Question

масса самосвала в 18 раз больше массы легкового автомобиля, а скорость самосвала в 6 раз меньше скорости легкового автомобиля. Сравнить импульсы и кинетические энергии этих автомобилей.

Answer 1

p=mv; e=mv^2/2 
M, V, E, P - самосвал 
m, v, e, p - легковая
M=18m; V=v/6 
E/e=(MV^2/2)/(mv^2/2)=(18mv^2/(2*36))/(mv^2/2)=(18mv^2/36)/(mv^2)=18/36=0,5 
P/p=MV/(mv)=18mv/(6mv)=18/6=3 
Энергия самосвала в 2 раза меньше, но импульс в 3 раза больше.

Answer 2

Comparison of Mass and Speed

To compare the impulses and kinetic energies of the dump truck and the car, we need to consider their respective masses and speeds.

According to the information provided, the mass of the dump truck is 18 times greater than the mass of the car, while the speed of the dump truck is 6 times slower than the speed of the car.

Impulse Comparison

Impulse is defined as the change in momentum of an object. It can be calculated by multiplying the mass of an object by its change in velocity.

Let's assume the mass of the car is represented by m and the mass of the dump truck is represented by M. The initial velocity of the car is represented by v and the initial velocity of the dump truck is represented by V.

The impulse of the car can be calculated as m * v, and the impulse of the dump truck can be calculated as M * V.

Since the mass of the dump truck is 18 times greater than the mass of the car, we can write M = 18m.

Similarly, since the speed of the dump truck is 6 times slower than the speed of the car, we can write V = (1/6)v.

Substituting these values into the equations for impulse, we get:

Impulse of the car: m * v Impulse of the dump truck: (18m) * (1/6)v

Simplifying the equations, we find:

Impulse of the car: mv Impulse of the dump truck: 3mv

Therefore, the impulse of the dump truck is 3 times greater than the impulse of the car.

Kinetic Energy Comparison

Kinetic energy is defined as the energy possessed by an object due to its motion. It can be calculated using the equation: KE = (1/2) * mass * velocity^2.

Let's calculate the kinetic energy of the car and the dump truck using their respective masses and speeds.

The kinetic energy of the car can be calculated as (1/2) * m * v^2, and the kinetic energy of the dump truck can be calculated as (1/2) * M * V^2.

Substituting the values we derived earlier, we get:

Kinetic energy of the car: (1/2) * m * v^2 Kinetic energy of the dump truck: (1/2) * (18m) * ((1/6)v)^2

Simplifying the equations, we find:

Kinetic energy of the car: (1/2) * m * v^2 Kinetic energy of the dump truck: (1/2) * (3/36) * m * v^2

Simplifying further, we find:

Kinetic energy of the car: (1/2) * m * v^2 Kinetic energy of the dump truck: (1/24) * m * v^2

Therefore, the kinetic energy of the dump truck is 1/24 times the kinetic energy of the car.

Summary

In summary, the impulse of the dump truck is 3 times greater than the impulse of the car, while the kinetic energy of the dump truck is 1/24 times the kinetic energy of the car.

Please note that these calculations are based on the information provided and assume ideal conditions.