A force of 9 lb is required to keep a spring compressed to 6. ft shorter than its equilibrium length. What is its spring constant? k = lb/ft

Suppose a woman has enough “spring” in her legs to jump (on earth) from the ground to a height of 2.25 feet. If she jumps straight upward with the same initial velocity on the moon—where the surface gravitational acceleration is (approximately) 5.3 ft/s2—how high above the surface will she rise?

A force of 175 newtons stretches a spring by 5 meters. What is the value of the constant of proportionality (the spring constant)? Round your answer to the nearest hundredth, if necessary.

To measure the physical properties of cells, a piezoelectric probe is used. The force applied by the probe is compared against how much the cell deforms. If F is the force applied by the probe, and w is the distance it moves into the cell, then the stiffness of the cell can be calculated from the rate of change, dF/dw. Zhang et al. found that if F is measured in uN and w in um then for a zebrafish embryo: F = 3 x 10-4³-4.4 x 10-³w² +3.93w+0.221 Calculate dF/dw for a sample when w = 100μm.

A rock thrown vertically upward from the surface of the moon at a velocity of 32 m/sec reaches a height of s=32t-0.8t² meters in t sec. a. Find the rock's velocity and acceleration at time t. b. How long does it take the rock to reach its highest point? c. How high does the rock go? d. How long does it take the rock to reach half its maximum height? e. How long is the rock aloft? a. Find the rock's velocity at time t. =m/s V = Find the rock's acceleration at time t. a= m/s² (Simplify your answer. Use integers or decimals for any numbers in the expression.) b. How long does it take the rock to reach its highest point? sec (Simplify your answer.) …….

Find the position of the mass after t seconds

A force of 15 Newtons stretches a spring 20 centimeters. After a 3 kilogram mass is attached to the spring, the mass is pulled down to a position √3 meters below equilibrium and released with an upward velocity of 5 meters per second. Find a. The equation of motion. b. The amplitude, period, and phase shift of the simple harmonic motion.

If it takes a force of 86 Newtons to stretch a spring 9 meters from its equilibrium state, what is the spring constant k? (Round your answer to one decimal place.)

It takes 15 J of work to stretch a spring 0.2 m from its equilibrium position. Find the spring constant k. (Hint: read the units!) How far would the spring need to be stretched in order to do twice the amount of work?

A mass weighing 4 pounds is attached to a spring whose constant is 2 Ib/ft. The medium offers a damping force that is numerically equal to the instantaneous velocity. The mass is initially released from a point 1 foot above the equilibrium position with a downward velocity of 16 ft/s. Determine the time (in s) at which the mass passes through the equilibrium position. (Use g = 32 ft/s? for the acceleration due to gravity.) Find the time (in s) after the mass passes through the equilibrium position at which the mass attains its extreme displacement from the equilibrium position. What is the position (in ft) of the mass at this instant? ft