Question

Лыжник массой 50 кг движется со скоростью 20 м/с по вогнутому, а затем по выпуклому участкам дороги с радиусом кривизны 80м. Определите вес лыжника в средней точке каждого участка. P1=?Н P2=?H

Answer 1

Ответ:

Объяснение:

Дано:

m = 50 кг

V = 20 м/с

R = 80 м

__________

P₁ - ?

P₂ - ?

Центростремительное ускорение:

a = V²/R = 20²/80 = 400 / 80 = 5 м/с²

На вогнутом участке:

Р₁ =m·(g+a) = 50·(10 + 5) = 750 Н

На выпуклом участке:

P₂ = m·(g-a) = 50·(10 - 5) = 250 Н

Answer 2

Calculation of Weight at Each Point

To determine the weight of the skier at the midpoint of each section, we need to consider the centripetal force acting on the skier as they move along the curved path. The centripetal force is responsible for keeping the skier moving in a circular path.

The formula for centripetal force is:

F = (m * v^2) / r

Where: - F is the centripetal force - m is the mass of the skier - v is the velocity of the skier - r is the radius of curvature of the path

Let's calculate the weight of the skier at the midpoint of each section.

Calculation for the Concave Section

In the concave section, the radius of curvature is given as 80 meters. The skier is moving with a velocity of 20 m/s.

Using the formula for centripetal force, we can calculate the weight of the skier at the midpoint of the concave section.

F = (m * v^2) / r

Substituting the given values:

F = (50 kg * (20 m/s)^2) / 80 m

Simplifying the equation:

F = (50 kg * 400 m^2/s^2) / 80 m

F = 250 N

Therefore, the weight of the skier at the midpoint of the concave section is 250 Newtons.

Calculation for the Convex Section

In the convex section, the radius of curvature is also given as 80 meters. The skier is still moving with a velocity of 20 m/s.

Using the same formula for centripetal force, we can calculate the weight of the skier at the midpoint of the convex section.

F = (m * v^2) / r

Substituting the given values:

F = (50 kg * (20 m/s)^2) / 80 m

Simplifying the equation:

F = (50 kg * 400 m^2/s^2) / 80 m

F = 250 N

Therefore, the weight of the skier at the midpoint of the convex section is also 250 Newtons.

Summary

The weight of the skier at the midpoint of both the concave and convex sections is 250 Newtons.

Please note that the calculations assume a constant speed and neglect other forces such as friction.