# Solving Spring Truck Problem 2: Compute Work, Speed, if Force is Conservative

• TyFelmingham
In summary, the force law for a spring that does not conform to Hooke's law is F = -k1x - k2x^2, with k1 = 52.8 N.m-1 and k2 = 38.4 N.m-2. The work required to stretch the spring from x = 0.500 m to x = 1.00 m is -91.2 N. With one end fixed and a particle of mass 2.17 kg attached to the other end when the spring is extended by x = 1.00 m, the speed of the particle at the instant the spring returns to x = 0.500 m is calculated by integrating F.dx from x =
TyFelmingham
2. A spring from the truck is found not to conform to Hooke’s law. The force law for this spring is
found to be:
F = – k1x – k2 x^2
where k1 = 52.8 N.m-1; k2 = 38.4 N.m-2.
a) Compute the work required to stretch the spring from x = 0.500 m to x = 1.00 m.
b) With one end of the spring fixed, a particle of mass 2.17 kg is attached to the other end of the
spring when it is extended by an amount x = 1.00 m. If the particle is then released from rest,
compute its speed at the instant the spring has returned to the configuration in which the extension
is x = 0.500 m.
c) Is the force exerted by the spring conservative or nonconservative? Explain your answer.

Ok, for a)

sub in the numbers for x = 1m and you get -91.2 N
sub in the numbers for x= .5m and you get - 36 N

So force is 127.2 N when the spring is stretched from .5 to 1m?

As W = F*x, do i just plug in x=.5m and F = 127.2 N?

Cheers

In a and b. Calculate the energy in x = 0,5 and x = 1,00. You can't do a with the simple W = Fs because F is changeable.

KingOfTwilight said:
In a and b. Calculate the energy in x = 0,5 and x = 1,00. You can't do a with the simple W = Fs because F is changeable.
So you have to integrate?

Yeah, I think so,

Work done = Integral F.dx : Limits of Integraton are from x = 0.5 to x = 1.00

Naeem said:
Yeah, I think so,

Work done = Integral F.dx : Limits of Integraton are from x = 0.5 to x = 1.00
Cheers

## What is the spring truck problem?

The spring truck problem involves a truck that is attached to a spring and is moving along a horizontal surface. The task is to calculate the work done, the speed of the truck, and the force acting on it if the force is conservative.

## What is work and how is it calculated?

Work is the product of the force acting on an object and the distance that the object moves in the direction of the force. In this problem, work can be calculated by multiplying the magnitude of the force by the displacement of the truck.

## How is speed calculated in this problem?

Speed can be calculated by dividing the displacement of the truck by the time it takes to cover that distance. Alternatively, it can also be calculated by taking the square root of the ratio of the kinetic energy of the truck to its mass.

## What is a conservative force?

A conservative force is a force that does not depend on the path taken by the object. In other words, the work done by a conservative force only depends on the initial and final positions of the object, not on the path it takes.

## What are some real-life applications of this problem?

Real-life examples of this problem include calculating the work done by a car engine, determining the speed of a rollercoaster, or analyzing the force acting on a pendulum. It can also be applied in industries such as transportation, engineering, and physics research.

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