A 16 kg block slides down a frictionless slope which is at angle θ = 20◦. Starting from rest,the time to slide down is t = 1.88 s.The acceleration of gravity is 9.8 m/s2.
To solve this problem, we can use the equations of motion related to objects sliding down an inclined plane.
1. The first step is to decompose the weight of the block along the inclined plane. We need to find the component of the weight that is parallel to the slope and the component perpendicular to the slope.
The weight of the block is given by W = mg, where m is the mass of the block (16 kg) and g is the acceleration due to gravity (9.8 m/s^2). Since the slope is inclined at an angle of 20 degrees, the component of the weight along the slope (parallel to the slope) is W_parallel = W * sin(θ) = mg * sin(20 degrees).
2. Next, we can use Newton's second law of motion (F = ma) along the slope to find the acceleration. The only force acting along the slope is the component of the weight, so we have F = ma_parallel, where a_parallel is the acceleration along the slope. Therefore, ma_parallel = W_parallel, and rearranging the equation, we get a_parallel = W_parallel / m.
3. Now, to find the acceleration along the slope, substitute the values into the equation:
a_parallel = (mg * sin(20 degrees)) / m.
The mass cancels out, giving us a_parallel = g * sin(20 degrees).
4. Now we know the acceleration along the slope, which allows us to find the distance traveled down the slope using the kinematic equation: s = ut + (1/2)at^2, where s is the distance traveled, u is the initial velocity (0 m/s), t is the time taken (1.88s), and a is the acceleration along the slope.
Since the initial velocity is 0 m/s, the equation simplifies to s = (1/2)at^2. Substitute the value of a_parallel into the equation, and calculate the distance (s).
5. Finally, we can calculate the acceleration along the slope using the distance traveled and the time taken. The equation to calculate the average velocity (v_avg) is v_avg = s/t. Rearrange the equation to find acceleration (a_parallel) using a_parallel = 2s/t^2.
By following these steps, you can calculate the acceleration along the slope using the given information.