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?

Question

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?

Emily Abbate · Accepted Answer

#F_c~~5053N# radially inward.

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 #romega^2#. Therefore, we can write: #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 #5xx10^3"N"# where significant figures are concerned.

Axel Acevedo · Answer

undefined The centripetal force acting on the object can be calculated using the formula:

Centripetal force = Mass * Angular velocity^2 * Radius

First, let's calculate the angular velocity using the frequency (f):

Angular velocity (ω) = 2π * frequency
Angular velocity (ω) = 2π * 4 Hz = 8π rad/s

Now, we can plug the given values into the centripetal force formula:

Centripetal force = 2 kg * (8π rad/s)^2 * 4 m

Calculating:

Centripetal force ≈ 2 * (64π^2) * 4 N
Centripetal force ≈ 512π^2 N