A 1.39-kg block slides across a rough surface such that it slows down with an acceleration of 1.43 m/s2. What is the coefficient of kinetic friction between the block and the surface?

Calculate the friction force Ff = m*a

The coefficient of kinetic friction is

Uk = Ff/(m*g) = a/g = ___

You don't need to know the mass.

To find the coefficient of kinetic friction between the block and the surface, we can use the formula:

\(F_{net} = m \cdot a\)

Where:
\(F_{net}\) is the net force acting on the block,
\(m\) is the mass of the block, and
\(a\) is the acceleration of the block.

In this case, the net force acting on the block is the force of kinetic friction (\(f_k\)). So, the formula becomes:

\(f_k = m \cdot a\)

Rearranging the equation, we get:

\(f_k = \mu_k \cdot N\)

Where:
\(f_k\) is the force of kinetic friction,
\(\mu_k\) is the coefficient of kinetic friction, and
\(N\) is the normal force.

The normal force is equal to the weight of the block (mg), which is given by:

\(N = m \cdot g\)

Where:
\(g\) is the acceleration due to gravity (approximately 9.8 m/s^2).

Substituting the value of N into the equation, we get:

\(f_k = \mu_k \cdot m \cdot g\)

Since the acceleration of the block is in the opposite direction of its motion, we have:

\(f_k = - m \cdot a\)

Substituting the given values into the equation:

\(1.43 \, \mathrm{m/s^2} = - \mu_k \cdot 1.39 \, \mathrm{kg} \cdot 9.8 \, \mathrm{m/s^2}\)

Simplifying the equation, we find:

\(\mu_k = \frac{{-1.43}}{{1.39 \cdot 9.8}}\)

Evaluating the expression, we get:

\(\mu_k \approx -0.102\)

Therefore, the coefficient of kinetic friction between the block and the surface is approximately -0.102. Note that the negative sign indicates that the friction is acting opposite to the motion of the block.

To find the coefficient of kinetic friction between the block and the surface, we can use Newton's second law of motion.

The formula for the force of kinetic friction (Fk) is given by:

Fk = μk * N

where μk is the coefficient of kinetic friction and N is the normal force.

First, we need to determine the normal force acting on the block. The normal force is the force exerted by a surface to support the weight of an object resting on it.

In this case, since the block is sliding, the gravitational force (mg) acting downwards is balanced by the normal force (N) acting upwards:

N = mg

where m is the mass of the block and g is the acceleration due to gravity (approximately 9.8 m/s^2).

Given:
Mass of the block (m) = 1.39 kg
Acceleration due to gravity (g) = 9.8 m/s^2

N = (1.39 kg) * (9.8 m/s^2)
N = 13.622 N

Now, we can calculate the force of kinetic friction (Fk) using the equation:

Fk = mass * acceleration

Given:
Mass of the block (m) = 1.39 kg
Acceleration (a) = -1.43 m/s^2 (negative due to the block slowing down)

Fk = (1.39 kg) * (-1.43 m/s^2)
Fk = -1.998 N

The force of kinetic friction (Fk) is equal in magnitude but opposite in direction to the applied net force.

Since Fk = μk * N, we can rearrange the equation to find the coefficient of kinetic friction:

μk = Fk / N

Substituting the given values:

μk = -1.998 N / 13.622 N
μk = -0.1466

However, coefficients of friction are non-negative values. Hence, the coefficient of kinetic friction between the block and the surface is 0.1466 (rounded to four decimal places).