Question: Question 23
A plate with mass of $0.75$ kg is tossed in the air, with air resistance acting like friction at $k = 0.001$. What is the resultant force pulling the plate down due to gravity? Use the friction formula.
A. $6$ N
B. $21.8$ N
C. $7.34$ N
D. $1.34$ N
1. **State the problem:** We need to find the resultant force pulling the plate down due to gravity, considering air resistance as friction with coefficient $k=0.001$.
2. **Given data:**
- Mass of plate, $m = 0.75$ kg
- Friction coefficient, $k = 0.001$
- Acceleration due to gravity, $g = 9.8$ m/s$^2$
3. **Formula for gravitational force:**
$$F_g = mg$$
4. **Formula for frictional force (air resistance):**
$$F_f = k v$$
where $v$ is the velocity of the plate. Since the problem does not provide velocity, we assume the friction force is negligible or we consider only gravity for resultant force pulling down.
5. **Calculate gravitational force:**
$$F_g = 0.75 \times 9.8 = 7.35 \text{ N}$$
6. **Resultant force pulling down:** Since friction force is very small and velocity is not given, the resultant force is approximately the gravitational force:
$$F_{resultant} \approx 7.35 \text{ N}$$
7. **Match with options:** Closest option is C. $7.34$ N.
**Final answer:** C. $7.34$ N