A wooden block of mass m = 2.3 kg starts from rest on an inclined plane sloped at an angle 26 degrees from the horizontal. The block is originally located 1.9 m from the bottom of the plane. Assume the inclined plane is friction less.
1)What is the magnitude of the component of the block's weight parallel to the incline?
2)What is the magnitude of the component of the block's weight perpendicular to the plane?
3)What is the magnitude of the normal force on the block?
4)What is the net force on the block?
5)What is the acceleration of the block?
6) How long does it take the block to reach the bottom of the incline?
To find the answers to these questions, we can use Newton's laws of motion. Let's go through each question step by step.
1) The magnitude of the component of the block's weight parallel to the incline can be found using the formula:
W_parallel = mg * sin(theta),
where m is the mass of the block (2.3 kg), g is the acceleration due to gravity (9.8 m/s^2), and theta is the angle of the incline (26 degrees).
So, W_parallel = (2.3 kg) * (9.8 m/s^2) * sin(26 degrees).
2) The magnitude of the component of the block's weight perpendicular to the plane can be found using the formula:
W_perpendicular = mg * cos(theta),
where m is the mass of the block (2.3 kg), g is the acceleration due to gravity (9.8 m/s^2), and theta is the angle of the incline (26 degrees).
So, W_perpendicular = (2.3 kg) * (9.8 m/s^2) * cos(26 degrees).
3) The magnitude of the normal force on the block can be found using the formula:
N = mg * cos(theta),
where m is the mass of the block (2.3 kg), g is the acceleration due to gravity (9.8 m/s^2), and theta is the angle of the incline (26 degrees).
So, N = (2.3 kg) * (9.8 m/s^2) * cos(26 degrees).
4) The net force on the block can be found using the formula:
Net force = W_parallel,
since there is no friction in this scenario.
5) The acceleration of the block can be found using the formula:
Acceleration = Net force / mass,
where Net force is the result from the previous step and mass is the mass of the block (2.3 kg).
6) To calculate the time it takes for the block to reach the bottom of the incline, we need to use the formula:
Time = sqrt((2 * distance) / acceleration),
where distance is the initial distance from the bottom of the plane (1.9 m) and acceleration is the result from the previous step.
Now, you have all the formulas and steps to find the answers to the given questions.