Question

Тело, брошенное вертикально вверх, через 4 секунды после начала движения упало. Масса тела 200г.Чему равна кинетическая энергия в момент падения?Чему равна потенциальная энергия в верхней точке траектории?

Answer 1

Calculation of Kinetic Energy at the Moment of Impact

To calculate the kinetic energy of the body at the moment of impact, we need to know the velocity of the body just before it hits the ground. Since the body was thrown vertically upwards, it will have a negative velocity when it reaches its highest point and starts falling back down. The time it takes for the body to reach its highest point is equal to the time it takes for it to fall back down and hit the ground.

Given that the body fell back down after 4 seconds, we can assume that it reached its highest point after 2 seconds (half of the total time). We can use this information to calculate the velocity of the body just before it hits the ground.

Using the equation for vertical motion under constant acceleration, we have:

v = u + at

Where: - v is the final velocity (which is 0 m/s at the highest point) - u is the initial velocity (which is the velocity at the start of the motion) - a is the acceleration due to gravity (approximately -9.8 m/s^2) - t is the time taken to reach the highest point (2 seconds)

Rearranging the equation, we can solve for the initial velocity:

u = v - at

Substituting the values, we get:

u = 0 - (-9.8 * 2) = 19.6 m/s

Now that we have the initial velocity, we can calculate the kinetic energy at the moment of impact using the formula:

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

Given that the mass of the body is 200 grams (0.2 kg) and the velocity is 19.6 m/s, we can calculate the kinetic energy:

Kinetic Energy = (1/2) * 0.2 * 19.6^2 = 19.216 Joules

Therefore, the kinetic energy of the body at the moment of impact is approximately 19.216 Joules.

Calculation of Potential Energy at the Highest Point of the Trajectory

At the highest point of the trajectory, the body has zero velocity and is momentarily at rest. The potential energy at this point is equal to the work done to lift the body against gravity from the initial position to the highest point.

The potential energy can be calculated using the formula:

Potential Energy = mass * gravitational acceleration * height

Given that the mass of the body is 200 grams (0.2 kg), the gravitational acceleration is approximately 9.8 m/s^2, and the height is the maximum height reached by the body.

To find the maximum height, we can use the equation for vertical motion under constant acceleration:

h = u*t + (1/2) * a * t^2

Where: - h is the maximum height - u is the initial velocity (which is 19.6 m/s) - a is the acceleration due to gravity (approximately -9.8 m/s^2) - t is the time taken to reach the highest point (2 seconds)

Substituting the values, we get:

h = 19.6 * 2 + (1/2) * (-9.8) * 2^2 = 19.6 meters

Now we can calculate the potential energy:

Potential Energy = 0.2 * 9.8 * 19.6 = 38.384 Joules

Therefore, the potential energy at the highest point of the trajectory is approximately 38.384 Joules.

Please note that the calculations provided are based on the given information and assumptions.