A clever engineer designs a "sprong" that obeys the force law fx =−q(x−xe)3, where xe is the equilibrium position of the end of the sprong and q is the sprong constant. for simplicity, we'll let xe =0m. then fx =−qx3.

Answers

Answer 1

Answer:

The unit of q is N/m³.While the potential energy of the compressed spring will be $\rm U(x)= -(qx^4)/(4)$ .

What is the potential energy of spring?

When a springdeviates from its mean position, it attempts to regain equilibrium by applying a force that is equivalent to but opposite to the external force.

Spring force has been used in bicycle carriers and launchingmechanisms, where the energy generated by disrupting the spring'sbalance is used as potential energy.

The given equation for the force law is;

$\rm f_x =-q(x-x_e)$

Where,

$\rm x_e$ is equilibrium position of the end of the spring

q is a spring constant

If at equilibriumposition;

$\rm x_e=0$

$\rm F_X= -qx^3 \n\n \rm q = (F_x)/(x^3) \n\n$

So the unit derived will be;

q = N/m³

The potential energy of the spring is found by;

$\rm F_x=- (du)/(dx) \n\n U(x)= -\int\limits^x_0 {F(x)} \, dx \n\n U(x)= -\int\limits^x_0 -qx^3 \, dx \n\n U(x)=- (qx^4)/(4)$

Hence the unit of q is N/m³.While the potentialenergy of the compressed spring will be $\rm U(x)= -(qx^4)/(4)$ .

To learn more about the potential energy of spring refer to the link;

brainly.com/question/2730954

Answer 2

Answer:

The objective of this question is to compute the units of q and calculate the expression for the P.E of the compressed spring

Answer:

q = N/m³

$\mathbf{U(x) = -(qx^4)/(4)}$

Explanation:

Given that:

The equation for the force law is:

$F_x = -q (x -x_e)^3$

where;

$x_e$ e = equilibrium position of the end of the spring

i.e. $x_e$ = 0

q = is the spring constant

Also;

$F_x = -qx^3$

From above the units of q can be calculated by making q the subject of the formula :

$q = (F_x)/(x^3)$

where x is in meters and F is in Netwon;

Then :

q = N/m³

The Potential energy P.E of the compressed spring can be calculated by using the integral:

$F_x = -(dU)/(dx)$

$U(x) = - \int F_x dx$

$U(x) = - \int ^x_0 (-qx^3) \ dx$

$\mathbf{U(x) = -(qx^4)/(4)}$

Related Questions

an apple in a tree has a gravitational potential energy of 175J and a mass of 0.36g . how high from the ground is the apple
Debby and Ben took different routes to travel from Point A to Point E. Debby took theroute along A, B, C, D, and E. Ben took the route along A, G, F, and E. Debby and Benboth took 4 hours to complete their walk. Their routes are shown.Route in milesD2 EEndB2CliF2LL310StartGAWhich statement is true about Debby and Ben's average speed?Debby's average speed was twice Ben's average speed,Ben and Debby's average speed was the same,Debby's average speed was three times Ben's average speed,Ben's average speed was twice Debby's average speed.
Physics principles involved in the tablecloth trick???
Which universal force acts on protons and neutrons in an atom's nucleus?
What will be the velocity of body in horizontal motion of the body in the air?

Which of the following is NOT an example of accelerated motion?A. an airplane taking off down a straight runway
B. a boulder falling off a cliff in a straight path
C. a ball being thrown straight up
D. a bicyclist moving in a straight line at a constant speed

Answers

Accelerated motion = any change in speed or direction.

A. No. The airplane's speed is increasing.

B. No. The boulder's speed increases as it falls.

C. No. The speed of the ball decreases as it approaches the peak,
then it changes direction, begins to move downward, and its speed
increases steadily after that.

D. Yes. The cyclist's speed and direction are not changing.

Final answer:

Accelerated motion refers to any motion with changing velocity, including changes in speed or direction. Most of the examples provided involve accelerated motion, except for the bicyclist moving in a straight line at a constant speed, as both speed and direction remain constant in such scenario.

Explanation:

In the context of physics, accelerated motion refers to any motion in which the velocity changes - either in magnitude (speed) or direction. This can be due to an increase or decrease in speed, or a change in direction. Examples of accelerated motion include an airplane taking off down a straight runway, a boulder falling off a cliff in a straight path, and a ball being thrown straight up.

However, a bicyclist moving in a straight line at a constant speed is NOT an example of accelerated motion. In this case, the speed (magnitude of velocity) and direction are both constant, and therefore there is no acceleration present.

Learn more about Accelerated Motion here:

brainly.com/question/2261259

#SPJ6

Seed is 4m/s 3 sec later at the bottom of the slope it's speed is 22m/s what is the average acceleration

Answers

U1 = 4 m/s
U2 = 22 m/s
t1 = 0
t2 = 3 sec.

α= $(U2 - U1)/(t2 - t1)$

what is the net force if you push a cart to the right with 5N of force and a friend pushes the cart to the left with 5N of force

Answers

The net force will be zero. Since the forces are in opposite direction and equal amount, they will cancel out.

When two or more elements chemically combine the result is?

Answers

Pretty sure this question is referring to a chemical compound.

A ball of a mass 0.3 kg is released from rest at a height of 8 m. How fast is it going when it hits the ground? Acceleration due to gravity is g=9.8 m/s^2

Answers

In order to solve this problem, there are two equations that you need to know to solve this problem and pretty much all of kinematics. The first is that d=0.5at^2 (d=vertical distance, a=acceleration due to gravity and t=time). The second is vf-vi=at (vf=final velocity, vi=initial velocity, a=acceleration due to gravity, t=time). So to find the time that the ball traveled, isolate the t-variable from the d=0.5at^2. Isolate the t and the equation now becomes $√((2d)/a)$ . Solving the equation where d=8 and a=9.8 makes the time $√((2*8)/9.8)$ =1.355 seconds. With the second equation, the vi=0 m/s, the vf is unknown, a=9.8 m/s^2 and t=1.355 sec. Substitute all these values into the equation vf-vi=at, this makes it vf-0=9.8(1.355). This means that the vf=13.28 m/s.

Answer:

The answer is 12.5 m/s

v=the square root of 2 x(gh)

or v = the square root of 2 x (9.8 x 8)

Explanation:

The orbits of planets being elliptical was one the planetary laws developed by

Answers

The correct answer is Kepler

Final answer:

The concept that planets move in elliptical orbits was established by Johannes Kepler in his First Law of Planetary Motion. This significant idea disrupted the earlier belief of circular orbits and brought tremendous knowledge in our solar system understanding.

Explanation:

The fact that the orbits of planets are elliptical was part of the planetary laws developed by the renowned astronomer and mathematician Johannes Kepler. Damaging the former belief of circular orbits, Kepler, based on detailed and exhaustive astronomic observations, established his First Law of Planetary Motion which stated that planets move in elliptical orbits with the Sun at one of the two foci. This was a significant breakthrough in understanding our solar system and continues to be fundamental in physics and astronomy today.

Learn more about Kepler's Laws,

brainly.com/question/35176068

#SPJ2

Other Questions

True or False Another name for constructive interference is intense interference

What instrument uses a magnetic field to magnify imags up to 100000000?

Are oranges called oranges because oranges are orange, or is orange called orange because oranges are orange?

7.If your driver license is suspended, you may drive only:a. If you obtain an essential need driver licenseb. If you have an accompanying licensed driverc. If you drive on less traveled roadsd. If you get permission from the local police