Explanation of the Solutions for Given Physics Problems
Have you come across challenging problems in physics that seemed to be a stepping stone to understanding more complex concepts? In this article, we will delve into the solutions for a few physics problems, explaining the steps and reasoning behind each one. Let's begin with the problem that focuses on recombination:
Recombination Problem
The first problem we will tackle is the recombination problem. We are given the total progeny, among which a certain number is recombinant. The answer is marked as b: 20 cm, with the unit cm representing centimorgan.
Solution:
To solve this, we need to calculate the recombination fraction first. The formula for recombination is given by:
Recombination fraction (Number of recombinant progeny / Total progeny) * 100
Using the given values (100 total progeny and 20 recombinant progeny), the calculation goes as follows:
Recombination fraction (20 / 100) * 100 20%
Since 1 recombination unit is equivalent to 1 centimorgan (cm), the result in percentage directly translates to 20 cm.
Power Calculation Problem
The second problem revolves around the calculation of power. To solve this, we need to understand the relationship between power, force, and velocity. The formula for power in terms of force and velocity is:
Power (P) Force (F) * Velocity (V)
The force is determined using the drag force formula:
Drag Force (Fd) 0.5 * A * Cd * ρ * V2
Here, A is the cross-sectional area, Cd is the drag coefficient, ρ is the density of the medium, and V is the velocity. The given velocity is in km/h, which needs to be converted to m/s (1 km/h 5/18 m/s).
Solution:
Let's break down the steps for the solution:
Convert the velocity from km/h to m/s.
100 km/h 100 * (5/18) 27.78 m/s
Calculate the drag force (Fd):
Fd 0.5 * 2 * 0.42 * 1.23 * (27.78)2
Compute the power (P):
P Fd * V 398.61 * 27.78 11075.8 W 11.08 kW
Relative Velocities Problem
The third problem involves determining the relative velocities and acceleration of two balls. The solution requires an understanding of relative motion and motion in parabolic paths.
Solution:
To solve this, we need to find the initial velocities of the balls relative to a person and then determine the final velocities considering the acceleration due to gravity.
Calculate the initial velocities:
Uapx v - v/2 v/2
Uapy 0 - 0 0
Ubpx 0 - v/2 -v/2
Ubpy 0 - 0 0
Determine the final velocities considering the acceleration due to gravity (g):
Vapx Uapx - Aapx * T v/2 - 0 * T v/2
Vbpx -v/2
Vapy Uapy - Aapy * T 0 - g * T -gT
Vbpy -gT
From the final velocities, it is evident that both balls will follow a parabolic path.
Conclusion
Understanding and solving physics problems requires a clear grasp of the fundamental principles. Whether it's recombination, power calculations, or relative motion, the key is to break down the problem into smaller, manageable steps and apply the appropriate formulas and concepts.