A 45kg block slides down an incline that is angled at 41 degrees. If the coefficient of kinetic friction between the block and the incline is 0.45 what is the block's acceleration?
To determine the block's acceleration, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration.
The first step is to calculate the force of gravity acting on the block. This force (also known as weight) is given by the formula:
Force of Gravity = mass * acceleration due to gravity
where the mass is 45 kg and the acceleration due to gravity is approximately 9.8 m/s^2.
Force of Gravity = 45 kg * 9.8 m/s^2
Force of Gravity = 441 N
Next, we need to determine the force of friction acting on the block as it slides down the incline. The force of friction can be calculated using the formula:
Force of Friction = coefficient of friction * normal force
The normal force is the perpendicular force exerted by the incline on the block, which is equal to the force of gravity in this case.
Normal Force = Force of Gravity
Normal Force = 441 N
Now, we can calculate the force of friction:
Force of Friction = 0.45 * 441 N
Force of Friction = 198.45 N
Since the block is sliding down the incline, the force of friction opposes its motion. Therefore, the net force acting on the block is the difference between the force of gravity and the force of friction:
Net Force = Force of Gravity - Force of Friction
Net Force = 441 N - 198.45 N
Net Force = 242.55 N
Finally, we can calculate the block's acceleration using Newton's second law:
Net Force = mass * acceleration
242.55 N = 45 kg * acceleration
Dividing both sides of the equation by 45 kg, we find:
acceleration = 242.55 N / 45 kg
acceleration ≈ 5.39 m/s^2
Therefore, the block's acceleration is approximately 5.39 m/s^2.