Question

Мальчик на санках скатывается с холма высотой 7м.Общая масса мальчика в санках составляет 50 кг.Если у подножья холма мальчик достиг скорости 10м/с,то какова работа силы трения (в Дж)

Answer 1

Дано h=7м    m=50 кг       V=10 м/с    А- ?

m*g*h+А= m*V^2/2

А= m*V^2/2 - m*g*h=50*100/2 - 50*10*7=2500-3500=-1000 Дж

Ответ A=-1000 Дж ( работа силы трения отрицательная)

Answer 2

Calculation of the Work Done by Friction

To calculate the work done by friction as the boy slides down the hill on his sled, we need to consider the change in kinetic energy. The work done by friction can be calculated using the formula:

Work = Change in Kinetic Energy

The initial kinetic energy of the boy at the top of the hill is zero because he is at rest. The final kinetic energy of the boy at the bottom of the hill can be calculated using the formula:

Kinetic Energy = (1/2) * mass * velocity^2

Given: - Height of the hill = 7m - Total mass of the boy and sled = 50kg - Initial velocity at the base of the hill = 10m/s

Let's calculate the final velocity of the boy at the bottom of the hill using the principle of conservation of energy. The potential energy at the top of the hill is converted into kinetic energy at the bottom of the hill.

Calculation of Final Velocity

The potential energy at the top of the hill is given by:

Potential Energy = mass * gravity * height

where: - mass = 50kg (total mass of the boy and sled) - gravity = 9.8m/s^2 (acceleration due to gravity) - height = 7m (height of the hill)

Substituting the values, we get:

Potential Energy = 50kg * 9.8m/s^2 * 7m = 3430 Joules

Since the potential energy is converted into kinetic energy at the bottom of the hill, we can equate the two:

Potential Energy = Kinetic Energy

3430 Joules = (1/2) * mass * velocity^2

Substituting the mass and solving for velocity, we get:

velocity^2 = (3430 Joules * 2) / 50kg

velocity^2 = 137.2 m^2/s^2

Taking the square root of both sides, we find:

velocity = √137.2 m/s ≈ 11.71 m/s

Therefore, the final velocity of the boy at the bottom of the hill is approximately 11.71 m/s.

Calculation of Work Done by Friction

Now that we have the final velocity, we can calculate the work done by friction. The work done by friction is equal to the change in kinetic energy:

Work = (1/2) * mass * (final velocity^2 - initial velocity^2)

Substituting the values, we get:

Work = (1/2) * 50kg * ((11.71 m/s)^2 - (10 m/s)^2)

Work = (1/2) * 50kg * (137.2 m^2/s^2 - 100 m^2/s^2)

Work = (1/2) * 50kg * 37.2 m^2/s^2

Work = 930 Joules

Therefore, the work done by the force of friction is 930 Joules.