Acceleration Down an Inclined Plane Problem

[nycjay222]

The block shown in figure below lies on a smooth plane tilted at an angle theta = 23.7o to the horizontal.

A) Determine the acceleration of the block as it slides down the plane. Ignore friction.

B) If the block starts from rest x = 9.87 m up the plane from its base, what will be the block's speed when it reaches the bottom of the incline?

 

[rock.freak667]

The block shown in figure below lies on a smooth plane tilted at an angle theta = 23.7o to the horizontal.

A) Determine the acceleration of the block as it slides down the plane. Ignore friction.

B) If the block starts from rest x = 9.87 m up the plane from its base, what will be the block's speed when it reaches the bottom of the incline?

Show some effort. Start with the free body diagram.

 

[tomcue]

A) To determine the acceleration of the block, we can use the formula a = gsin(theta), where g is the acceleration due to gravity (9.8 m/s^2) and theta is the angle of inclination (23.7 degrees). Plugging in the values, we get a = (9.8 m/s^2)(sin 23.7) = 3.94 m/s^2. Therefore, the block will have an acceleration of 3.94 m/s^2 as it slides down the plane.

B) To calculate the speed of the block when it reaches the bottom of the incline, we can use the formula v^2 = u^2 + 2as, where v is the final velocity, u is the initial velocity (which is 0 m/s since the block starts from rest), a is the acceleration (3.94 m/s^2), and s is the distance traveled (9.87 m). Plugging in the values, we get v^2 = (0 m/s)^2 + 2(3.94 m/s^2)(9.87 m) = 77.59 m^2/s^2. Taking the square root, we get v = 8.81 m/s. Therefore, the block will have a speed of 8.81 m/s when it reaches the bottom of the incline.