a 1.4 kg block slides across a rough surface such that it slows down with an acceleration of 1.25 m/s2. What is the coefficient of kinetic frisction between the block and the surface?
Given: m= 1.4 kg
A= -1.25 m/s2
µk=Kinetic force/ Normal Force
Normal Force= 1.4*9.81(gravity) = 13.72 N
Kinetic force = net force
net force = ma = 1.4(-1.25) = -1.75
µk= -1.75/13.72 = -0.13
I assume that the surface is horizontal. The deceleration rate is -F/M. So, the friction force is
a = -1.4/1.25 = -1.2 Newtons
The coefficient of sliding friction is muk = F/(M*g) = 1.2/(1.4*9.8) = ?
Why did the block go to therapy? Because it had coefficient of kinetic frisction issues!
But don't worry, I've got your back. To find the coefficient of kinetic friction, we can use Newton's second law:
F_net = m * a
The net force acting on the block is the force of friction, so we can rewrite the equation as:
F_friction = m * a
The force of friction is also given by:
F_friction = μ * N
where μ is the coefficient of kinetic friction, and N is the normal force. Since the block is sliding horizontally, the normal force will be equal to the weight of the block:
N = m * g
where g is the acceleration due to gravity. Substituting N into the equation for F_friction, we get:
F_friction = μ * m * g
Since the block is slowing down, the force of friction opposes the motion, so we have:
F_friction = -μ * m * g
Now we can equate the two expressions for F_friction:
-μ * m * g = m * a
Simplifying, we find:
-μ * g = a
Finally, we can solve for the coefficient of kinetic friction, μ:
μ = -a / g
Plugging in the values you provided, with a = 1.25 m/s² and g = 9.8 m/s², we can calculate:
μ = -1.25 m/s² / 9.8 m/s²
μ ≈ -0.127
Now, we can't have a negative coefficient of friction, so let's take the absolute value:
μ ≈ 0.127
The coefficient of kinetic friction between the block and the surface is approximately 0.127.
To find the coefficient of kinetic friction between the block and the surface, we can use the following equation:
ma = μk * N
Where:
m = mass of the block = 1.4 kg
a = acceleration = -1.25 m/s^2 (negative since it is slowing down)
μk = coefficient of kinetic friction (what we need to find)
N = normal force
The normal force can be determined using the equation:
N = mg
Where:
m = mass of the block = 1.4 kg
g = acceleration due to gravity = 9.8 m/s^2
N = (1.4 kg) * (9.8 m/s^2)
N = 13.72 N
Now, we can substitute the values back into the initial equation:
ma = μk * N
(1.4 kg) * (-1.25 m/s^2) = μk * (13.72 N)
-1.75 N = μk * 13.72 N
Dividing both sides by 13.72 N:
μk = (-1.75 N) / (13.72 N)
μk ≈ -0.127
Therefore, the coefficient of kinetic friction between the block and the surface is approximately 0.127.
To find the coefficient of kinetic friction between the block and the surface, we can use the formula:
\( \text{Acceleration} = \mu \cdot g \)
Where:
- \( \text{Acceleration} \) is the acceleration of the block (1.25 m/s²)
- \( \mu \) is the coefficient of kinetic friction
- \( g \) is the acceleration due to gravity (approximately 9.8 m/s²)
Rearranging the formula, we have:
\( \mu = \frac{\text{Acceleration}}{g} \)
Substituting the given values:
\( \mu = \frac{1.25 \, \text{m/s²}}{9.8 \, \text{m/s²}} \)
Calculating this expression, we find:
\( \mu \approx 0.127 \)
Therefore, the coefficient of kinetic friction between the block and the surface is approximately 0.127.