A 2-kg thin hoop with a 50-cm radius rolls down a 30-degree slope without slipping.If the hoop starts at rest at the top of the slope,what is its translational velocity after it rolls 10 m along the slope?
A)14.5 m/s
B)3.22 m/s
C)7.00 m/s
D)44.8 m/s
E)20.5 m/s

Question

A 2-kg thin hoop with a 50-cm radius rolls down a 30-degree slope without slipping.If the hoop starts at rest at the top of the slope,what is its translational velocity after it rolls 10 m along the slope? 
A)14.5 m/s 
B)3.22 m/s 
C)7.00 m/s 
D)44.8 m/s 
E)20.5 m/s

Quizplus · Accepted Answer

We can use the conservation of energy principle to solve this problem:

Initial energy = Potential energy at the top of the slope
Final energy = Kinetic energy + Potential energy at the bottom of the slope

Initial energy = 2kg * 9.81m/s^2 * 0.5m = 9.81J
Final energy = 0.5 * 2kg * V^2 + 2kg * 9.81m/s^2 * (0.5m - 10m*sin(30)) = 0.5 * 2kg * V^2 + 49.05 J

Since there is no slipping, the hoop's velocity can be determined from the relationship between the linear velocity and the angular velocity:

V = ω * R
ω = V / R

The hoop's translational velocity after rolling 10m along the slope is 7.00 m/s, which is answer choice C.

A 2-Kg Thin Hoop with a 50-Cm Radius Rolls Down