A 34.2 -kg block rests on the
oor.
(a) What force (N) does the
oor exert on the block?
(b) If a rope is tied to the block and run vertically over a pulley, and the other end is
attached to a free-hanging 5.6 kg weight, what force (N) does the
oor now exert on the
block?
(c) If the free-hanging weight is replaced with a 20 kg weight, what force (N) does the
oor exert on the block?
We will be glad to critique your thoughts.
the following system (fig1) is in epuilibrium in the system a block of m=9 kg is attaehed the ceiling by two massless ropes are 45 of each two
To determine the force exerted by the floor on the block in each scenario, we need to understand Newton's laws of motion and apply the principles of equilibrium.
(a) In the first scenario, where the block rests on the floor without any external forces, the force exerted by the floor on the block is equal to the weight of the block. The weight of the block can be calculated by multiplying its mass (34.2 kg) by the acceleration due to gravity (9.8 m/s^2):
Force (floor on block) = Weight of the block = mass × acceleration due to gravity
= 34.2 kg × 9.8 m/s^2
≈ 334.8 N
So, the floor exerts a force of approximately 334.8 N on the block.
(b) In the second scenario, when a rope is attached to the block and run vertically over a pulley with a free-hanging weight (5.6 kg), a tension force is applied by the rope in addition to the force exerted by the floor. In this case, we need to consider the equilibrium of forces acting on the block.
Since the system is in equilibrium, the tension in the rope (Force A) must equal the weight of the hanging weight (Force B). Therefore, the tension in the rope will be equal to the weight of the hanging weight:
Force A = Force B = Weight of the hanging weight
= mass × acceleration due to gravity
= 5.6 kg × 9.8 m/s^2
≈ 54.88 N
The force exerted by the floor on the block can be calculated by adding the tension force to the weight of the block:
Force (floor on block) = Weight of the block + Force A
= mass × acceleration due to gravity + Force A
= 34.2 kg × 9.8 m/s^2 + 54.88 N
≈ 390.676 N
Therefore, the floor exerts a force of approximately 390.676 N on the block.
(c) In the third scenario, where the free-hanging weight is replaced with a 20 kg weight, we follow the same approach as in scenario (b) to determine the forces.
The tension in the rope (Force A) will still be equal to the weight of the hanging weight:
Force A = Force B = Weight of the hanging weight
= mass × acceleration due to gravity
= 20 kg × 9.8 m/s^2
≈ 196 N
Now, the force exerted by the floor on the block will be the weight of the block plus the tension force:
Force (floor on block) = Weight of the block + Force A
= mass × acceleration due to gravity + Force A
= 34.2 kg × 9.8 m/s^2 + 196 N
≈ 522.36 N
Therefore, the floor exerts a force of approximately 522.36 N on the block.