A force of 44.0 N accelerates a 5.0-kg block at 6.3 m/s2 along a horizontal surface.
(a) How large is the frictional force?
(b) What is the coefficient of friction?
To find the answers to these questions, we need to apply Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration (F = m * a).
Let's break down the steps to find the answers:
(a) How large is the frictional force?
The frictional force can be calculated using the equation: Frictional Force = Applied Force - Net Force on the object.
In this case, the applied force is 44.0 N, and we need to find the net force on the object.
Since the object is being accelerated along the horizontal surface, there are two forces acting on it: the applied force and the frictional force. Therefore, the net force can be calculated as the difference between these two forces.
Net Force = Applied Force - Frictional Force
We can rearrange the equation to solve for the frictional force:
Frictional Force = Applied Force - Net Force
Given:
Applied Force (F) = 44.0 N
Mass of the object (m) = 5.0 kg
Acceleration of the object (a) = 6.3 m/s^2
Using Newton's second law: F = m * a
Net Force = m * a
= 5.0 kg * 6.3 m/s^2
Now, let's substitute the values in the equation to find the frictional force:
Frictional Force = 44.0 N - (5.0 kg * 6.3 m/s^2)
Compute the expression:
Frictional Force = 44.0 N - 31.5 N
= 12.5 N
Therefore, the frictional force acting on the block is 12.5 N.
(b) What is the coefficient of friction?
The coefficient of friction (μ) represents the ratio between the frictional force and the normal force (N) acting on the object.
Frictional Force = μ * N
To find the coefficient of friction, we need to know the normal force. The normal force is the force exerted by the surface perpendicular to the object, which is equal to the weight of the object when on a horizontal surface.
Normal Force (N) = mass of the object * acceleration due to gravity
Given:
Mass of the object (m) = 5.0 kg
Acceleration due to gravity (g) = 9.8 m/s^2 (approximate value)
Substitute the values in the equation to find the normal force:
Normal Force (N) = 5.0 kg * 9.8 m/s^2
Compute the expression:
Normal Force (N) = 49.0 N
Now, substitute the values in the equation to find the coefficient of friction:
Frictional Force = μ * Normal Force
12.5 N = μ * 49.0 N
Rearrange the equation to solve for the coefficient of friction:
μ = Frictional Force / Normal Force
μ = 12.5 N / 49.0 N
Compute the expression:
μ ≈ 0.255
Therefore, the coefficient of friction between the block and the surface is approximately 0.255.