A metal rod rolls down the slope. The radius of the rod is 1 cm and the mass is
ID: 1911380 • Letter: A
Question
A metal rod rolls down the slope. The radius of the rod is 1 cm and the mass is 100 g. The angle of the slope measured from the base is 30degree and the length of the slope is 2 m, as shown in the figure below. Answer the following questions. Fig. 3 A rod on a slope. Find the total mechanical energy of this rod. Find the potential energy of this rod when it is point P, which is 1 m above the bottom of the slope. Find the total kinetic energy of this rod at the bottom of the slope. When the translational velocity of this rod along the slope is v (m/s), what is the angular (rotational) velocity of the rod? The moment of inertia of a solid rod around its axis (the axis around which the rod rotates as it rolls down the slope) is I = mR2/2. Express the rotational kinetic energy in terms of the mass and translational velocity of the rod. Hint: the rotational kinetic energy is 1/2 Iomega2. Find the translational velocity of this rod at the moment it reaches the bottom of the slope.Explanation / Answer
a) E total = m g h = .1*9.81*2*sin(30)=0.981 J b) PE = m gh = .1*9.81*1*sin(30)=0.4905 J c)KE = E total = 0.981 J d) w = v/r = v/.01= 100 v e) 1/2 I w ^2 = 1/2 (1/2 M R^2) (v/r)^2 = 1/4 M v^2 f) KE = 1/2 mv^2 + 1/4 mv^2 = 0.981 3/4*.1*v^2 = 0.981 v=3.62 m/s