A 20 kg block rests on a rough horizontal table. A rope is attached to the block and is pulled with a force of 80 N to the left. As a result, the block accelerates at 2.5 m/s2. The coefficient of kinetic friction μk between the block and the table is ___ .( Round the answer to the nearest hundredth.)
This is big boi stuff!
Frictional force after calculation = 30N
Coefficient of friction = 0.15
0.15
To find the coefficient of kinetic friction (μk), we can use the following equation:
μk = (Ffriction) / (Fn)
Where:
- μk is the coefficient of kinetic friction
- Ffriction is the force of friction between the block and the table
- Fn is the normal force acting on the block
First, let's calculate the normal force (Fn). The normal force is the force exerted by a surface to support the weight of an object resting on it. In this case, the weight of the block is balanced by the normal force. The formula for calculating the normal force is:
Fn = mg
Where:
- Fn is the normal force
- m is the mass of the block (20 kg)
- g is the acceleration due to gravity (approximately 9.8 m/s^2)
Fn = 20 kg * 9.8 m/s^2
Fn = 196 N
Now, calculate the force of friction (Ffriction). The force of friction can be calculated using the equation:
Ffriction = μk * Fn
As the block is accelerating, the net force acting on it can be found using Newton's second law of motion:
Net force = mass * acceleration
The net force is the difference between the force applied by the rope and the force of friction:
Net force = Force applied - Force of friction
Rearranging the equation, we get:
Force of friction = Force applied - Net force
Force applied = 80 N (given)
Net force = mass * acceleration = 20 kg * 2.5 m/s^2
Force of friction = 80 N - (20 kg * 2.5 m/s^2)
Force of friction = 30 N
Now that we have the force of friction and the normal force, we can calculate the coefficient of kinetic friction:
μk = Ffriction / Fn
μk = 30 N / 196 N
μk ≈ 0.1531
Rounded to the nearest hundredth, the coefficient of kinetic friction (μk) is approximately 0.15.
What is the answer rounded to the nearest hundred?
Typically people would get numeric values for these types of questions. If you were to do the math on the calculator correctly you should get Syntax Error. It seems odd but i put that on all my tests and my teachers call my parents to let them know how good i am doing
calculator broken??
20 kg * 2.5 m/s^2 = 50 N
so the frictional force is ... 80 N - 50 N = 30 N
Ff = m * g * μk
μk = 30 N / (20 kg * 9.8 m/s^2) = 30 N / 196 N
the coefficient of friction is just a number ... no units