Question

определите полную механическую энергию стрелы массой 200г, летящей со скоростью 20м/с на высоте 10мс какой высоты упало яблоко, если при ударе о землю оно имело скорость 5 м/с ?

Answer 1

$E=E_k+E_p$
$E_k=\frac{mv^2}{2}$
$E_p=mgh$
$E_k=\frac{0.2*400}{2}=40$Дж
$E_p=0.2*10*10=20$Дж
E=20+40=60Дж

$v=gt$
$t=\frac{v}{g}$
$t=\frac{5}{10}=0.5c$
$h=\frac{gt^2}{2}$
$h=\frac{10*0.25}{2}=1.25$м
 

Answer 2

Calculation of the Total Mechanical Energy of the Arrow

To calculate the total mechanical energy of the arrow, we need to consider both its kinetic energy and potential energy.

The kinetic energy (KE) of an object is given by the formula KE = (1/2)mv^2, where m is the mass of the object and v is its velocity.

Given that the mass of the arrow is 200g (or 0.2kg) and its velocity is 20m/s, we can calculate its kinetic energy as follows:

KE = (1/2) * 0.2kg * (20m/s)^2 = 0.2kg * 200m^2/s^2 = 40 Joules

The potential energy (PE) of an object is given by the formula PE = mgh, where m is the mass of the object, g is the acceleration due to gravity (approximately 9.8m/s^2), and h is the height of the object.

Given that the arrow is at a height of 10m, we can calculate its potential energy as follows:

PE = 0.2kg * 9.8m/s^2 * 10m = 19.6 Joules

Therefore, the total mechanical energy (E) of the arrow is the sum of its kinetic energy and potential energy:

E = KE + PE = 40 Joules + 19.6 Joules = 59.6 Joules

The total mechanical energy of the arrow is 59.6 Joules.

Calculation of the Height at which the Apple Fell

To calculate the height at which the apple fell, we can use the principle of conservation of mechanical energy. According to this principle, the total mechanical energy of an object remains constant as long as no external forces, such as friction or air resistance, are acting on it.

Since the apple is falling and no external forces are mentioned, we can assume that the total mechanical energy of the apple is conserved.

At the initial state, the apple has a total mechanical energy equal to the mechanical energy of the arrow, which is 59.6 Joules.

At the final state, when the apple hits the ground, its potential energy is zero because it is at the ground level. Therefore, the remaining energy is in the form of kinetic energy.

Using the formula KE = (1/2)mv^2, where m is the mass of the apple and v is its velocity, we can calculate the velocity of the apple when it hits the ground.

Given that the mass of the apple is not provided, we cannot calculate the exact height at which the apple fell without this information.