Question

Мальчик на санях спускается с горки высотой 20 м. Чему была равна скорость санеё в конце спуска,если бы механическая энергия во время спуска сохранялась? сравните эту скорость со скоростью автомобиля,движущегося со скоростью 60 км/ч.

Answer 1

приравниваем 2 энергии Eк=Eп

mgh=mv^2\2 массы сокращаем получим

gh=v^2\2

отсюда выражаем скорость

v=корень(2gh)=корень(2*10*20)=20м\с

 

скорость авто 16.6м\с,а скорость саней 20 м\с следовательно скорость саней больше на 3.4 м\с

Answer 2

Calculation of the Speed of the Sled at the End of the Descent

To calculate the speed of the sled at the end of the descent, we can use the principle of conservation of mechanical energy. According to this principle, the total mechanical energy of a system remains constant as long as no external forces are acting on it.

In this case, the mechanical energy of the system consists of the potential energy at the top of the hill and the kinetic energy at the bottom of the hill. The potential energy is given by the formula:

Potential Energy = mass * gravity * height

where: - mass is the mass of the sled, - gravity is the acceleration due to gravity (approximately 9.8 m/s^2), - height is the height of the hill (20 m).

The kinetic energy is given by the formula:

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

where: - mass is the mass of the sled, - velocity is the velocity of the sled at the end of the descent.

Since the mechanical energy is conserved, we can equate the potential energy to the kinetic energy:

Potential Energy = Kinetic Energy

Using the formulas above, we can solve for the velocity of the sled at the end of the descent.

Let's calculate it step by step.

1. Calculate the potential energy: - mass = unknown (not provided in the question) - gravity = 9.8 m/s^2 - height = 20 m

Potential Energy = mass * gravity * height

2. Calculate the kinetic energy: - mass = unknown (not provided in the question) - velocity = unknown (to be calculated)

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

3. Equate the potential energy to the kinetic energy and solve for velocity:

Potential Energy = Kinetic Energy

Substitute the formulas for potential energy and kinetic energy:

mass * gravity * height = (1/2) * mass * velocity^2

Simplify the equation:

gravity * height = (1/2) * velocity^2

Solve for velocity:

velocity = sqrt(2 * gravity * height)

Substitute the values of gravity (9.8 m/s^2) and height (20 m) into the equation and calculate the velocity.

velocity = sqrt(2 * 9.8 * 20)

velocity ≈ 19.8 m/s

Therefore, the speed of the sled at the end of the descent, assuming the conservation of mechanical energy, is approximately 19.8 m/s.

Comparison with the Speed of a Car

The question also asks to compare this speed with the speed of a car moving at 60 km/h.

To make a comparison, we need to convert the speed of the car from kilometers per hour to meters per second.

1 kilometer = 1000 meters 1 hour = 3600 seconds

Therefore, to convert 60 km/h to m/s:

60 km/h = (60 * 1000) / 3600 m/s

60 km/h ≈ 16.7 m/s

Comparing the speed of the sled at the end of the descent (approximately 19.8 m/s) with the speed of the car (approximately 16.7 m/s), we can conclude that the sled is moving faster than the car.