Q: © Macmillan Learning A small boat is crossing a lake on a windy day. During some interval of time,…

A:

Q: A mass weighting 64 lbs stretches a spring 2 inches. The mass is in a medium that exerts a damping…

A: We must have all the units are in same system

Q: The force F on an object is the product of the mass m and the acceleration a. In this problem,…

A: F(t)=m(t)a(t) at t=7 s,  m(t)=51 gramschanging rate=m'(t)=9 gsat t=7, a(t)=8 ms2  changing…

Q: A mass weighing 16 pounds stretches a spring feet. The mass is initially released from rest from a…

A: Let m be the mass attached, k be the spring constant and β be the positive damping constant. The…