A block slides down a frictionless plane having an inclination of 13.0°.
If the block starts from rest at the top and the length of this incline is 1.62 m, find the acceleration of the block.
the net force down the plane is mg*Sin13
acceleration= Force/mass
To find the acceleration of the block, we can use the principles of physics related to motion on an inclined plane. This can be done by resolving the gravitational force acting on the block into two components: one perpendicular to the incline and one parallel to the incline.
The weight of the block can be calculated using the formula:
Weight (W) = mass (m) x gravity (g)
Where the mass of the block is not given in the question, so we will ignore it as it cancels out while finding acceleration.
The gravitational force acting parallel to the incline can be calculated as:
Force parallel (Fp) = Weight x sin(angle)
Similarly, the gravitational force acting perpendicular to the incline can be calculated as:
Force perpendicular (Fn) = Weight x cos(angle)
Since the incline is frictionless, the net force acting on the block in the direction parallel to the incline is equal to the force parallel:
Net force (Fnet) = Fp
And the acceleration (a) can be calculated using the equation:
Fnet = m x a
From the above equations, we can relate Fp and a as:
Weight x sin(angle) = m x a
Replacing Weight with mass x gravity:
m x g x sin(angle) = m x a
The mass cancels out:
g x sin(angle) = a
Now we can substitute the known values to find the acceleration.
g = 9.8 m/s^2 (acceleration due to gravity)
angle = 13.0°
a = 9.8 m/s^2 x sin(13.0°)
a = 2.212 m/s^2
Therefore, the acceleration of the block is 2.212 m/s^2.