A block of mass 25.5 kg is released on a ramp with an angle of 31.70 degrees. The coefficient of friction is 0.45. Find the acceleration.
To find the acceleration of the block, we need to consider the forces acting on it.
First, let's find the gravitational force or weight of the block. We can use the formula:
Weight = mass × acceleration due to gravity
The acceleration due to gravity, denoted by "g," is approximately 9.8 m/s².
Weight = 25.5 kg × 9.8 m/s² = 249.9 N (approximately)
Next, let's consider the forces acting on the block along the ramp. We have the weight acting straight downward. We also have the normal force, which is the force exerted by the ramp perpendicular to its surface. The normal force cancels out the vertical component of the weight.
Normal force = weight component perpendicular to the ramp
Normal force = weight × cos(angle of the ramp)
Normal force = 249.9 N × cos(31.70°)
Now, the frictional force can be determined as:
Frictional force = coefficient of friction × normal force
Frictional force = 0.45 × (249.9 N × cos(31.70°))
Since the block is on the verge of sliding down the ramp, the frictional force will be limiting the motion. So the frictional force is equal to the force component parallel to the ramp, which is the force responsible for the acceleration.
Frictional force = mass × acceleration
Equating the frictional force with the mass times acceleration, we have:
0.45 × (249.9 N × cos(31.70°)) = 25.5 kg × acceleration
Simplifying the equation, we can solve for acceleration:
acceleration = (0.45 × (249.9 N × cos(31.70°))) / 25.5 kg
Using this equation, you can calculate the numerical value of the acceleration using a scientific calculator or spreadsheet software.