Question

Лінійна швидкість точки на ободі колеса дорівнює 7 м/с, а швидкість точки, що лежить ближче до осі обертання на 10 см, дорівнює 5м/с. Визначити радіус колеса

Answer 1

Ответ:

Радиус колеса (R) ≈ 1.11 метра, расстояние до точки ближе к оси (r) ≈ 0.79 метра.

Answer 2

Calculation of the Wheel Radius

To determine the radius of the wheel, we can use the relationship between linear velocity and angular velocity. The linear velocity of a point on the circumference of a wheel is equal to the product of the angular velocity and the radius of the wheel.

Given: - Linear velocity of a point on the wheel's circumference = 7 m/s - Linear velocity of a point closer to the axis of rotation (10 cm from the axis) = 5 m/s

Let's assume the radius of the wheel is R.

The linear velocity of a point on the wheel's circumference is given by the formula:

Linear velocity = Angular velocity × Radius

For the point on the circumference: 7 m/s = Angular velocity × R

For the point closer to the axis: 5 m/s = Angular velocity × (R - 0.1 m)

We can solve these two equations simultaneously to find the value of R.

Subtracting the second equation from the first equation, we get: 7 m/s - 5 m/s = Angular velocity × R - Angular velocity × (R - 0.1 m)

2 m/s = Angular velocity × R - Angular velocity × R + Angular velocity × 0.1 m

2 m/s = Angular velocity × 0.1 m

Angular velocity = 2 m/s / 0.1 m

Angular velocity = 20 rad/s

Substituting the value of angular velocity into the first equation: 7 m/s = 20 rad/s × R

R = 7 m/s / 20 rad/s

R = 0.35 m

Therefore, the radius of the wheel is 0.35 meters.