A hoop with a mass of 2.75 kg is rolling without slipping along a horizontal surface with a speed of 4.5 m/s when it starts down a ramp that makes an angle of 2 $25 ^ { \circ }$ below the horizontal. What is the
Forward speed of the hoop after it has rolled 3.0 m down as measured along the surface of the
Ramp?
A) 5.7 m/s
B) 6.3 m/s
C) 4.9 m/s
D) 8.0 m/s
E) 5.2 m/s

Question

Quizplus · Accepted Answer

Explanation:The correct answer is A.The hoop's initial kinetic energy is:$$K_i = \frac{1}{2}mv^2 = \frac{1}{2}(2.75 	ext{ kg})(4.5 	ext{ m/s})^2 = 29.6 	ext{ J}$$The hoop's potential energy after rolling 3.0 m down the ramp is:$$U_f = mgh = (2.75 	ext{ kg})(9.8 	ext{ m/s}^2)(3.0 	ext{ m}) = 81.2 	ext{ J}$$The hoop's kinetic energy after rolling 3.0 m down the ramp is:$$K_f = U_i - U_f = 29.6 	ext{ J} - 81.2 	ext{ J} = -51.6 	ext{ J}$$The negative sign indicates that the hoop is losing kinetic energy as it rolls down the ramp.The hoop's speed after rolling 3.0 m down the ramp is:$$v_f = \sqrt{\frac{2K_f}{m}} = \sqrt{\frac{2(-51.6 	ext{ J})}{2.75 	ext{ kg}}} = 5.7 	ext{ m/s}$$

A Hoop with a Mass of 2 25∘25 ^ { \circ }25∘

A Hoop with a Mass of 2 $25 ^ { \circ }$