A force of 50 N accelerates a 5.0 kg block at 6.0 m/s2 along a horizontal surface.
(a) What is the frictional force acting on the block?
(b) What is the coefficient of friction?
To find the answers to these questions, we need to use Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and acceleration.
(a) To find the frictional force, we need to identify the net force acting on the block. The net force is the difference between the applied force and the frictional force.
Step 1: Calculate the net force.
Given:
Applied force (F) = 50 N (since it is mentioned that a force of 50 N is acting on the block)
Mass of the block (m) = 5.0 kg
Acceleration (a) = 6.0 m/s^2
Using Newton's second law of motion:
Net force (F_net) = m * a
Substituting the given values:
F_net = 5.0 kg * 6.0 m/s^2
F_net = 30 N
Step 2: Calculate the frictional force.
Since the net force is the difference between the applied force and the frictional force, we can rearrange the equation to find the frictional force.
Frictional force (F_friction) = F - F_net
Substituting the known values:
F_friction = 50 N - 30 N
F_friction = 20 N
Therefore, the frictional force acting on the block is 20 N.
(b) To find the coefficient of friction, we need to use the formula:
Frictional force (F_friction) = coefficient of friction (μ) * Normal force (F_normal)
The normal force is the force exerted by a surface to support the weight of an object resting on it. On a horizontal surface, the normal force is equal in magnitude but opposite in direction to the weight of the object.
Step 1: Calculate the normal force.
The normal force is equal to the weight of the object when it is at rest on a horizontal surface.
Weight (W) = mass (m) * gravitational acceleration (g)
W = 5.0 kg * 9.8 m/s^2 (approximate value of the acceleration due to gravity)
W = 49 N (approximate value)
Since the block is not accelerating vertically but horizontally, the normal force is equal in magnitude to the weight of the block.
F_normal = 49 N
Step 2: Calculate the coefficient of friction.
We need to rearrange the formula to solve for the coefficient of friction:
μ = F_friction / F_normal
Substitute the known values:
μ = 20 N / 49 N
Calculate the numerical value:
μ ≈ 0.408
Therefore, the coefficient of friction is approximately 0.408.
(a)ma=F-F(fr)
F(fr)= F-ma
(b) F(fr) =μmg
μ=F(fr)/mg