Question

По склону горы длиной 500 м и высотой 10 м скатываются сан­ ки массой 60 кг. Определите среднюю силу сопротивления при скатывании санок, если у основания горы они имели скорость 8 мjс. Начальная скорость санок равна нулю.

Answer 1

M=60 кг
h=10 м
v=8 м/с
l=500 м
F-?

Закон Сохранения Энергии:
m*g*h=m*v²/2+F*l  (часть энергии переходит в работу)

Выражаем F:
F=m*(g*h-v²/2)/l=7,92 Н

Ответ: 7,92 Н

Answer 2

Calculation of Average Resistance Force

To determine the average resistance force during the descent of the sled down the slope, we can use the principle of conservation of mechanical energy. The initial potential energy of the sled is converted into kinetic energy as it slides down the slope. The work done by the resistance force is equal to the change in mechanical energy.

The potential energy of the sled at the top of the slope can be calculated using the formula:

PE = mgh

Where: - m is the mass of the sled (60 kg) - g is the acceleration due to gravity (approximately 9.8 m/s^2) - h is the height of the slope (10 m)

Using the given values, we can calculate the potential energy at the top of the slope:

PE = (60 kg) * (9.8 m/s^2) * (10 m) = 58800 J

Since the initial velocity of the sled is zero, the initial kinetic energy is also zero.

At the bottom of the slope, the potential energy is zero, and all the initial potential energy is converted into kinetic energy. The kinetic energy can be calculated using the formula:

KE = (1/2) * mv^2

Where: - m is the mass of the sled (60 kg) - v is the velocity of the sled at the bottom of the slope (8 m/s)

Using the given values, we can calculate the kinetic energy at the bottom of the slope:

KE = (1/2) * (60 kg) * (8 m/s)^2 = 1920 J

The work done by the resistance force is equal to the change in mechanical energy:

Work = KE - PE

Work = 1920 J - 58800 J = -56880 J

Since the work done by the resistance force is negative, it indicates that the resistance force is acting in the opposite direction to the motion of the sled.

To calculate the average resistance force, we can divide the work done by the sled by the distance traveled. The distance traveled can be calculated using the formula:

Distance = 500 m

Therefore, the average resistance force can be calculated as follows:

Average Resistance Force = Work / Distance

Average Resistance Force = -56880 J / 500 m = -113.76 N

The negative sign indicates that the average resistance force is acting in the opposite direction to the motion of the sled.

Therefore, the average resistance force during the descent of the sled down the slope is approximately -113.76 N.