Imagine that a small bug is trapped between two blocks ( 10kg and 5kg) In each case a person applies a force of 150 N to the right, but the order of the blocks is reversed. In which case will the bug have a better chance of surviving? Calculate the force acting on the bug in each case?
The bug must apply the force necessary to accelerate, or overcome the friction of, the block in front of it (in the direction of motion). The lighter that block is, the less the bug is stressed.
Two blocks are connected by a very light string passing over a massless and frictionless pulley (the figure ). Traveling at constant speed, the 20.0- block moves 80.0 to the right and the 12.0- block moves 80.0 downward
To determine in which case the bug has a better chance of surviving and to calculate the force acting on the bug in each case, we need to consider the net force acting on the bug and the resulting acceleration.
Case 1: Bug trapped between a 10kg block and a 5kg block.
In this case, the person applies a force of 150 N to the right on the 10kg block. Since the bug is trapped between the blocks, it experiences the same force as the 10kg block.
The net force acting on the bug can be calculated as the applied force minus the force applied by the 5kg block. Since the 5kg block is not moving, it must be countering the applied horizontal force, resulting in no horizontal force acting on the bug from the 5kg block.
Net force on bug = 150 N - 0 N = 150 N
Since the mass of the bug is tiny compared to the blocks, we can assume that the bug accelerates at the same rate as the blocks. Therefore, the acceleration experienced by the bug is:
Acceleration = Net force / Mass of the bug = 150 N / 10 kg = 15 m/s²
Case 2: Bug trapped between a 5kg block and a 10kg block.
In this case, the person applies a force of 150 N to the right on the 5kg block. Again, since the bug is trapped between the blocks, it experiences the same force as the 5kg block.
The net force acting on the bug can be calculated as the applied force minus the force applied by the 10kg block. Since the 10kg block is not moving, it must be countering the applied horizontal force, resulting in no horizontal force acting on the bug from the 10kg block.
Net force on bug = 150 N - 0 N = 150 N
Again, assuming the bug accelerates at the same rate as the blocks:
Acceleration = Net force / Mass of the bug = 150 N / 5 kg = 30 m/s²
Conclusion:
In both cases, the bug experiences the same net force of 150 N. However, the bug will experience a higher acceleration in Case 2 (30 m/s²) compared to Case 1 (15 m/s²). Therefore, the bug has a better chance of surviving when trapped between the 10kg and 5kg blocks (Case 1) since the lower acceleration means less impact force on the bug.
To determine in which case the bug will have a better chance of surviving, we need to consider the forces acting on the blocks. We will also calculate the force acting on the bug in each case.
Case 1: Bug between 10kg and 5kg blocks
In this case, the person applies a force of 150 N to the right.
To find the net force on the blocks, we need to calculate the difference in forces applied to both blocks. Since the force is being applied to the right, the 5kg block experiences a force of 150 N to the right, and the 10kg block experiences a force of 150 N to the left (opposite direction).
Net force on 5kg block = force applied = 150 N (to the right)
Net force on 10kg block = force applied - force experienced by 10kg block = 150 N - 150 N = 0 N
Since the net force on the 10kg block is zero, it does not move. Therefore, the bug will be crushed.
Case 2: Bug between 5kg and 10kg blocks
In this case, the order of the blocks is reversed, meaning the bug is now between the 5kg and 10kg blocks.
Again, the person applies a force of 150 N to the right.
Net force on 5kg block = force applied - force experienced by 5kg block = 150 N - 150 N = 0 N
Net force on 10kg block = force applied = 150 N (to the right)
Here, the net force on the 5kg block is zero, so it doesn't move. The 10kg block, however, experiences a net force of 150 N to the right. Since the 10kg block moves to the right, the bug between the blocks will have a better chance of survival as it won't get crushed.
In both cases, the bug experiences a force of 150 N. However, the bug has a better chance of surviving in Case 2 where the 10kg block is in front of the 5kg block.