Question

50 баллов за решение!!! Груз массой 2,1 т поднимается с помощью ворота. Какая сила прилагается к концу рукоятки длиной 50 см, если груз поднимается на высоту 15 см за время, в течение которого рукоятка делает 10 оборотов? Трение не учитывать. Ответ: 98 Н

Answer 1

Изменение потенциальной энергии груза: дельта Eп=Mgh
Работа силы A=F*l=F*2Пи/n
дельта Eп=A
Mgh=F*2пи/n
F=mgh/2пиln
F=2*10^3кг*10м/c^2*0,15м / 2*3,14*0,5м*10=95,54H

Answer 2

Calculation of the Force Applied to the Handle

To calculate the force applied to the handle, we can use the principle of work done. The work done on an object is equal to the force applied multiplied by the distance over which the force is applied. In this case, the work done on the load is equal to the force applied to the handle multiplied by the distance the handle moves.

Given: - Mass of the load (m): 2.1 t (tonnes) = 2100 kg - Height the load is lifted (h): 15 cm = 0.15 m - Length of the handle (L): 50 cm = 0.5 m - Number of revolutions of the handle (n): 10

To find the force applied to the handle, we need to calculate the work done on the load. The work done is given by the formula:

Work (W) = Force (F) × Distance (d)

In this case, the distance is the height the load is lifted, and the force is what we need to find. Rearranging the formula, we get:

Force (F) = Work (W) / Distance (d)

The work done can be calculated by multiplying the force applied to the handle by the distance the handle moves. Since the handle makes 10 revolutions, the distance the handle moves is equal to the circumference of the circle traced by the handle, which is given by:

Distance (d) = 2π × Radius (r)

The radius of the circle traced by the handle is equal to half the length of the handle. Therefore:

Radius (r) = Length of the handle (L) / 2

Substituting the values into the formula, we can calculate the force applied to the handle.

Let's perform the calculations:

1. Calculate the radius of the circle traced by the handle: - Radius (r) = 0.5 m / 2 = 0.25 m

2. Calculate the distance the handle moves: - Distance (d) = 2π × 0.25 m = 1.57 m

3. Calculate the work done on the load: - Work (W) = Force (F) × Distance (d) - Work (W) = m × g × h - m: mass of the load = 2100 kg - g: acceleration due to gravity ≈ 9.8 m/s² - h: height the load is lifted = 0.15 m - Work (W) = 2100 kg × 9.8 m/s² × 0.15 m = 3087 J (Joules)

4. Calculate the force applied to the handle: - Force (F) = Work (W) / Distance (d) - Force (F) = 3087 J / 1.57 m ≈ 1966.24 N

Therefore, the force applied to the handle is approximately 1966.24 N.

Please note that this calculation does not take into account friction or other factors that may affect the actual force required to lift the load.