How much work is required to move an object horizontally???

Question

The definition of work, W, done by a force F in moving an object from point a to point b is given below. How much work is required to move an object horizontally from a = 1 m to b = 3 m by force F?

 

w=∫_a^b f(x) dx

f(x)=2/x^2

 

 

Answer 1

 

Hi Daniel,

Looks like you and Marlene started up on this problem

 

W=∫_a^b f(x) dx  , f(x)=2/x^2  and you have the limit of integration at a = 1 and b = 3

 

a^b = 1^3 =1

 

W = ∫ 2/x²  dx = 2∫x^-2dx =-2x^-1     evaluated at a = 1 and b = 3

 

    = [-2/3 - (-2/1) ]

    = -2/3 +2

 

W = 4/3 J   where J is the unit of energy Joules if the force F is measured in N (Newtons)

Answer 2

Work is defined as the integral from a to b of the dot product of a force F and a displacement vector dx. If we are dealing with a one-dimensional problem, then the dot product in the integrand reduces to F(x)dx. If f(x) = 2/x^2 = 2x^(-2), then we just integrate that from a = 1 to b = 3. The integral of 2x^(-2) = -2x^(-1) = 2/x. Evaluating the definite integral gives 2/b - 2/a = 2/3 - 2/1 = 2/3 - 6/3 = -4/3

 

This answer should be in energy units like Joules or Calories, but no units were specified in this problem, so I am just leaving the answer as W = -4/3