# From what minimum height of the inclined plane should the bar slide without friction in order

**From what minimum height of the inclined plane should the bar slide without friction in order to describe the “dead loop” of radius R without applying pressure at the top of the loop?**

R

P = 0.

hmin -?

When passing the upper point of the loop, 2 forces act on the bar: gravity Ft directed vertically downward, force N of surface pressure directed vertically downward.

m * a = m * g + N – 2 Newton’s law in vector form.

For projections onto the vertical axis 2, Newton’s law will take the form: m * a = Fт + N.

N = Fт – m * a.

The force of gravity Ft is determined by the formula: Ft = m * g.

N = m * g – m * a = m * (g – a).

The centripetal acceleration a is expressed by the formula: a = V ^ 2 / R.

N = m * (g – V ^ 2 / R).

Since at the upper point P = T = 0, then g = V ^ 2 / R.

V2 = R * g.

According to the law of conservation of energy: m * g * hmin = m * V ^ 2/2.

hmin = V ^ 2/2 * g = R * g / 2 * g = R / 2.

Answer: the minimum height is half the radius of the loop: hmin = R / 2.