Physics Question

Question

I need help solving this physics problem. A 30 kg ice skater goes around a circle of radius 5 m at a constant speed of 5 m/s on a level ice rink.

1) Draw a sketch of the situation

2) what are the magnitude and direction of the force that the ice exerts on the skater? (The total force, not just the horizontal or vertical component of the force)

3) Draw a force diagram for the ice skater going in a circle

4) Why is the magnitude of my answer reasonable? How do I know what the sign of my answer should be? How is it consistent with my representation? Be as detailed as possible. Thank you!

Answer 1

I can't draw a diagram but can describe the forces involved.

There are two forces acting on the skater, an upward reaction force equal to the normal force due to the skaters weight which is mg or 30 kg x 9.8 m/s² = 294 N and a centripetal force acting toward the center of the circle equal to mv² / r or 30kg x 5² m²/s² / 5m = 150 N. The total force then is the resultant of the two forces which you can calculate using the pythagorean theorem F_T = √ 294² + 150² = 330 N at an angle = arctan 294/150 = 63 degrees from the horizontal.