(1 point) Finding the work done in stretching or compressing a spring. Hooke's Law for Springs....
To understand the use of Hooke's law for a spring. Hooke's law states that the restoring force F⃗ on a spring when it has been stretched or compressed is proportional to the displacement x⃗ of the spring from its equilibrium position. The equilibrium position is the position at which the spring is neither stretched nor compressed. Recall that F⃗ ∝x⃗ means that F⃗ is equal to a constant times x⃗ . For a spring, the proportionality constant is called the spring constant and denoted...
Suppose a force of 40 N is required to stretch and hold a spring 0.1 m from its equilibrium position. a. Assuming the spring obeys Hooke's law, find the spring constant k. b. How much work is required to compress the spring 0.2 m from its equilibrium position? c. How much work is required to stretch the spring 0.5 m from its equilibrium position? d. How much additional work is required to stretch the spring 0.1 m if it has...
Consider a spring that does not obey Hooke's law very faithfully. One end of the spring is fixed. To keep the spring stretched or compressed an amount x, a force along the x-axis with x-component Fx=kx−bx2+cx3 must be applied to the free end. Here k=100N/m, b=700N/m2, and c=12000N/m3. Note that x>0 when the spring is stretched and x<0 when it is compressed. A)How much work must be done to stretch this spring by 0.050 m from its unstretched length? B)How...
021 (part 1 of 2) 10.0 points The force required to stretch a Hooke's-law spring varies from 0 N to 69.3 N as we stretch the spring by moving one end 9.11 cm from its unstressed position. Find the force constant of the spring Answer in units of N/m. 022 (part 2 of 2) 10.0 points Find the work done in stretching the spring Answer in units of J.
Consider a spring of mass 1 Kg attached to a spring obeying Hooke's Law with spring constant K Problem 4. (15 pts) Consider a spring of mass 1 kg attached to a spring obeying Hooke's Law with spring constant k N/m. Suppose an external force F(t) = 2 cos 3t is applied to the mass, and suppose the spring experiences no damping. Suppose the spring can be displaced 0.2 m by a 1.8 N force. If the spring is stretched...
A spring is found to not obey Hooke's law. It exerts a restoring force F(x) =-ax- 2 N if it stretched or compressed, where α = 60 N/m and β 18.0 Nm2/3. The mass of the spring is negligible. (a) Calculate the work function W(x) for the spring. Let U=0 when x=0. (b) An object of mass 0.900 kg on a horizontal surface is attached to this spring. The surface provides a friction force that is dependent on distance Fr(x)2x2...
1. According to Hooke's law, the force exerted by a spring is proportional to the amount of stretch (or change in length Ax) and is given by F = -KAX, where the minus sign indicates it is a restoring force. If a force of 120 N acts on a mass 250 g attached to a spring of constant K = 54.55 x 103 N/m. Calculate the following: The change in length Ax The angular frequency (w) The frequency (f) The...
1. According to Hooke's law, the force exerted by a spring is proportional to the amount of stretch (or change in length Ax) and is given by F = -KAx, where the minus sign indicates it is a restoring force. If a force of 120 N acts on a mass 250 g attached to a spring of constant K = 54.55 x 10 N/m. Calculate the following: The change in length Ax The angular frequency (w) The frequency (f) The...
Consider a mass m suspended from a massless spring that obeys Hooke's Law (i.e. the force required to stretch or compress it is proportional to the distance stretched/compressed). The kinetic energy T of the system is mv2/2, where v is the velocity of the mass, and the potential energy V of the system is kr-/2, where k is the spring constant and x is the displacement of the mass from its gravitational equilibrium position. Using Lagrange's equations for mechanics (with...
3) Consider Hooke's Law: The force required to keep a spring in a compressed or stretched position x units from the spring's equilibrium position is F(x)-kr Calculate the work required, in joules, to stretch a spring 0.4 meters beyond its equilibrium position for each of the following scenarios. a) The spring requires 50 Newtons of force to hold it 0.1 m from its equilibrium position. b) The spring requires 2 Joules of work to stretch the spring 0.1 meter from...