A person pushes horizontally with a force of 190 N on a 67 kg crate to move it across a level floor. The coefficient of kinetic friction is 0.23. (a) What is the magnitude of the frictional force? (b) What is the magnitude of the crate's acceleration?
pushing force-friction=ma
190-.23*67*9.8=ma
solve for a.
To find the magnitude of the frictional force, we can use the formula:
frictional force = coefficient of friction * normal force
where the normal force is the force exerted on an object perpendicular to the surface it is in contact with. For an object on a level surface, the normal force is equal in magnitude and opposite in direction to the gravitational force acting on the object, which can be calculated as:
normal force = mass * acceleration due to gravity
Given that the coefficient of kinetic friction is 0.23, the mass of the crate is 67 kg, and the acceleration due to gravity is approximately 9.8 m/s^2, we can calculate the normal force:
normal force = 67 kg * 9.8 m/s^2
Now, let's calculate the frictional force:
frictional force = 0.23 * normal force
To find the magnitude of the crate'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:
net force = force applied - frictional force
Since the force applied by the person is in the horizontal direction and the frictional force acts in the opposite direction, the net force can be expressed as:
net force = force applied - frictional force
Finally, we can find the crate's acceleration using the equation:
acceleration = net force / mass
Now, let's substitute the given values and calculate the answers:
(a) To find the magnitude of the frictional force:
normal force = 67 kg * 9.8 m/s^2
frictional force = 0.23 * normal force
(b) To find the magnitude of the crate's acceleration:
net force = force applied - frictional force
acceleration = net force / mass
By following these steps, you can calculate the answers to parts (a) and (b).