A small bug is placed between two masses (m1>m2) on a frictionless table. A horizontal force F is applied to either m1 or to m2, as shown.
1) In which case does the bug have a better chance of survival? HINT: Find the force of contact between the blocks in each case.
Please do it step by step with equations
The acceleration produced in either case will be F/(m1+m2).
We have to check the case in which the normal force will be the least.
In case 1: normal force = m2 * a = Fm2/(m1+m2).
In case 2: normal force = m1*a = Fm1/(m1+m2)
Clearly normal force of case 1 is less than normal force of case 2 (since m2>m1) and hence the insect has greater chance of survival in case 1.
Help ASAP please!!
To determine in which case the bug has a better chance of survival, we need to compare the force of contact between the blocks in each case.
Let's consider the two cases separately:
Case 1: The horizontal force F is applied to mass m1.
In this case, the force of contact between the blocks (denoted as Fc1) is equal to the applied force F. This is because the applied force F is transmitted through mass m1 and directly acts on mass m2.
Case 2: The horizontal force F is applied to mass m2.
In this case, the force of contact between the blocks (denoted as Fc2) can be determined by using Newton's Third Law of motion. According to this law, the force exerted by m2 on m1 is equal in magnitude but opposite in direction to the force exerted by m1 on m2. Therefore, Fc2 is equal to F.
Now, we can compare the forces of contact between the blocks in both cases:
Fc1 (Case 1) = F
Fc2 (Case 2) = F
Since the forces of contact are equal in both cases, the chance of survival for the bug is the same in both cases.
To determine in which case the bug has a better chance of survival, we need to find the force of contact between the blocks in each case.
Let's consider both scenarios:
Scenario 1: Force is applied to mass m1.
In this case, we can use Newton's third law of motion, which states that for every action, there is an equal and opposite reaction. Hence, the force applied to mass m1 will result in a force of the same magnitude but in the opposite direction acting on mass m2.
Let F1 be the applied force.
The force of contact between the blocks, denoted as F_contact1, will be equal to F1.
Scenario 2: Force is applied to mass m2.
Similarly, if the force is applied to mass m2, there will be a reaction force of the same magnitude but in the opposite direction acting on mass m1.
Let F2 be the applied force.
The force of contact between the blocks, denoted as F_contact2, will be equal to F2.
Next, we can compare the forces of contact for both scenarios to determine the better chance of survival for the bug.
If F_contact1 > F_contact2, i.e., the force of contact in Scenario 1 is greater than in Scenario 2, then the bug will have a better chance of survival in Scenario 1. This is because in Scenario 1, the force of contact between the blocks is greater, increasing the chances of the bug being displaced or surviving.
If F_contact2 > F_contact1, i.e., the force of contact in Scenario 2 is greater than in Scenario 1, then the bug will have a better chance of survival in Scenario 2.
So, to determine which scenario provides a better chance of survival for the bug, you need to compare the forces of contact in both cases using the given equations and values of F1 and F2.