向心力公式举例

向心力是作用在沿圆周方向运动的物体上并指向物体运动所围绕的中心的力。

当一个物体绕圆形路线匀速运动时，它会遇到一个向中心加速的向心力。

向心力公式

F_c = m × v²/r

Where,

F_c is the centripetal force

m is mass

v is velocity

r is the radius of the path

公式的推导

运动物体的力是

F = 马

PQ + QS = PS

-v ₁ + v ₂ = Δv

Δv = v ₂ – v ₁

PQS 和 AOB 三角形是相似的。所以，

Δv/AB = v/r

AB = vΔt

Δv/v×Δt = v/r

Δv/Δt = v ² /r

a = v ² /r

现在，

F _c = ma

因此， F _c = m × v ² /r

示例问题

问题 1：一辆 1,250 Kg 的货车以 50.0 m/s 的速度行驶，行驶半径为 200 m。计算向心力。

解决方案

Mass = 1,250 Kg

Radius = 200 m

Velocity = 50.0 m/s

We know that ,

Centripetal force (F_c)= mv²/r

= 1250 × (50)² / 200

= 15,625 N

问题 2：一辆质量为 1000 kg 的汽车以 1.8 km/h 的速度沿圆周运动。如果圆形路径的半径为 10 m，那么作用在汽车上的向心力是多少？

解决方案

Mass of a car, m = 1000 kg

Velocity of a car, v = 1.8 km/h = 0.5 m/s

Radius of a circular path, r = 10 m

Using the equation of centripetal force,

F_c = m v² /r

F_c = [1000 × (0.5)²] /10

F_c = 250 /10

F^c = 25 N

Therefore, the centripetal force acting on a car is 25 N.

问题 3：一个体重 30 公斤的男孩正在享受旋转木马的乐趣。一个男孩坐在旋转木马上，以 2 m/s 的速度沿半径为 6 m 的圆形路径旋转。计算作用在男孩身上的向心力。

解决方案

Mass of a boy, m = 30 kg

Radius of a circular path, r = 6 m

Velocity of a boy, v = 2 m/s

Using the equation of centripetal force,

F_c = mv² / r

F_c = [30 × (2)²] /6

F_c = 120 /6

F_c = 20 N

Therefore, the centripetal force acting on a boy is 20 N.

问题 4：计算作用在 2500 kg 卡车上以 1.2 km/h 的速度在半径为15 m的圆形路径上运动的向心力。

解决方案

Mass of a truck, m = 2500 kg

Velocity of a truck, v = 1.2 km/h = 0.33 m/s

Radius of a circular path, r = 15 m

Using the equation of centripetal force,

F_c = mv²/ r

F_c = [2500 × (0.33)²] /15

F_c = 272.25 /15

F_c = 18.15 N

Therefore, the centripetal force acting on a truck is 18.15 N

问题 5：质量为 140 kg 的运动自行车以 2.5 km/h 的速度沿半径为 25 m 的圆形路径运动，其向心力是多少？

解决方案

Mass of a sports bike, m = 140 kg

Radius of a circular path, r = 25 m

Velocity of a sports bike, v = 2.5 km/h = 0.69 m/s

Using the equation of centripetal force,

F_c = mv²/r

F_c = [140 × (0.69)²] /25

F_c = 66.654 /25

F_c = 2.6 N

Therefore, the centripetal force acting on a sports bike is 2.6 N.