A person pushes horizontally with a force of 170 N on a 68 kg crate to move it across a level floor. The coefficient of kinetic friction is 0.22. (a) What is the magnitude of the frictional force? (b) What is the magnitude of the crate's acceleration?
Wc = mg = 68kg * 9.8N/kg = 666.4N. =
Weight of crate.
Fc = (666.4N,0deg.).
Fp = Fh = 666.4sin(0) = 0 Newtons. =
Force parallel to floor = Hor. cmp.
Fv = ver. = 666.4cos(0) = 666.4N. =
Force perpendicular to floor.
a. Ff = u*Fv = 0.22 * 666.4 = 147N. = Force of friction.
b. Fn = Fap - Ff = 170 - 147 = 23N.
Fn = ma,
a = Fn/m = 23 / 68 = 0.39m/s^2.
Correction: a = 23 / 68 = 0.34m/s^2.
To find the magnitude of the frictional force, we need to multiply the coefficient of kinetic friction by the normal force. The normal force can be determined by multiplying the mass of the crate by the acceleration due to gravity.
(a) The formula to calculate the frictional force is given by:
Frictional force = coefficient of kinetic friction * normal force
The normal force is equal to the weight of the crate:
Normal force = mass * acceleration due to gravity
Acceleration due to gravity is approximately 9.8 m/s². So, substituting the given values into the equation:
Normal force = 68 kg * 9.8 m/s²
Now we can calculate the frictional force:
Frictional force = 0.22 * (68 kg * 9.8 m/s²)
(b) To find the magnitude of the crate's acceleration, we need to use Newton's second law of motion, which states that the net force acting on an object is equal to its mass multiplied by its acceleration. In this case, the force pushing the crate horizontally is the net force, as there is no vertical force.
The formula is given by:
Net force = mass * acceleration
The pushing force is equal to the net force:
Net force = 170 N
Now we can calculate the acceleration:
170 N = 68 kg * acceleration
To solve for the acceleration, divide both sides of the equation by 68 kg.
We can use a calculator to find the numerical values for both the frictional force and the crate's acceleration.