A block slides down a frictionless inclined ramp and experiences no significant air resistance. If the ramp angle is 17.0° above the horizontal and the length of the surface of the ramp is 20.0 m, find
The speed of the block as it reaches the bottom of the ramp, assuming it started sliding from rest at
The top.
A) 19.6 m/s
B) 114 m/s
C) 10.7 m/s
D) 7.57 m/s

Question

Quizplus · Accepted Answer

The speed of the block at the bottom can be found using energy conservation principles. The potential energy at the top is converted into kinetic energy at the bottom. The potential energy at the top is given by $PE = mgh$, where $h$ is the height of the ramp, and $g$ is the acceleration due to gravity (9.8 m/s$^2$). The kinetic energy at the bottom is given by $KE = \frac{1}{2}mv^2$, where $v$ is the velocity we want to find. Since $PE = KE$, we can solve for $v$.First, find the height $h$ using trigonometry: $h = L \sin(\theta)$, where $L$ is the length of the ramp (20.0 m) and $\theta$ is the angle (17.0°). So, $h = 20.0 \sin(17.0°) \approx 5.79$ m.Then, set $mgh = \frac{1}{2}mv^2$, and solve for $v$: $v = \sqrt{2gh} = \sqrt{2 \cdot 9.8 \cdot 5.79} \approx 10.7$ m/s.

A Block Slides Down a Frictionless Inclined Ramp and Experiences