Two cubic blocks are in contact, resting on a frictionless horizontal surface. The block on the left has a mass of mL = 6.70 kg, and the block on the right has a mass of mR = 18.4 kg. A force of magnitude 112 N is applied to the left face of the left block, toward the right but at an upward angle of 30.0° with respect to the horizontal. It causes the left block to push on the right block. What is the magnitude of the force that the right block applies to the left block?
To find the magnitude of the force that the right block applies to the left block, we can use Newton's Third Law of motion, which states that for every action, there is an equal and opposite reaction.
Step 1: Resolve the applied force into horizontal and vertical components.
The vertical component can be found using the formula: F_vertical = F_applied * sin(theta), where F_applied is the applied force and theta is the angle with respect to the horizontal.
F_vertical = 112 N * sin(30°)
F_vertical = 112 N * 0.5
F_vertical = 56 N
The horizontal component can be found using the formula: F_horizontal = F_applied * cos(theta), where F_applied is the applied force and theta is the angle with respect to the horizontal.
F_horizontal = 112 N * cos(30°)
F_horizontal = 112 N * sqrt(3)/2
F_horizontal = 56 N * sqrt(3)
Step 2: Use Newton's Third Law to find the force exerted by the right block on the left block.
According to Newton's Third Law, the force exerted by the right block on the left block is equal in magnitude but opposite in direction to the force exerted by the left block on the right block.
Therefore, the magnitude of the force that the right block applies to the left block is also 56 N * sqrt(3).
To find the magnitude of the force that the right block applies to the left block, we can use Newton's Third Law, which states that every action has an equal and opposite reaction.
In this case, the force applied to the left block is the action, and the force exerted by the right block on the left block is the reaction. Therefore, the magnitude of the force that the right block applies to the left block is the same as the magnitude of the force that the left block applies to the right block.
The force applied to the left block can be resolved into two components: one along the horizontal direction (Fh) and one along the vertical direction (Fv).
Fh = F * cos(30°)
Fh = 112 N * cos(30°)
Fh = 96.83 N
Fv = F * sin(30°)
Fv = 112 N * sin(30°)
Fv = 56 N
Since the surface is frictionless and there are no other external forces acting on the blocks, the horizontal component of the force applied to the left block will be balanced by the horizontal component of the force exerted by the right block, resulting in a net force of zero in the horizontal direction.
Therefore, the magnitude of the force that the right block applies to the left block is equal to the vertical component of the force applied to the left block, which is 56 N.