A force of 36.1 N is required to start a 4.0 -kg box moving across a horizontal concrete floor. If the 36.1 N force continues, the box accelerates at 0.71 m/s^2. What is the coefficient of kinetic friction?
I got 0.072 as my answer and this is showing as incorrect.
I did:
36.1 - mu x 4.0kg x 9.8 = 4.0kg x 0.71
0.71 / 9.8 = 0.072
YOur math is amazing. Next time, follow rules of algebra.
36.1-mu*4*9.8=4*.71
mu=(36.1-4*.71)/(4*9.8)=.85 check that.
To find the coefficient of kinetic friction, you can use the formula:
force of friction = coefficient of kinetic friction * normal force
First, calculate the normal force acting on the box:
normal force = mass x gravity
normal force = 4.0 kg x 9.8 m/s^2
normal force = 39.2 N
The force of friction can be calculated using the equation:
force of friction = mass x acceleration
force of friction = 4.0 kg x 0.71 m/s^2
force of friction = 2.84 N
Now you can substitute the values into the formula for force of friction:
2.84 N = coefficient of kinetic friction x 39.2 N
Divide both sides of the equation by 39.2 N:
coefficient of kinetic friction = 2.84 N / 39.2 N
coefficient of kinetic friction ≈ 0.0724
Therefore, the correct coefficient of kinetic friction is approximately 0.0724, not 0.072 as you previously calculated.
To find the coefficient of kinetic friction in this problem, we can use the equation:
net force = frictional force
First, let's calculate the net force acting on the box. The net force is equal to the applied force minus the frictional force:
net force = applied force - frictional force
Given: applied force = 36.1 N
The mass of the box is 4.0 kg, and its acceleration is 0.71 m/s^2. We can use Newton's second law to find the applied force:
applied force = mass x acceleration
applied force = 4.0 kg x 0.71 m/s^2
applied force = 2.84 N
Now we can substitute this into the net force equation:
2.84 N - frictional force = 0
Rearranging the equation:
frictional force = 2.84 N
Next, we can use the formula for frictional force:
frictional force = coefficient of friction x normal force
The normal force is equal to the weight of the box, which can be calculated as:
normal force = mass x gravity
normal force = 4.0 kg x 9.8 m/s^2
normal force = 39.2 N
Now we can substitute the values into the equation for the frictional force:
2.84 N = coefficient of friction x 39.2 N
Solving for the coefficient of friction:
coefficient of friction = 2.84 N / 39.2 N
coefficient of friction ≈ 0.0724
If you rounded the coefficient of friction to three decimal places, you would get 0.072. However, the correct answer should be rounded to four decimal places, which gives us approximately 0.0724. Therefore, the correct coefficient of kinetic friction is 0.0724, not 0.072.