Find the work done in stretching a spring of natural length 8 cm, from 10 cm to 13 cm. Assume a force of 6 N is needed to hold it at a length of 11 cm. (Solve using Integral Functions)

The hydraulic cylinder on a woodsplitter has a 4-inch bore (diameter) and a stroke of 2 feet. The hydraulic pump creates a maximum pressure of 2000 pounds per square inch. Therefore, the maximum force created by the cylinder is 2000( π . 22 ) 8000 π, pounds :- Find the work done through one extension of the cylinder, given that the maximum force is required?

A spring has a natural length of 10 feet, and when an 64lb weight is attached, the spring measures 13.2 feet. The weight is initially displaced 4 feet above equilibrium and given a downward velocity of 3 ft/sec. Find its displacement for t>0 if the medium resists the motion with a force of two Ibs for each ft/sec of velocity.

A 600-lb cable is 100 ft long and hangs vertically from the top of a tall building. (a) How much work is required to lift the cable to the top of the building? (b) How much work is required to pull up only 25 feet of the cable? Solution (a) Here we don't have a formula for the force function, but we can use an argument similar to the one that led to the definition of work. Let's place the origin at the top of the building and the x-axis pointing downward as in the following figure. 0- 100+ - We divide the cable into small parts with length Ax. If x; is a point in the ith such interval, then all points in the interval are lifted by approximately the same amount, namely x;". The cable weighs 6x;* Ax W = lim 74x2 i=1 (6Ax). xi* force distance We get the total work done by adding all these approximations and letting the number of parts become large (so Ax → 0). *100 n W₁ = ▬▬▬▬▬▬▬▬▬ 6x;'Ax 6x dx = £Ax W₂ = lim ▬▬▬▬▬▬▬▬ 00 - U (b) The work required to move the top 25 ft of cable to the top…

A shell of mass 4 kg is shot upward with an initial velocity of 200 m/sec. The magnitude of the force on the shell due to air resistance is 20 the ground? What is the maximum height? Assume the acceleration due to gravity to be 9.81 m/s². When will the shell reach its maximum height above the ground? The shell will reach maximum height after 18.16 seconds. (Round to two decimal places as needed.) What is the maximum height? The maximum height is 1747 m. (Round to the nearest whole number as needed.) 3 (...) When will the shell reach its maximum height above

A ball with mass 0.05 kg is thrown upward with initial velocity 25 m/s from the roof of a building 60 m high. Assume there is a force due to |v| air resistance of magnitude directed opposite to the velocity, where 30 the velocity v is measured in m/s. NOTE: Use g=9.8 m/s² as the acceleration due to gravity. Round your answers to 2 decimal places. a) Find the maximum height above the ground that the ball reaches. Height: m b) Find the time that the ball hits the ground. Time: seconds

A wrench 1m long lies along the positive y-axis and grips a bolt at the origin (i.e. the wrench can be represented by vector <0,1,0>). A force is applied in the direction of the unit vector <0, 1/sqrt(2), 1/sqrt(2)> at the end of the wrench. Find the magnitude of the force in Newtons (N) needed to supply 5sqrt(2) N*m of torque to the bolt.  torque = | r x F |  if r = <0,1,0> and F = <0, 1/sqrt(2), 1/sqrt(2)> so the torque is equal to the magnitude of the cross product of these two vectors but I don't understand how to get incorporate the 5sqrt(2) N*m I know that the magnitude of the cross product must be equal to 5sqrt(2) but I am not sure how to work backwards to that answer, please help!.

An object is shot straight upward from sea level with an initial velocity of 400 ft/sec. a. Assuming that gravity is the only force acting on the object, give an upper estimate for its velocity after 5 sec have elapsed. Use g = 32 ft/sec2 for the gravitational acceleration. b. Find a lower estimate for the height attained after 5 sec.

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During a hockey match a forward shoots at goal and the ball is caught by the goalkeeper. When the ball hits the goalkeeper's glove it has a velocity of 42 m s-1. During the catch by the goalkeeper the force of the ball hitting the glove displaces the glove backwards by 22 cm after the ball has stopped moving. The mass of the hockey ball is 1 kg. Calculate: How much kinetic energy the ball posses immediately before it hits the glove. The work done by the goalkeeper when catching the ball. The impact force exerted by the goalkeeper's glove on the ball.