A 4-kg mass is launched with zero initial velocity on a frictionless circular tr
ID: 2257839 • Letter: A
Question
A 4-kg mass is launched with zero initial velocity on a frictionless circular track. The speed of the mass at point 1 is 20 m/s. The mass than travels along a rough horizontal surface between points 1 and 2 (L=4 m, uk=0.3). It then travels up a frictionless slope.
a. (5 pts) Given the speed at point 1 find the height H from which the mass was released
b. (5 pts) Find the acceleration of the system as it travels from point 1 to 2
c. (5 pts) Find the kinetic energy of the system at point 2
d. (5 pts) Find the maximum height reached by the mass up the slope
e. (5 pts) Find the distance up the slope corresponding to the maximum height
Please show how to work this problem step by step.
Explanation / Answer
a. Energhy conservation:
mgH = 0.5*mv^2
=> H = v^2 /2g = 20.41 m
b. a = ug = 0.3*9.8 = 2.94 m/s^2
c. Friction force = ma = 11.76
Work done by friction = F*L = 47.04 J
Final KE = 0.5mv^2 - F*L = 752.96 J
d. Energy conservation :
mgh = KE Final
=> h = (752.96)/(4*9.8) = 19.21 m
e. L'Sin30 = h
=> L' = 38.42 m