A small ball is attached to one end of a spring that has an unstrained length of 0.193 m. The spring is held by the other end, and the ball is whirled around in a horizontal circle at a speed of 3.98 m/s. The spring remains nearly parallel to the ground during the motion and is observed to stretch by 0.0176 m. By how much would the spring stretch if it were attached to the ceiling and the ball allowed to hang straight down, motionless?

Any object moving with a specified angular velocity is known to be an object that moves in simple harmonic motion. The displacement (d) of an object moving in simple harmonic motion is described by the function d = R sin(wt) such that d is the radius of the rotating object, w is the angular velocity of the rotating object. The moon is a satellite that rotates around Earth with a nearly circular elliptic orbit. With this orbit, the approximate distance of the moon from the Earth is 385,000 km rotating at 14,091.21 km per hour. Using this information, sketch a graph of the moon's orbit around Earth and the a. domain and range: b. amplitude: с. period: d. interval:

The drawing shows two crates that are connected by a steel wire that passes over a pulley. The unstretched length of the wire is 1.5 m, and its cross-sectional area is 1,3×10-5 m2. The pulley is frictionless and massless. When the crates are accelerating, determine the change in length of the wire. Ignore the mass of the wire.

You pull on a string with a horizontal force of magnitude F = 40 N that is attached to a block of mass m, = 7.5 kg, then to the axle of a solid cylinder of mass m. = 4.8 kg and radius r = 0.4 m, then to a spring of spring constant k = 140 N/m. This is all done on an inclined plane where there is friction ( 4s = 0.68 and , = 0.31 ), and the incline angle is e = 25 degrees. Everything starts at rest, and the spring is unstretched. The block slides down the plane, the cylinder rolls down the plane (without slipping), and the Cylinder, Spring, and Block on Ramp spring stretches. 000000000- b yb First, what is the speed of the block and cylinder after you have pulled the block and cylinder 86 cm down the plane?

A force of 30 N stretches a spring 15 cm.  a) What is the mass attached to such a spring if it oscillates on a horizontal frictionless surface with a period of π/4 seconds? b) If the mass is released from rest at t=0 from its amplitude of +5 cm, where will it be and what direction is it moving after π/12 seconds? c) What force does the spring exert on the body when it is +3 cm from its equilibrium position.

When a body of mass 0.25 kg is attached to a vertical massless spring, it is extended 5.0 cm from its unstretched length of 4.0 cm. The body and spring are placed on a horizontal frictionless surface and rotated about the held end of the spring at 2.0 rev/s. How far is the spring stretched?

All spiders are very sensitive to vibrations. An orb spider will sit at the center of its large, circular web and monitor radial threads for vibrations created when an insect lands. Assume that these threads are made of silk with a linear density of 1.0 × 10-5 kg/m under a tension of 0.40 N, both typical numbers. If an insect lands in the web 30 cm from the spider, how long will it take forthe spider to find out?

A spring is hung from the ceiling. A 0.588-kg block is then attached to the free end of the spring. When released from rest, the block drops 0.101 m before momentarily coming to rest, after which it moves back upward. (a) VWhat is the spring constant of the spring? (b) Find the angular frequency of the block's vibrations. (a) Number i 57.09 Units N/m (b) Number i 97.0989 Units rad/s

A spring with spring constant k and equilibrium length zero is attached tothe top of a frictionless hoop of radius R. The spring is stretched and connected to a bead of mass m at the bottom of the hoop. At t = 0 the bead is given an initial speed v0 and the bead moves up the hoop. Find the speed of the bead as a function of position on hoop v(θ).

In a car’s suspension system, each wheel is connected to a vertical spring; these springs absorb shocks when the car travels on bumpy roads. In one car, each spring has a spring constant of 5.0 x 104 N/m. If this 1400 kg car is driven at 25 m/s through the bottom of a circular dip in the road that has a radius of 600 m, by how much do these springs compress compared to when the car is driven on a flat road?