На движущееся тело по горизонтальной плоскости тело на протяжении пути длиной 15 метров действует сила трения 100 Ньютонов. На сколько изменилась механическая энергия тела?
To calculate the change in mechanical energy of an object moving along a horizontal surface, we can use the equation: ΔE = W - Fd, where ΔE is the change in mechanical energy, W is the work done on the object, F is the force acting on the object, and d is the distance traveled by the object. In this case, we are given the force of friction (F) as 100 N and the distance (d) as 15 meters.Thus, the calculation would be: ΔE = W - (100 N)(15 m)
Since the object is moving along a horizontal surface, we can assume that the work done is equal to the change in kinetic energy (K), which is calculated as K = ½ mv^2, where m is the mass of the object and v is its velocity.
Therefore, we can rewrite the equation as follows: ΔE = ½ mv^2 - (100 N)(15 m)
To calculate the final velocity (v) of the object, we can use the equation: v = √(2K/m).
Using the given information, we can determine the mass of the object by rearranging the equation to m = 2K/v^2 and plugging in the values (K = 100 N, v = 15 m/s). This gives us a mass of approximately 4.44 kilograms.
Plugging this mass value into our original equation, we get: ΔE = ½ (4.44 kg)(15 m/s)^2 - (100 N)(15 m)
Simplifying, we get ΔE = 333 J - 1500 J
Therefore, the change in mechanical energy is -1167 J (since the object is losing energy due to the work of friction).
So, to answer the question, the mechanical energy of the object has decreased by 1167 joules along its 15-meter journey.
