A 4.52 kg block slides down a smooth, fric-
tionless plane having an inclination of 31◦ .
The acceleration of gravity is 9.8 m/s2 .
Find the acceleration of the block.
Answer in units of m/s2.
Utexas? I hate it too =(
To find the acceleration of the block, we can use the following equation:
acceleration = g * sin(theta)
Where:
g = acceleration due to gravity = 9.8 m/s^2
theta = angle of inclination = 31 degrees
First, we need to convert the angle from degrees to radians, since the trigonometric functions in most programming languages and calculators use radians as the input. To convert degrees to radians, we use the following formula:
radians = degrees * (π / 180)
Let's plug in the values:
theta = 31 degrees
radians = 31 * (π / 180)
Now, we can calculate the acceleration using the equation:
acceleration = 9.8 * sin(radians)
To find the sine of an angle, we can use the sin() function available in most programming languages or calculators.
Let's calculate it step by step:
Step 1: Convert degrees to radians
radians = 31 * (π / 180)
radians ≈ 0.5411
Step 2: Calculate the acceleration
acceleration = 9.8 * sin(radians)
acceleration ≈ 9.8 * sin(0.5411)
acceleration ≈ 9.8 * 0.5145
acceleration ≈ 5.03 m/s^2
Therefore, the acceleration of the block is approximately 5.03 m/s^2.