Question

How high would a skater need to start on a previous incline to make it up and around a loop that is 6.1meters high?

Answer 1

The skater need to start 7.525 meter high.

Let,

The skater need to start on a previous incline at height = h.

Mass of the skater = m

Given, height of the loop = 6.1 meter.

Radius of the loop; r = 6.1/2 meter = 3.05 meter.

Let to make it up and around a loop that is 6.1meters high, the man required minimum velocity v on the highest point of the loop.

So, centripetal force at highest point = weight of the man

⇒ mv²/r = mg

⇒ v = √(gr)

Then, potential energy of the skater at height h is = mgh.

And, minimum energy  of the skater at the highest point of the loop is = potential energy + minimum kinetic energy.

= mg(2r) + 1/2 mv²

= 2mgr + 1/2 mgr

= 5/2 mgr

According to conservation of energy,

potential energy of the skater at height h = minimum energy  of the skater at the highest point of the loop

⇒ mgh = 5/2 mgr

⇒ h = 5/2 r =( 5/2 )× 3.05 meter = 7.525 meter.

Hence, required height is 7.525 meter.

Learn more about energy here:

brainly.com/question/1932868

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