When 20 N of force is applied to a spring of natural length 2 m, the resulting compression is 0.5 m. The work (in joules) done in compressing the spring from 1.5m to 1.0 m is given by the integral 40x dx B 40x dx 0.5 •1.5 40x dx 1.0 0.5 40x dx

When 20 N of force is applied to a spring of natural length 2 m, the resulting compression is 0.5 m. The work (in joules) done in compressing the spring from 1.5m to 1.0 m is given by the integral 40x dx B 40x dx 0.5 •1.5 40x dx 1.0 0.5 40x dx

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter5: Energy

Section5.5: Spring Potential Energy

Problem 5.5QQ: Calculate the elastic potential energy of a spring with spring constant k = 225 N/m that is (a)...

See similar textbooks

Related questions

Q: An ideal spring has a spring constant k=28.2 N/m. What is the amount of work that must be done to…

Q: The force required to compress a non-standard spring as a function of displacement is given by the…

Q: An elevator cable breaks. The elevator falls at the bottom of the shaft. The spring, whose force…

A: Given:- The spring constant k= 2.0 x 104 N/m The energy absorbed by the spring E = 3.0 x104 J Find:-…

Q: The force constant of a wire is (K) and that of another wire of the same material is (2 K). When…

A: To find- Relation between work done. Given- Force constant of first wire= K1=K Force constant…

Q: Consider a spring with constant k= 200 N/m, If the spring is compressed 4 cm, so the integral that…

A: Given Consider a spring with constant k = 200N . If the spring is compressed 4 cm, so the…

Q: A wire of length 5 m and 1 mm is stretched by 1load of 10 N. If Y = 2 x 10" N/m2, find the work done…

A: To find-Work done per unit volume (W)=?Given-Length of wire (L)=5 mRadius of wire (r)=1 mm=1×10-3…

Q: An ideal spring is hung vertically from the ceiling. When a 2.0-kg mass hangs at rest from it the…

Q: An elevator cable breaks when a 985kg elevator is 25.5m above the top of a huge spring (k= 8.00 x…

A: (a) Let us calculate the gravity on the planet. gp-gE=30%gEgp=gE+30%gE=1.3gE=1.39.81 m/s2=12.8 m/s2

Q: block with mass m = 2500 gram slides towards a spring with spring constant k = 320 N/m. When the…

Q: When a crate of mass m is dragged a distance d along a surface with coefficient of kinetic friction…

Q: A 287-kg crate is being pushed across a horizontal floor by a force P that makes an angle of 17.1°…

A: Given that, Mass of crate M = 287 kg angle below the horizontal direction Θ =17.1 0 the coefficient…

Q: If it requires 9.0 JJ of work to stretch a particular spring by 2.0 cmcm from its equilibrium…

A: Write the expression for the work done by the spring.

Q: A metal wire of length 2.5 m and area of cross-section 1.5 x 106 m² is stretched through 2 mm.…

A: We have to find work done (W) Given that, Length of wire L is 2.5 m Y is 1.25×1011 N/m2

Q: A block of weight w sits on a plane inclined at an angle as shown. (Figure 1) The coefficient of…

A: The weight of the block is w. The angle of iinclination is θ. The coefficient of kinetic friction is…

Q: A force F→ in the positive direction of an x axis acts on an object moving along that axis. If the…

A: Let a force (F) in the positive direction of the x-axis act on an object moving along that axis. The…

Q: . When the load on a wire is increased slowly from 1 kg wt to 2 kg wt the elongation increases from…

Q: A toy car of mass m is pushed against a spring, compressing it a distance d from its natural rest…

Q: A trunk of mass m = 0.6 kg is pushed a distance d = 30 cm up an incline with an angle of inclination…

Q: A 2 kg block is pushed 4.0 m along a horizontal floor by a force of magnitude 25 N at an angle…

Q: The force required to compress a non-standard spring as a function of displacement is given by the…

Q: A 2 kg block is pushed 4.0 m along a horizontal floor by a force of magnitude 25 N at an angle…

Q: The work done on a stretching a spring it to 3.50 cm from its equilibrium length is 14.0 J. (a) How…

A: Work done in stretching a spring = (1/2) kx^2 Where x is the displacement K= spring constant From…

Q: A block of mass m is placed on a rough incline surface making an angle 0 = 28.3 with horizontal. A…

Q: The force required to compress a non-standard spring as a function of displacement is given by the…

A: We have an expression for force that is required to compress a non-standard spring as a function of…

Concept explainers

Spring Potential Energy

The potential energy is the energy possessed by a body by virtue of its position or the energy held by the object due to its position relative to other objects, its force like stresses, charge, and other factors affecting the particles of the body. The potential energy is the measure of the net work done by or on the body. The spring potential energy is the potential energy stored due to the deformation of an elastic spring and this elasticity is due to the stretched spring. The elasticity is the ability of a solid-state matter to come back to its equilibrium position or original position after any kind of external force is acted on it. It is also known as Elastic potential energy. The potential energy here is caused due to the displacement of the spring from its equilibrium position to another position and this potential energy is equal to the net work done due to the stretching of the spring. It also resembles the same mechanics of the oscillation of a simple pendulum, where due to the external force, the object moves from its equilibrium position to its maximum ends and the periodic motion continues till it comes back to the equilibrium position to rest. 

Question

When 20 N of force is applied to a spring of natural length 2 m, the resulting compression is 0.5 m. The work (in joules) done in
compressing the spring from 1.5m to 1.0 m is given by the integral
(A
40x dx
1
40x dx
0.5
© S*
1.5
40х dx
1.0
© S*
0.5
(D
40х dx

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.

Similar questions

A block of mass 0.250 kg is placed on top of a light, vertical spring of force constant 5 000 N/m and pushed downward so that the spring is compressed by 0.100 m. After the block is released from rest, it travels upward and then leaves the spring. To what maximum height above the point of release does it rise?
Calculate the elastic potential energy of a spring with spring constant k = 225 N/m that is (a) compressed and (b) stretched by 1.00 102 m.
A childs pogo stick (Fig. P7.69) stores energy in a spring with a force constant of 2.50 104 N/m. At position (x = 0.100 m), the spring compression is a maximum and the child is momentarily at rest. At position (x = 0), the spring is relaxed and the child is moving upward. At position , the child is again momentarily at rest at the top of the jump. The combined mass of child and pogo stick is 25.0 kg. Although the boy must lean forward to remain balanced, the angle is small, so lets assume the pogo stick is vertical. Also assume the boy does not bend his legs during the motion. (a) Calculate the total energy of the childstickEarth system, taking both gravitational and elastic potential energies as zero for x = 0. (b) Determine x. (c) Calculate the speed of the child at x = 0. (d) Determine the value of x for which the kinetic energy of the system is a maximum. (e) Calculate the childs maximum upward speed. Figure P7.69
Consider a block of mass 0.200 kg attached to a spring of spring constant 100 N/m. The block is placed on a frictionless table, and the other end of the spring is attached to the wall so that the spring is level with the table. The block is then pushed in so that the spring is compressed by 10.0 cm. Find the speed of the block as it crosses (a) the point when the spring is not stretched, (b) 5.00 cm to the left of point in (a), and (c) 5.00 cm to the right of point in (a).
When a 4.00-kg object is hung vertically on a certain light spring that obeys Hookes law, the spring stretches 2.50 cm. If the 4.00-kg object is removed, (a) how far will the spring stretch if a 1.50-kg block is hung on it? (b) How much work must an external agent do to stretch the same spring 4.00 cm from its unstretched position?
A horizontal spring attached to a wall has a force constant of k = 850 N/m. A block of mass m = 1.00 kg is attached to the spring and rests on a frictionless, horizontal surface as in Figure P7.55. (a) The block is pulled to a position xi = 6.00 cm from equilibrium and released. Find the elastic potential energy stored in the spring when the block is 6.00 cm from equilibrium and when the block passes through equilibrium. (b) Find the speed of the block as it passes through the equilibrium point. (c) What is the speed of the block when it is at a position xi/2 = 3.00 cm? (d) Why isnt the answer to part (c) half the answer to part (b)? Figure P7.55
Check Your Understanding What potential energy U(x) can you substitute in Equation 8.13 that will result in motion with constant velocity of 2 m/s for a particle of mass 1 kg and mechanical energy 1 J?
The force required to compress a non-standard spring as a function of displacement is given by the equationF(x) = -Asin(bx) + kx,where A = 11 N, b = 11 rad/m, and k = 78 N/m. Calculate the work done in joules as the spring is compressed from x = 0 to x1 = 32 cm. Calculate the work done in joules as the spring is compressed from x1 = 32 cm to x2 = 69 cm
The force required to compress a non-standard spring as a function of displacement is given by the equationF(x) = -Asin(bx) + kx,where A = 11 N, b = 11 rad/m, and k = 78 N/m. Part (b) Calculate the work done in joules as the spring is compressed from x = 0 to x1 = 32 cm. Part (c) Calculate the work done in joules as the spring is compressed from x1 = 32 cm to x2 = 69 cm
Q. 14: Work done in blowing a soap bubble of diameter 2 cm, is (S.T. = 3 x 10-² N/m) (a) 7.54 x 10 J (b) 7.54 × 10“ J (c) 7.54 x 10 J (d) 7.54 J
Nilo phi
SQU is trying a new particle accelerator design with a mechanical component using a spring that does not obey Hooke's law. When stretched/compressed x metres, it exerts a force of 39.6x+51.6x2 (a) Compute the work required to stretch the spring from x= 1.0 m to x 1.3 m.