An object with a mass of #2 kg# is revolving around a point at a distance of #4 m#. If the object is making revolutions at a frequency of #4 Hz#, what is the centripetal force acting on the object?
1 Answer
Explanation:
The centripetal force is given in accordance with Newton's second law as:
#F_c=ma_c# where
#m# is the mass of the object and#a_c# is the centripetal acceleration experienced by the object
The centripetal acceleration is given by:
#a_c=v^2/r#
which is equivalent to
#F_c=mromega^2# where
#r# is the radius and#omega# is the angular velocity of the object
The angular velocity can also be expressed as:
#omega=2pif# where
#f# is the frequency of the revolution
And so our final expression becomes:
#color(blue)(F_c=mr(2pif)^2#
We are given:
-
#|->"m"=2"kg"# -
#|->"r"=4"m"# -
#|->f=4"s"^-1#
Substituting these values into the equation we derived above:
#F_c=(2"kg")(4"m")(2pi(4"s"^-1))^2#
#=5053.237"N"#
#~~5053N# radially inward
This may also be expressed in scientific notation as
