Question

a 1.82 kg sled moving on flat snow slows down and comes to a complete stop due to a frictional force. the coefficient of kinetic friction is 0.212.

what is the acceleration of the sled?

(a = ? \text{ m/s}^2)

be sure to indicate if the sled is speeding up (+) or slowing down (-).

Explanation:

⚡ Using what you learned: newton's laws of motion

Step 1: Identify forces and normal force

On a flat surface, the normal force \( F_N \) acting on the sled balances its weight:

$$ F_N = m \cdot g $$

Using \( g = 9.8\text{ m/s}^2 \):

$$ F_N = 1.82\text{ kg} \times 9.8\text{ m/s}^2 = 17.836\text{ N} $$

Step 2: Calculate frictional force

The kinetic frictional force \( F_f \) opposing the motion is:

$$ F_f = \mu_k \cdot F_N $$

$$ F_f = 0.212 \times 17.836\text{ N} \approx 3.7812\text{ N} $$

Step 3: Determine acceleration

Using Newton's second law (\( F_{\text{net}} = m \cdot a \)), where the only horizontal force is friction acting in the opposite direction of motion:

$$ a = -\frac{F_f}{m} = -\frac{\mu_k \cdot m \cdot g}{m} = -\mu_k \cdot g $$

$$ a = -0.212 \times 9.8\text{ m/s}^2 \approx -2.08\text{ m/s}^2 $$

(Note: The negative sign indicates the sled is slowing down.)

Answer:

-2.08