Find Amount of Required Work

[nycmathguy]

Section 1.10
Question 70

The work W required to lift an object varies jointly with the object’s mass m and the height h that the object is lifted. The work required to lift a 120-kilogram object 1.8 meters is 2116.8 joules. Find the amount of work required to lift a 100-kilogram object 1.5 meters.

Let me try this one.

W = km•h

I need to find k, the constant of proportionality.

120 = k(2116.8)(1.8)

120 = k(3,810.24)

120/(3,810.24) = k

0.0314940791 = k

I now need to find W.

W = (0.0314940791)(100)(1.5)

W = 4.724111865

W = 4.72 joules

Yes?

 

[MathLover1]

Work done can be computed using the formula:

W=Fd
where:
W = work (J)
F = Force (N)
d = Distance (m)
Looking at the given, you know that you do not have a value for force, so you will have to solve for it.

F =W/d
recall F =m*a ( m=mass, a=acceleration)

Because the object is being lifted, the acceleration will rely on gravity. Acceleration due to gravity is a constant 9.8 m/s^2.

Let's list our given first:

F =m*9.8( m/s^2)
m = 100kg

Put that into our equation and solve:

F =100kg*9.8( m/s^2)
F =980kg( m/s^2)............since 1kg( m/s^2)=1N
F =980N

Now that we have force we can solve for Work. The given for work is as follows:
F= 980N
d = 1.4m

Put that into our formula W=Fd and solve:
W=980N*1.4m
W=1372Nm......................1Nm=1J

so, the work done is 1372J

 

[nycmathguy]

Work done can be computed using the formula:

W=Fd
where:
W = work (J)
F = Force (N)
d = Distance (m)
Looking at the given, you know that you do not have a value for force, so you will have to solve for it.

F =W/d
recall F =m*a ( m=mass, a=acceleration)

Because the object is being lifted, the acceleration will rely on gravity. Acceleration due to gravity is a constant 9.8 m/s^2.

Let's list our given first:

F =m*9.8( m/s^2)
m = 100kg

Put that into our equation and solve:

F =100kg*9.8( m/s^2)
F =980kg( m/s^2)............since 1kg( m/s^2)=1N
F =980N

Now that we have force we can solve for Work. The given for work is as follows:
F= 980N
d = 1.4m

Put that into our formula W=Fd and solve:
W=980N*1.4m
W=1372Nm......................1Nm=1J

so, the work done is 1372J

Nicely-done. I tried. I did show effort. This is more a physics-like problem. I had no idea that mass is distance. I have idea what joules is, really. This will be my excuse for not getting it right.

 

[MathLover1]

This IS a physics problem.

 

[nycmathguy]

This IS a physics problem.

I know nothing about physics. This problem is in the Ron Larson Precalculus textbook. Moving on to Chapter 2.