Question

wr2. a curling rock slides with a constant velocity down the ice surface. if the mass of the curling rock is \\(20.0\text{ kg}\\) and the force due to friction is \\(3.92 \times 10^{-1}\text{ n}\\). find the coefficient of kinetic friction. (2 marks) show all work and give the answer in significant digits.

Explanation:

Identify given values and target unknown

We are given:

• Mass of the curling rock, \(m = 20.0\text{ kg}\)
• Force of kinetic friction, \(F_f = 3.92 \times 10^{-1}\text{ N} = 0.392\text{ N}\)
• Acceleration due to gravity, \(g = 9.81\text{ m/s}^2\)

We need to find:

• Coefficient of kinetic friction, \(\mu_k\)

Calculate the normal force

On a horizontal ice surface, the normal force \(F_N\) balances the gravitational force:

$$ F_N = m \cdot g $$

$$ F_N = 20.0\text{ kg} \times 9.81\text{ m/s}^2 = 196.2\text{ N} $$

Relate friction to normal force

The force of kinetic friction is related to the normal force by:

$$ F_f = \mu_k \cdot F_N $$

Solve for the coefficient of kinetic friction

Rearranging the formula to solve for \(\mu_k\):

$$ \mu_k = \frac{F_f}{F_N} $$

$$ \mu_k = \frac{0.392\text{ N}}{196.2\text{ N}} \approx 0.00199796 $$

Express with correct significant digits

The given values have three significant digits:

• \(20.0\text{ kg}\) (3 sig figs)
• \(3.92 \times 10^{-1}\text{ N}\) (3 sig figs)
• \(g = 9.81\text{ m/s}^2\) (3 sig figs)

Rounding our result to three significant digits:

$$ \mu_k = 2.00 \times 10^{-3} $$

Answer:

\(2.00 \times 10^{-3}\)