Answer:
The force of friction is 36.88 N
The coefficient of friction is 0.94
Explanation:
Lets explain how to solve the problem
The force applied is 50 N rightward
The mass of the cart is 4 kg
The applied force makes the cart accelerate across a horizontal surface
The acceleration is 3.28 m/sΒ²
We need to find the force of friction acting upon the cart
According to Newton's law
β β F in direction of motion = mass Γ acceleration
We have two horizontal forces acting on the cart
β The force applied = 50 N
β The force of friction [tex]F_{x}[/tex] in opposite direction of motion
β The mass = 4 kg
β Acceleration = 3.28 m/sΒ²
Substitute these values in the rule
β 50 - [tex]F_{x}[/tex] = 4 Γ 3.28
β 50 - Β [tex]F_{x}[/tex] = 13.12
Add Β [tex]F_{x}[/tex] for both sides
β 50 = Β [tex]F_{x}[/tex] + 13.12
Subtract 13.12 from both sides
β 36.88 = Β [tex]F_{x}[/tex]
The force of friction is 36.88 N
β The force of friction = ΞΌ R
where R is the normal reaction and ΞΌ is the coefficient of friction
β R = mg
where m is the mass of the cart and g is the acceleration of gravity
β [tex]F_{x}[/tex] = ΞΌ mg
β g = 9.8 m/sΒ² , m = 4 kg , [tex]F_{x}[/tex] = 36.88 N
Substitute these values in the rule
β 36.88 = ΞΌ (4)(9.8)
β 36.88 = 39.2 ΞΌ
Divide both sides by 39.2
β ΞΌ = 0.94
The coefficient of friction is 0.94
