F4 Blocks
and
have masses
and
, respectively. Neglecting friction between all surfaces, draw the FBD and KD for each mass
The Correct Answer and Explanation is:
To analyze the given problem, we need to break it down into two parts: the Free Body Diagram (FBD) and the Kinetic Diagram (KD). I’ll walk you through the process step-by-step:
Step 1: Free Body Diagram (FBD)
For two masses (let’s call them Mass 1 and Mass 2), each mass will have its own set of forces acting on it. The main forces typically acting on the masses include:
- Gravitational Force (Weight): This is the force due to gravity acting vertically downward on each mass. The formula for weight is: W=mgW = mgW=mg where mmm is the mass of the object and ggg is the acceleration due to gravity.
- Normal Force (N): If the masses are in contact with a horizontal surface, the normal force is the upward force exerted by the surface, opposing the gravitational force.
- Applied Force (F): If there is an applied force, it will act in the direction specified (typically horizontally). For simplicity, assume no applied force or external influence.
- Tension Force (T): If the masses are connected by a rope or string, the tension force will act along the line of the rope, between the two masses.
In the FBD for each mass:
- For Mass 1, you’ll have a weight W1W_1W1 downward and a normal force N1N_1N1 upward.
- For Mass 2, the weight W2W_2W2 acts downward and the normal force N2N_2N2 acts upward.
- If there is tension, a force TTT will act horizontally on both masses, pulling them in opposite directions.
Step 2: Kinetic Diagram (KD)
The KD focuses on the motion of the system and how forces lead to acceleration. Using Newton’s Second Law of Motion (F=maF = maF=ma), the net forces on each mass are given by:
For Mass 1:T−Ffriction 1=m1aT – F_{\text{friction 1}} = m_1 aT−Ffriction 1=m1a
For Mass 2:T−Ffriction 2=m2aT – F_{\text{friction 2}} = m_2 aT−Ffriction 2=m2a
Since there is no friction (as stated), the friction terms cancel out. The system moves with the same acceleration aaa for both masses.
Step 3: Analysis and Explanation
If the two masses are connected by a rope and a tension force is applied, the system will accelerate based on the total mass. The key here is that both masses share the same acceleration, which means that the forces acting on them will be in equilibrium if there is no net external force acting on them. The tension in the rope adjusts to ensure that both masses accelerate in sync.
This analysis assumes that there is no friction, making it simpler. If friction were present, we would need to add frictional forces Ffriction=μNF_{\text{friction}} = \mu NFfriction=μN into the equations.
By applying Newton’s Second Law, you can determine the acceleration of the system by considering the total mass and the applied forces, such as tension. The key is recognizing that the tension force is the connecting element between the two masses and allows them to accelerate together.
