Friction equations?

Question

1. The Druids who built stonehenge had to contend with lots o' friction. If the coefficient of friction between stone and dirt is µk=0.6, a) what would be the force necessary to drag a 1300 kg rock at constant velocity? (You must find the weight of the rock first!!)
1.2 if the rock was dragged by a rope horizontally with a force of 19000 N, what is its acceleration?
2. What is the acceleration of a 19 kg sled with plastic runners on dry snow (µk=0.3) if a horizontal pulling force of 100 N is applied to it?
2.2 how much force must it be pulled with so it goes at a constant velocity?
3. What is the acceleration of a 4 kg crate, if you push it with a force of 110 N, and the coefficient of kinetic friction between the crate and the floor is µk=0.3?
3.1 how much force must it be pushed with so it goes at a constant velocity?

Answer 1

For each of these problems, you must multiply the mass by g to get the weight w in newtons. In other words, w = m * g.
Since all these problems assume a horizontal sliding surface, the weight is the normal force needed to find friction force ff, so ff = µk * w. This answers all the questions that ask what force is needed to drag the object at constant velocity (1, 2.2, 3.1).
In the questions that ask what the acceleration 'a' is (1.2, 2, 3), just subtract ff from the total applied force, and the result fr is what accelerates the mass. Then use f=ma to get the acceleration (a = fr / m).

Answer 2

Here's my try:
1) Since each stone has a mass of 1300 kg, it's weight is 12740 N. The friction opposes the motion and it is determined as the product of the Normal Force done on an object times the coefficient of friction:

Force of Friction = Normal Force * µk
Force of Friction = 12740 N * .6
Force of Friction = 7644 N

This force is done against the direction of motion, so, with the equation of Sum of Forces equals Mass times Accelereation we now that the Drag Force done on the stone, minus the Force of Friction, would be equal to Mass times Acceleration, which in this case is zero, since it is a constant velocity.

Drag Force - Force of Friction = 0
Drag Force = Force of Friction
Drag Force = 7644 N

1.2) For this one, we just apply a Drag Force and solve for Acceleration:

Sum of Forces = Mass times Acceleration
Drag Force - Force of Friction = Mass * Acceleration
19000 N - 7644 N = 1300 kg * Acceleration
Acceleration = 11356 N / 1300 kg
Acceleration = 8.74 m/s^2

2) With the same concept as the last problem, Sum of Forces equals Mass times Acceleration. So we need first to determine the Friction Force done on the sled.

Friction Force = Normal Force * µk
Friction Force = 186.2 N * .3
Friction Force = 55.86 N

Sum of Forces = Mass times Acceleration
100 N - 55.86 N = 19 kg * Acceleration
Acceleration = 44.14 N / 19 kg
Acceleration = 2.32 m/s^2

2.2) If you want a constant velocity, that means that acceleration needs to be equal to Zero, so the Sum on the Forces applied to the sled would be equal to Zero.

Sum of Forces = 0
Pull Force - Friction Force = 0
Pull Force = Friction Force
Pull Force = 55.86 N

3) Again, the same method.

Friction Force = Normal Force * µk
Friction Force = 39.2 N * .3
Friction Force = 11.76 N

Sum of Forces = Mass times Acceleration
Push Force - Friction Force = Mass * Acceleration
110 N - 11.76 N = 4 kg * Acceleration
Acceleration = 98.24 N / 4 kg
Acceleration= 24.56 m/s^2

3.1) The same as before:

Sum of Forces = 0
Push Force - Friction Force = 0
Push Force = Frictio Force
Push Force = 11.76 N

That's all, hope I explained myself well, and you understood the concepts, any questions you can message me ;)

Answer 3

Acceleration by way of gravity is 9.6m/s^2 so if the extremely acceleration of the firefighter is 4 m/s^2 then friction is slowing acceleration with the help of 5.6m/s^2. pressure is the same as mass x acceleration so the pressure of friction often is the mass of the firefighter (80kg) x 5.6m/s^2 that's the same as 448 Newtons