A 50 N sled rests on a horizontal surface. A horizontal pull of 10 N is required just to start the sled moving. After motion is started, only a 5 N force is needed to move the sled with a constant velocity. The coefficient of static and kinetic friction are respectively:

Question

Accepted Answer

To determine the coefficients of static and kinetic friction, we need to understand the forces involved in moving the sled.

1. **Static Friction**: This is the frictional force that must be overcome to start moving an object from rest. The maximum static friction force ($f_s$) can be calculated using the formula:
   $$
   f_s = \mu_s \cdot N
   $$
   where $\mu_s$ is the coefficient of static friction and $N$ is the normal force. For the sled, the normal force is equal to its weight, which is 50 N. Given that a 10 N force is required to start the sled moving, we have:
   $$
   10 = \mu_s \cdot 50
   $$
   Solving for $\mu_s$, we get:
   $$
   \mu_s = \frac{10}{50} = 0.20
   $$

2. **Kinetic Friction**: Once the sled is in motion, the frictional force is determined by the coefficient of kinetic friction ($\mu_k$). The force required to keep the sled moving at a constant velocity is 5 N. The kinetic friction force ($f_k$) is given by:
   $$
   f_k = \mu_k \cdot N
   $$
   Using the given force to maintain constant velocity:
   $$
   5 = \mu_k \cdot 50
   $$
   Solving for $\mu_k$, we get:
   $$
   \mu_k = \frac{5}{50} = 0.10
   $$

Thus, the coefficients of static and kinetic friction are 0.20 and 0.10, respectively, which corresponds to Option 2.

**Explanation for Incorrect Options:**

- **Option 1 (0.10, 0.20)**: This option incorrectly reverses the values for static and kinetic friction. The static friction must be greater than the kinetic friction because it takes more force to start moving the sled than to keep it moving.

- **Option 3 (0.10, 0.15)**: This option underestimates both the static and kinetic friction coefficients. The calculations show that the static friction is 0.20, not 0.10, and the kinetic friction is 0.10, not 0.15.

- **Option 4 (0.15, 0.20)**: This option incorrectly suggests that the kinetic friction is greater than the static friction, which contradicts the physical principle that static friction is typically greater than kinetic friction for the same surfaces.

Therefore, Option 2 is the correct answer, as it accurately reflects the calculated coefficients of static and kinetic friction based on the given forces.