Question

A body of mass 2 kg is kept by pressing to a vertical wall by a force of 100 N . The friction is 0.04 , what is the car's aceeleration ?

Answer 1

To determine the acceleration of the body being pressed against the wall, we can assess the forces acting on it.

1. **Given Data:**
- Mass of the body \( m = 2 \, \text{kg} \)
- Applied force \( F_{applied} = 100 \, \text{N} \)
- Coefficient of friction \( \mu = 0.04 \)
- Gravitational acceleration \( g \approx 9.81 \, \text{m/s}^2 \)

2. **Calculate the normal force \( F_N \):**
The normal force is equal to the applied force, as the body is pressed against the wall:
\[
F_N = F_{applied} = 100 \, \text{N}
\]

3. **Calculate the frictional force \( F_f \):**
The maximum static friction can be calculated using the coefficient of friction and the normal force:
\[
F_f = \mu \times F_N = 0.04 \times 100 \, \text{N} = 4 \, \text{N}
\]

4. **Assess the forces acting on the body:**
- The gravitational force acting downward:
\[
F_{gravity} = m \times g = 2 \, \text{kg} \times 9.81 \, \text{m/s}^2 \approx 19.62 \, \text{N}
\]

- The frictional force acting upward (opposing the gravitational force):
\[
F_f = 4 \, \text{N}
\]

5. **Calculate the net force acting on the body:**
The net force acting on the body can be calculated as the difference between the gravitational force and the frictional force:
\[
F_{net} = F_{gravity} - F_f = 19.62 \, \text{N} - 4 \, \text{N} = 15.62 \, \text{N}
\]

6. **Calculate the acceleration \( a \) of the body:**
By applying Newton's second law \( F = m \times a \), we can find the acceleration:
\[
a = \frac{F_{net}}{m} = \frac{15.62 \, \text{N}}{2 \, \text{kg}} \approx 7.81 \, \text{m/s}^2
\]

Therefore, the car's acceleration is approximately \( 7.81 \, \text{m/s}^2 \).