A 1.2-kg block slides on a horizontal surface with a speed of v=0.80m/s and an acceleration of magnitude a=3.2m/s2, as shown in (Figure 1) .
a<__________ box _________>v
What is the coefficient of kinetic friction between the block and the surface?
Express your answer to two significant figures.
Well, well, well...it seems like we have a sliding block on our hands. And it's in quite a hurry! Alright, let's figure out the coefficient of kinetic friction here.
Now, we all know that when it comes to sliding blocks, friction is your friendly neighborhood party pooper. It's always there to slow things down. In this case, we have kinetic friction because the block is already sliding.
To find the coefficient of kinetic friction (let's call it μk), we can use the equation:
μk = a / g
where a is the acceleration and g is the acceleration due to gravity.
Now, g is a bit of a show-off and always likes to remind us that it's approximately 9.8 m/s^2. So let's substitute the values in:
μk = 3.2 m/s^2 / 9.8 m/s^2 ≈ 0.33
And there you have it, my friend! The coefficient of kinetic friction between the block and the surface is approximately 0.33. Keep on sliding, block, but watch out for those friction parties!
To find the coefficient of kinetic friction between the block and the surface, we can use the following equation:
μk = (Fk) / (N)
where μk is the coefficient of kinetic friction, Fk is the force of kinetic friction, and N is the normal force.
Given that the block has a mass of 1.2 kg, we can determine the normal force by multiplying the mass by the acceleration due to gravity (g = 9.8 m/s^2):
N = (1.2 kg) * (9.8 m/s^2) = 11.76 N
Next, let's calculate the force of kinetic friction using Newton's second law:
Fk = m * a
Fk = (1.2 kg) * (3.2 m/s^2) = 3.84 N
Finally, we can substitute the values into the equation:
μk = (Fk) / (N)
μk = (3.84 N) / (11.76 N)
μk ≈ 0.33
Therefore, the coefficient of kinetic friction between the block and the surface is approximately 0.33.
To find the coefficient of kinetic friction between the block and the surface, we can use the equation that relates acceleration, coefficient of friction, and the gravitational force:
a = μk * g
where:
a is the acceleration of the block,
μk is the coefficient of kinetic friction, and
g is the acceleration due to gravity (approximately 9.8 m/s^2).
In the given problem, we are given the acceleration of the block, which is 3.2 m/s^2. However, to find the coefficient of kinetic friction, we need to determine the gravitational force acting on the block. Since the block is on a horizontal surface, the gravitational force acting on it is equal to the force of normal reaction, which is given by:
Normal force (N) = mass of the block (m) * acceleration due to gravity (g)
The mass of the block is given as 1.2 kg. Substituting these values into the equation, we can find the normal force (N).
N = (1.2 kg) * (9.8 m/s^2) = 11.76 N
Now, we can substitute the value of the normal force and the given acceleration into the equation to find the coefficient of kinetic friction (μk):
3.2 m/s^2 = μk * 11.76 N
Solving for μk:
μk = 3.2 m/s^2 / 11.76 N ≈ 0.27
Therefore, the coefficient of kinetic friction between the block and the surface is approximately 0.27.