Question

Тело массой 10 кг свободно падает с высоты 20 м из состояния покоя. На какой высоте кинетическая энергия в три раза больше потенциальной

Answer 1

Дано  m=10 кг    h1=20 м     Eк2=3*Ep2

h2- ?

m*g*h1=Eк2+Ep2

m*g*h1=4*Ep2
m*g*h1=4*m*g*h2
h2=h1/4=20/4=5 м

Answer 2

Calculation of Kinetic and Potential Energy

To determine the height at which the kinetic energy is three times greater than the potential energy, we need to calculate the kinetic and potential energy at different heights.

Let's assume that the potential energy at height h is given by PE = mgh, where m is the mass of the object, g is the acceleration due to gravity, and h is the height.

The kinetic energy at any height can be calculated using the formula KE = (1/2)mv^2, where m is the mass of the object and v is its velocity.

Given: - Mass of the object (m) = 10 kg - Height (h) = 20 m

We need to find the height at which the kinetic energy is three times greater than the potential energy.

Calculation Steps:

1. Calculate the potential energy (PE) at height h: - PE = mgh

2. Calculate the kinetic energy (KE) at height h: - KE = (1/2)mv^2

3. Set up the equation to find the height at which KE is three times greater than PE: - KE = 3 * PE

4. Solve the equation for height (h).

Let's calculate the height at which the kinetic energy is three times greater than the potential energy.

Calculation:

1. Calculate the potential energy (PE) at height h: - PE = mgh - PE = 10 kg * 9.8 m/s^2 * 20 m - PE = 1960 J

2. Calculate the kinetic energy (KE) at height h: - KE = (1/2)mv^2 - Since the object is freely falling, its initial velocity is 0 m/s. - KE = (1/2) * 10 kg * (0 m/s)^2 - KE = 0 J

3. Set up the equation to find the height at which KE is three times greater than PE: - KE = 3 * PE - 0 J = 3 * 1960 J

4. Solve the equation for height (h): - Since the equation has no solution, there is no height at which the kinetic energy is three times greater than the potential energy.

Based on the calculations, there is no height at which the kinetic energy is three times greater than the potential energy for an object with a mass of 10 kg freely falling from a height of 20 m.