Question

You apply a 50 N rightward force to a 4 kg cart to accelerate it across a horizontal surface at a rate of 3.28m/s2.

Answer 1

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/s²

We need to find the force of friction acting upon the cart

According to Newton's law

→ ∑ F in direction of motion = mass × acceleration

We have two horizontal forces acting on the cart

→ The force applied = 50 N

→ The force of friction $F_{x}$ in opposite direction of motion

→ The mass = 4 kg

→ Acceleration = 3.28 m/s²

Substitute these values in the rule

→ 50 - $F_{x}$ = 4 × 3.28

→ 50 -  $F_{x}$ = 13.12

Add  $F_{x}$ for both sides

→ 50 =  $F_{x}$ + 13.12

Subtract 13.12 from both sides

→ 36.88 =  $F_{x}$

The force of friction is 36.88 N

→ The force of friction = μ R

where R is the normal reaction and μ is the coefficient of friction

→ R = mg

where m is the mass of the cart and g is the acceleration of gravity

→ $F_{x}$ = μ mg

→ g = 9.8 m/s² , m = 4 kg , $F_{x}$ = 36.88 N

Substitute these values in the rule

→ 36.88 = μ (4)(9.8)

→ 36.88 = 39.2 μ

Divide both sides by 39.2

→ μ = 0.94

The coefficient of friction is 0.94