a 4.00 kg mass is moving in a circular path of radius 3.20 m with a...

a 4.00 kg mass is moving in a circular path of radius 3.20 m with a constant linear speed of 6.29 m/s. The radial force on the mass is

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Expert Solution

Information provided- mass=m=4.00 kg

Radius=R=3.20 m

linear speed=v=6.29 m/s

concept to be used-curvilinear motion.

When a body moves in a curved path its velocity changes both in magnitude and direction giving rise to two components of acceleration namely and .

is the component of acceleration due to change in direction of velocity.

=v²/R in magnitude and acts radially towards the centre.

= dv/dt in magnitude and acts in the direction of v (if velocity increases with time)

In this question the body is moving with a constant linear velocity v so making the =0 (as derivative of a constant is zero)

let be the total acceleration .

as =0

=v²/R and directed towards the centre.

=6.29²/3.2=12.364 m/s²

we know F=ma=m=4.00x12.364=49.456 N and direction of the force is towards the centre.(in the direction of acceleration)

The radial force on the mass is 49.456 N.

genius_generous answered 1 year ago

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