A block has a volume of #0.07# #m^3# and a density of #3,500# #kg##/##m^3#. What's the force of gravity acting on the block (and weight) in the air?

1 Answer
Morgan
Aug 13, 2017

#F_G=24035" N"# (downward)

Explanation:

Density (volumetric mass density) is a mass-to-volume ratio, or the mass of a substance per unit volume. The equation for density is given by:

#rho=m/V#

Additionally, the equation for the force of gravity acting on a stationary object at or near the surface of the earth is given by:

#F_G=mg#

We have the following information:

  • #|->V=0.07" m"^3#

  • #|->rho=3,500 " kg"//"m"^3#

  • #|->g=9.81"m"//"s"^2#

We can use the above information to calculate the object's mass, and then use that to calculate the force of gravity acting upon it.

#rho=m/V#

#=>m=rhoV#

#=>=(3,500 " kg"//"m"^3)(0.07" m"^3)#

#=>=2450" kg"#

Now we have:

#F_g=mg#

#=>=(2450" kg")(9.81"m"//"s"^2)#

#=>=24034.5" N"#

#=>=color(blue)(24035" N")#

Or, you might choose to write this in scientific notation as #2.4xx10^4" N"#.

Note that this quantity is equal to the object's weight so long as it is stationary and at/near the earth's surface, as assumed above.

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