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4. In the display window of the toy store at the local mall, a battery-powered plane is suspended from a string and flying in a horizontal circle. The 631 gram plane makes a complete circle every 2.15 seconds. The radius of the circle is 0.950 m. Determine the velocity, angular velocity, acceleration, and net force acting upon the plane.

Sagot :

Answer:

The solution is given below

Explanation:

The computation is shown below:

Given that

Mass of plane, m is 631 g = 0.631 Kg

The Time period for one circle is 2.15 s

The Radius of circle = 0.95 m

Now the velocity of the plane, v = rω

where,

angular velocity, ω = (θ ÷ t)

For one complete circle, θ = 2π

and Time period T is provided = 2.15 s

Thus, ω = 2π ÷ T = 2π  ÷ 2.15

So, velocity, v = rω

= r × ( 2π  ÷ 2.15 )

= 0.95 × (2π ÷2.15)

= 2.776 m/s

The Acceleration of the plane, a = rω^2

= 0.95 × (2π ÷ 2.15)^2

= 8.114 m/s^2

The Net force acting upon the plane, F = Centripetal force i.e.

= mv2 ÷  r

F = mv2 / r

= (0.631 × 2.7762) ÷ 0.95

= 5.118 N