A truck and a car are driving along the highway. The mass of a truck is 4 tons, and the mass of a passenger car is 1 ton

| July 3, 2021 | education

A truck and a car are driving along the highway. The mass of a truck is 4 tons, and the mass of a passenger car is 1 ton. At what speed does the truck travel if the kinetic energy of the cars is the same, and the speed of a passenger car is 100 km / h?

mg = 4 t = 4000 kg.

ml = 1 t = 1000 kg.

Vl = 100 km / h = 27.8 m / s.

Ekl = Ekg.

Vg -?

The kinetic energy of a moving body Ek is determined by the formula: Ek = m * V2 / 2, where m is the mass of the body, V is the speed of movement.

We express the kinetic energy of a passenger car Ecl by the formula: Ecl = ml * Vl2 / 2.

mg = 4 t = 4000 kg.

ml = 1 t = 1000 kg.

Vl = 100 km / h = 27.8 m / s.

Ekl = Ekg.

Vg -?

The kinetic energy of a moving body Ek is determined by the formula: Ek = m * V ^ 2/2, where m is the mass of the body, V is the speed of movement.

We express the kinetic energy of a passenger car Еcl by the formula: Еcl = ml * Vl ^ 2/2.

We express the kinetic energy of a truck Ekg by the formula: Ekg = mg * Vg ^ 2/2.

Since the kinetic energies of cars are equal according to the condition Ecl = Ecg, then ml * Vl ^ 2/2 = mg * Vg ^ 2/2.

Vg ^ 2 = ml * Vl ^ 2 / mg.

Vg = Vl * √ml / √mg.

Vg = 27.8 m / s * √1000 kg / √4000 kg = 13.9 m / s.

Answer: the truck travels at a speed Vg = 13.9 m / s.



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