A ball weighing 100 g rolls along a horizontal plane at a speed of 150 cm / s. can he climb up the slope to a height of 2.5 cm.

Data: mw – the mass of the specified ball (mw = 100 g = 0.1 kg); Vpost – the speed of translational motion (Vpost = 150 cm / s = 1.5 m / s); h – slope height (h = 2.5 cm = 0.025 m); will throw. the energy of the rotational motion of the specified ball is not taken into account (Eur = 0.5 * I * ω2).

Const: g – acceleration due to gravity (g ≈ 10 m / s2).

In order for the indicated ball to be able to climb the slope, the inequality must be fulfilled: Ek.post ≥ Ep and 0.5 * msh * Vpost2 ≥ msh * g * h.

Let’s calculate: 0.5 * 0.1 * 1.52 ≥ 0.1 * 10 * 0.025.

0.5 * 0.1 * 1.5 ^ 2 ≥ 0.1 * 10 * 0.025.

0.1125 J ≥ 0.025 J (correct).

Answer: The specified ball will be able to climb the slope.