Chapter 1: 40P (page 1)

A can of sardines is made to move along an x axis from $x = 0.25 m$ to $x = 1.25 m$ by a force with a magnitude given by $F = \exp (- 4 x^{2})$ with x in meters and Fin newtons. (Here exp is the exponential function.) How much work is done on the can by the force?

Short Answer

Expert verified

The work done on the can by the force is, 0.21 J.

Step by step solution

Given

The motion of can starts from $x_{i} = 0.25 m$
The final position of the can is, $x_{f} = 1.25 m$
The function of force is, $F = e^{- 4 x^{2}}$
The scale for vertical axis is, $F_{s} = 10.0 N$

Concept of calculating force done by a variable force.

The problem deals with the concept of work done. It includes both forces exerted on the body and the total displacement of the body. We can use the equation of the work done by a variable force.

Formula:

$W = \int_{x_{i}}^{x_{f}} F (x) d x$

Calculate the work done

The equation for work done is,

$W = \int_{x_{i}}^{x_{f}} F (x) d x$

Substitute the value of F(x) in the above equation.

$W = \int_{0.25}^{1.25} e^{- 4 x^{2}} d x$

By solving this integral, we get

$W = 0.21 J$

Therefore, work done by the force on the can is 0.21 J.

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A can of sardines is made to move along an x axis from $x = 0.25 m$ to $x = 1.25 m$ by a force with a magnitude given by $F = \exp (- 4 x^{2})$ with x in meters and Fin newtons. (Here exp is the exponential function.) How much work is done on the can by the force?

Short Answer

Step by step solution

Given

Concept of calculating force done by a variable force.

Calculate the work done

One App. One Place for Learning.

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A can of sardines is made to move along an x axis from x=0.25m tox=1.25m by a force with a magnitude given byF=exp(-4x2) with x in meters and Fin newtons. (Here exp is the exponential function.) How much work is done on the can by the force?

Short Answer

Step by step solution

Given

Concept of calculating force done by a variable force.

Calculate the work done

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Circular Motion and Gravitation

Astrophysics

Linear Momentum

Nuclear Physics

Wave Optics

Electricity and Magnetism

Study anywhere. Anytime. Across all devices.

A can of sardines is made to move along an x axis from $x = 0.25 m$ to $x = 1.25 m$ by a force with a magnitude given by $F = \exp (- 4 x^{2})$ with x in meters and Fin newtons. (Here exp is the exponential function.) How much work is done on the can by the force?