Two-step problems in physics involve breaking down a complex problem into two simpler parts. The solution to the first part is then used as input for the second part, and the final answer is obtained by combining the results of both parts. These types of problems are commonly encountered in physics, and mastering them is essential for success in physics courses and in solving real-world problems that involve physics.
In this article, we will discuss the steps involved in solving two-step problems in physics and provide some examples to illustrate the process.
Steps for Solving Two-Step Problems in Physics
Step 1: Identify the Problem
The first step in solving a two-step problem in physics is to identify the problem. This involves reading the problem statement carefully, understanding the problem’s context and the physical principles involved, and identifying what is being asked in the problem.
Step 2: Break the Problem into Two Parts
Once you have identified the problem, the next step is to break it down into two simpler parts. This involves identifying the physical principles that are relevant to the problem and determining the best way to apply them. You should also consider what information you are given and what information you need to find to solve the problem.
Step 3: Solve the First Part
After breaking the problem into two parts, the next step is to solve the first part. This involves using the information given in the problem and applying the relevant physical principles to find a solution. Once you have found a solution, record it and move on to the second part of the problem.
Step 4: Use the First Part Solution to Solve the Second Part
The next step is to use the solution obtained in the first part to solve the second part of the problem. This involves using the solution from the first part as input and applying the relevant physical principles to find the final answer. Once you have found the final answer, check your work and make sure that it makes sense in the context of the problem.
Step 5: Check Your Answer
The final step is to check your answer to make sure that it is reasonable and makes sense in the context of the problem. You should also check your calculations to make sure that you have not made any errors.
Examples of Two-Step Problems in Physics
Example 1: A bullet of mass 0.02 kg is fired into a block of wood of mass 0.5 kg. The bullet enters the block and stops. If the block and the bullet move together after the collision, what is the velocity of the block and bullet immediately after the collision? Assume that the initial velocity of the bullet is 400 m/s.
Step 1: Identify the problem. The problem involves a bullet of mass 0.02 kg being fired into a block of wood of mass 0.5 kg. The problem asks for the velocity of the block and bullet immediately after the collision.
Step 2: Break the problem into two parts. The problem can be broken down into two parts: (1) finding the velocity of the bullet immediately after the collision, and (2) using the velocity of the bullet to find the velocity of the block and bullet immediately after the collision.
Step 3: Solve the first part. To find the velocity of the bullet immediately after the collision, we can use the principle of conservation of momentum. According to this principle, the total momentum of the system before the collision is equal to the total momentum of the system after the collision. In this case, the initial momentum of the system is:
P_initial = m_bullet * v_bullet_initial
where m_bullet is the mass of the bullet and v_bullet_initial is the initial velocity of the bullet. Substituting the given values, we get:
P_initial = 0.02 kg * 400 m/s = 8 kg m/s
After the collision, the bullet and the block move together, so their final velocity is the same. Let v be the final velocity of the bullet and block. The final momentum of the system is:
P_final = (m_bullet + m_block) * v
where m_block is the mass of the block. Substituting the given values, we get:
P_final = 0.52 kg * v
According to the principle of conservation of momentum, P_initial = P_final. Therefore, we have:
m_bullet * v_bullet_initial = (m_bullet + m_block) * v
Substituting the given values, we get:
0.02 kg * 400 m/s = (0.02 kg + 0.5 kg) * v
Solving for v, we get:
v = 3.85 m/s
The velocity of the bullet immediately after the collision is 3.85 m/s.
Step 4: Use the first part solution to solve the second part. To find the velocity of the block and bullet immediately after the collision, we can use the fact that they move together with the same velocity. Therefore, the velocity of the block and bullet immediately after the collision is also 3.85 m/s.
Step 5: Check your answer. We can check our answer by verifying that the principle of conservation of momentum is satisfied. The total momentum before the collision was:
P_initial = m_bullet * v_bullet_initial = 0.02 kg * 400 m/s = 8 kg m/s
The total momentum after the collision is:
P_final = (m_bullet + m_block) * v = (0.02 kg + 0.5 kg) * 3.85 m/s = 8 kg m/s
Since P_initial = P_final, our answer is consistent with the principle of conservation of momentum. Therefore, our answer of 3.85 m/s is reasonable and makes sense in the context of the problem.
Example 2: A car of mass 1000 kg traveling at 20 m/s collides with a stationary truck of mass 2000 kg. After the collision, the car and truck move together with a velocity of 10 m/s. What was the initial velocity of the truck?
Step 1: Identify the problem. The problem involves a car of mass 1000 kg colliding with a stationary truck of mass 2000 kg. The problem asks for the initial velocity of the truck.
Step 2: Break the problem into two parts. The problem can be broken down into two parts: (1) finding the velocity of the car and truck immediately after the collision, and (2) using the velocity of the car and truck to find the initial velocity of the truck.
Step 3: Solve the first part. To find the velocity of the car and truck immediately after the collision, we can use the principle of conservation of momentum. According to this principle, the total momentum of the system before the collision is equal to the total momentum of the system after the collision. In this case, the initial momentum of the system is:
P_initial = m_car * v_car_initial + m_truck * 0
where m_car is the mass of the car, v_car_initial is the initial velocity of the car, and m_truck is the mass of the truck. The second term in the equation is zero because the truck is stationary before the collision.
Substituting the given values, we get:
P_initial = 1000 kg * 20 m/s + 2000 kg * 0 = 20000 kg m/s
After the collision, the car and truck move together, so their final velocity is the same. Let v be the final velocity of the car and truck. The final momentum of the system is:
P_final = (m_car + m_truck) * v
Substituting the given values, we get:
P_final = 3000 kg * 10 m/s = 30000 kg m/s
According to the principle of conservation of momentum, P_initial = P_final. Therefore, we have:
m_car * v_car_initial = (m_car + m_truck) * v
Substituting the given values, we get:
1000 kg * v_car_initial = 3000 kg * 10 m/s
Solving for v_car_initial, we get:
v_car_initial = 30 m/s
The velocity of the car and truck immediately after the collision is 10 m/s.
Step 4: Use the first part solution to solve the second part. To find the initial velocity of the truck, we can use the fact that the car and truck move together with a velocity of 10 m/s after the collision. Therefore, the initial momentum of the system was:
P_initial = m_car * v_car_initial + m_truck * 0
Substituting the given values and using the fact that v_car_initial = 30 m/s
