Question

Вал,диаметром 40 см с насаженным на него шкивом диаметром 2 м вращается равномерно. Во сколько раз линейная скорость и центростремительное ускорение на ободе шкива больше, чем на внешней границе вала?

Answer 1

R1=D1/2=40см/2=20см=0.2 м

R2=D2/2=2м/2=1м

w - угловая скорость ОДИНАКОВА для вала и шкива

линейная скорость v=wR

вал

v1=w*R1

шкив

v2=w*R2

v2/v1=w*R2 / w*R1 = R2/R1=1/0.2 = 5 раз

центростремительное ускорение a=v^2/R=w^2*R

вал

a1=w^2*R1

шкив

a2=w^2*R2

a2/a1 = w^2*R2 /w^2*R1 = R2/R1=1/0.2 = 5 раз

Answer 2

Calculating Linear Speed and Centripetal Acceleration

To calculate the linear speed and centripetal acceleration at the edge of the pulley and the outer boundary of the shaft, we can use the following formulas:

1. Linear Speed (v): The linear speed at the edge of the pulley can be calculated using the formula: - v = ωr, where ω is the angular velocity and r is the radius of the pulley.

2. Centripetal Acceleration (a): The centripetal acceleration at the edge of the pulley can be calculated using the formula: - a = ω^2r, where ω is the angular velocity and r is the radius of the pulley.

Given: - Diameter of the pulley (D) = 40 cm - Diameter of the shaft (d) = 2 m

Calculating Linear Speed and Centripetal Acceleration at the Edge of the Pulley

First, we need to calculate the radius of the pulley (r) using the given diameter (D).

Radius of the pulley (r): - The radius of the pulley can be calculated as half of the diameter: - r = D/2

Substitute the given value of the diameter: - r = 40 cm / 2 = 20 cm = 0.2 m

Now, we can calculate the linear speed (v) and centripetal acceleration (a) at the edge of the pulley using the above formulas.

Linear Speed (v): - v = ωr

Centripetal Acceleration (a): - a = ω^2r

Calculating Linear Speed and Centripetal Acceleration at the Outer Boundary of the Shaft

For the outer boundary of the shaft, we can use the same formulas to calculate the linear speed and centripetal acceleration.

Given: - Diameter of the shaft (d) = 2 m - Radius of the shaft (R) = d/2

Radius of the shaft (R): - The radius of the shaft can be calculated as half of the diameter: - R = d/2

Substitute the given value of the diameter: - R = 2 m / 2 = 1 m

Now, we can calculate the linear speed (V) and centripetal acceleration (A) at the outer boundary of the shaft using the same formulas: - V = ΩR - A = Ω^2R

Comparing Linear Speed and Centripetal Acceleration

To compare the linear speed and centripetal acceleration at the edge of the pulley and the outer boundary of the shaft, we can calculate the ratios of the values.

Ratio of Linear Speed: - v/V = (ωr)/(ΩR)

Ratio of Centripetal Acceleration: - a/A = (ω^2r)/(Ω^2R)

By calculating these ratios, we can determine in how many times the linear speed and centripetal acceleration at the edge of the pulley are greater than those at the outer boundary of the shaft.