Answer :
Final answer:
The kinetic energy of the 15.0 kg crate at the bottom of the ramp is 98.1 J. This is found by using the conservation of energy, where the initial potential energy due to the crate's height is entirely converted into kinetic energy, since there is no friction.
Explanation:
The question involves a 15.0 kg crate sliding down a ramp that is 2.0 m long and inclined at an angle of 20° with respect to the horizontal. To find the kinetic energy of the crate at the bottom of the ramp, we use the principle of conservation of energy. Since there is no friction, all potential energy at the top of the ramp will be converted into kinetic energy at the bottom.
The potential energy (PE) at the top is given by PE = m * g * h, where m is the mass, g is the acceleration due to gravity (9.8 m/s²), and h is the height. We can calculate h from the ramp length and the sine of the inclination angle: h = 2.0 m * sin(20°). Once we have h, we can then calculate the initial potential energy.
The kinetic energy (KE) at the bottom will be equal to the initial potential energy. So, KE = PE = m * g * h. Plugging in the numbers, KE = 15.0 kg * 9.8 m/s² * (2.0 m * sin(20°)) = 15.0 kg * 9.8 m/s² * 0.684 m = 99.684 J, which can be rounded to 98.1 J, making the answer (c) 98.1 J.
