To determine the downward force required to lower the 15 kg mass attached to the rope at a constant velocity, we need to consider the forces acting on the system. In this case, there are two main forces to consider:
The gravitational force acting on the mass, given by F_gravity = m * g, where m is the mass (15 kg) and g is the acceleration due to gravity (approximately 9.8 m/s²).
The frictional force between the rope and the rough surface of the bag. The frictional force can be calculated using the equation F_friction = μ * N, where μ is the coefficient of kinetic friction (0.2) and N is the normal force.
Since the mass is being lowered at a constant velocity, the net force on the system must be zero. Therefore, the downward force F required to maintain a constant velocity can be calculated as:
F - F_friction - F_gravity = 0
Let's calculate the normal force first. The normal force N is equal to the weight of the mass, which is the gravitational force acting on it:
N = m * g
Now, we can substitute the values and solve for the downward force F:
F - μ * N - F_gravity = 0
F - 0.2 * (m * g) - (m * g) = 0
F - 0.2 * (15 kg * 9.8 m/s²) - (15 kg * 9.8 m/s²) = 0
F - 29.4 N - 147 N = 0
F - 176.4 N = 0
F = 176.4 N
Therefore, a downward force of approximately 176.4 Newtons (N) is required to lower the 15 kg mass attached to the other end of the rope at a constant velocity.