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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 jo...
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 req...
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 mass m suspended from a massless spring that obeys Hooke's Law (i.e. the force...
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...
To understand the use of Hooke's law for a spring. Hooke's law states that the restoring...
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...
A spring is found to not obey Hooke's law. It exerts a restoring force F(x) =-ax-...
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...
Hooke’s Law states that the force required to maintain a spring stretched x units beyond its...
Hooke’s Law states that the force required to maintain a spring stretched x units beyond its natural length is proportional to x, i.e. f(x) = kx where k is a positive constant. Suppose that 4 J of work is needed to stretch a spring from its natural length 10 cm to a length of 36 cm. Find the exact value of work needed to stretch the spring from 15 cm to 28 cm.
2. Question from 1.1: Rectangular Coordinatas Use Hooke's Law for springs, which states that the distance a spring is stretched (or compressed) varies directly as the force on the spring An overh...
2. Question from 1.1: Rectangular Coordinatas Use Hooke's Law for springs, which states that the distance a spring is stretched (or compressed) varies directly as the force on the spring An overhead garage door has two springs, one on each side of the door. A force of 11 pounds is required to stretch each spring 1 foot. Because of a pulley system, the springs stretch only one-half the distance the door travels. The door moves a total of 10 feet,...
Consider a spring that does not obey Hooke's law very faithfully. One end of the spring...
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...
A spring is stretched from x=0 to x=d, where x=0 is the equilibrium position of the...
A spring is stretched from x=0 to x=d, where x=0 is the equilibrium position of the spring. It is then compressed from x=0 to x=−d. What can be said about the energy required to stretch or compress the spring?
A spring of force constant 3 N/m is compressed by 5.0 em from its equilibrium position....
A spring of force constant 3 N/m is compressed by 5.0 em from its equilibrium position. The spring is then released and stretched by 5.0 ㎝ from its equilibrium position. Find the difference in potential energy between the two positions of the spring (stretched and compressed).
Caloulate the work required to stretch the following springs 1.5 m from their equilibrium positions. Assume...
Caloulate the work required to stretch the following springs 1.5 m from their equilibrium positions. Assume Hooke's law is obeyed a. A spring that required 80 J of work to be stretched 0.2 m from its equilibrium position. b.A spring that required a force of 250 N to be stretched 0.4 m from its equibrium position a. Set up the integral that gives the work done in strotching the spring 1.5 m from its equilibrium position. Use increasing Imits of...
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 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...
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...
2. Question from 1.1: Rectangular Coordinatas Use Hooke's Law for springs, which states that the distance a spring is stretched (or compressed) varies directly as the force on the spring An overhead garage door has two springs, one on each side of the door. A force of 11 pounds is required to stretch each spring 1 foot. Because of a pulley system, the springs stretch only one-half the distance the door travels. The door moves a total of 10 feet,...
A spring of force constant 3 N/m is compressed by 5.0 em from its equilibrium position. The spring is then released and stretched by 5.0 ㎝ from its equilibrium position. Find the difference in potential energy between the two positions of the spring (stretched and compressed).
Caloulate the work required to stretch the following springs 1.5 m from their equilibrium positions. Assume Hooke's law is obeyed a. A spring that required 80 J of work to be stretched 0.2 m from its equilibrium position. b.A spring that required a force of 250 N to be stretched 0.4 m from its equibrium position a. Set up the integral that gives the work done in strotching the spring 1.5 m from its equilibrium position. Use increasing Imits of...
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