Michael L. answered • 24d
Basketball Coach | Skills Training, Strategy & Player Development
Final Answer: The acceleration of the system is approximately 6.99 m/s².
We can solve this using Newton's Second Law, which tells us that the acceleration of a system depends on the net force acting on it and its total mass.
Step 1: Identify the given information.
Mass of block = 3.5 kg
Mass of hanging ball = 2.5 kg
Applied pulling force = 75 N
Coefficient of friction = 0.25
Acceleration due to gravity = 9.8 m/s²
We assume the pulling force is horizontal, the pulley and rope are ideal, and the coefficient of friction applies while the block is moving.
Step 2: Calculate the friction force.
Friction opposes the motion of the block along the table.
Friction = Coefficient of friction x Normal force
Normal force = 3.5 x 9.8 = 34.3 N
Friction = 0.25 x 34.3
Friction = 8.575 N
Step 3: Calculate the weight of the hanging ball.
Gravity pulls the hanging ball downward, opposing its upward acceleration.
Weight = Mass x Gravity
Weight = 2.5 x 9.8
Weight = 24.5 N
Step 4: Calculate the net force on the system.
The applied force pulls the system forward, while friction and the hanging ball's weight oppose the motion.
Net force = Applied force - Friction - Hanging weight
Net force = 75 - 8.575 - 24.5
Net force = 41.925 N
Step 5: Calculate the acceleration.
Using Newton's Second Law:
Net force = Total mass x Acceleration
Total mass = 3.5 + 2.5 = 6.0 kg
Acceleration = Net force / Total mass
Acceleration = 41.925 / 6.0
Acceleration = 6.9875 m/s²
Final Answer: 6.99 m/s²
The block accelerates horizontally in the direction of the applied force, while the hanging ball accelerates upward at the same rate.
The important idea is that we treat the block and hanging ball as one connected system. The tension in the rope is an internal force, so it cancels when we consider the entire system.
This makes the problem much easier because we only need to calculate the external forces and divide by the combined mass!
