Friction force equations?

Question

1. What is the horizontal force necessary to drag a brick that weighs 60 N on a wooden table (µk= 0.7) at constant velocity?
1.1 if you pull on the brick horizontally with a force of 80 N, what is its acceleration?

Answer 1

1)
The key here is the phrase "at constant velocity", meaning that the block is not accelerating and the net force is zero. When the net force is zero, the force of friction and the applied force are equal in magnitude and act in opposite directions to cancel each other out.
The force is kinetic friction is equal to,
F_f = mu * F_n
Where F_f is the frictional force, mu is the coefficient of kinetic friction (µk= 0.7), and F_n is the normal force (equal to the weight if the block is on a horizontal surface). You can see that the kinetic frictional force is independent of the block's velocity or other applied forces; it is constant as long as the block is moving.
Plugging into the equation, we find the frictional force to be,
F_f = 60 Newtons * 0.7 = 42 Newtons
In order to cancel the frictional force and allow the block to move at a constant velocity, a force of equal magnitude must be applied in the direction of motion, thus a force of 42 Newtons is needed.

1.1)
We calculated earlier that in order or the block to move at a constant velocity, a 42 Newton force was needed. Anything less than 42 Newtons and the block would slow to a stop. Anything more than 42 Newtons and the block would begin the speed up.
In this part of the question, an 80 Newton force is applied...greater than the 42 Newtons needed...thus the block will accelerate and its speed will increase
According to Newton's second Law,
F_net = ma --> a = F / m
The acceleration the object experiences is equal to the net force applied divided by the object's mass. The net force applied on the object is the sum of all the forces acting on the object (remember that a force is a vector). If we have a frictional force acting one direction and an applied force acting in the opposite direction, we can add these together (taking into account they act in opposite directions) to get the net force of 38 Newtons.
We know the weight of the object to be 60 Newtons.
Weight = mass * gravity
60 N = mass * 9.81 m/s^2
mass = 6.12 kg
We now know both the net force and the mass of the object.
a = F/m
a = 38 N / 6.12 kg
a = 6.21 m/s^2
The object will accelerate at a rate of 6.21 m/s^2.

Answer 2

Friction = µk x F(normal)

Friction = 0.7 x 60 N (since it is moving at constant velocity, the accel. = 0 --> Fnet = 0 N --> Friction = horizontal force necessary) ; F = 42 N

If you pull it with 80 N than 80N-42N = Fnet = mass x accel.

accel = Fnet / mass = 38 / 6

Answer 3

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