🌀 Detailed Explanation of Momentum
Momentum is a key topic in Year 10 Physics, especially for those studying the Higher Tier. Understanding momentum helps us explain how objects move and interact during collisions. It is a fundamental concept in the study of motion and forces.
❓ What is Momentum?
Momentum is a measure of how hard it is to stop a moving object. It depends on two things: the object’s mass and its velocity. The more mass an object has, or the faster it moves, the greater its momentum will be. Momentum tells us about the quantity of motion an object has.
📐 Definition of Momentum
Momentum is defined as the product of an object’s mass and its velocity. It is a vector quantity, which means it has both size and direction.
🧮 Formula for Momentum
The formula to calculate momentum is:
Momentum (p) = mass (m) × velocity (v)
Where:
- p is momentum, measured in kilogram metres per second (kg·m/s)
- m is mass in kilograms (kg)
- v is velocity in metres per second (m/s)
🔍 Why is Momentum Important in Motion?
Momentum helps us understand how moving objects behave in different situations. For example:
- When two cars collide, their momenta before and after the crash help explain the forces and motions involved.
- In sports, a football’s momentum changes when kicked, showing how mass and velocity affect its movement.
- Momentum conservation is a key principle where, in an isolated system, total momentum remains constant unless acted on by an external force.
📋 Summary
- Momentum depends on both mass and velocity.
- It is a vector quantity, meaning direction matters.
- The formula p = m × v is straightforward but powerful for solving motion problems.
- Studying momentum enables us to predict and understand collisions and many real-life situations involving moving objects.
Understanding momentum is essential for grasping many other physics concepts related to forces and motion at Key Stage 4. Keep practising problems involving the momentum formula to become confident in explaining and calculating momentum!
📝 10 Examination-style 1-Mark Questions on Momentum with 1-Word Answers
- What is the product of mass and velocity called?
Answer: Momentum - Is momentum a vector or scalar quantity?
Answer: Vector - Which physical law explains the conservation of momentum?
Answer: Newton’s - What does a change in momentum require?
Answer: Force - What does ‘p’ usually represent in physics equations on momentum?
Answer: Momentum - Is momentum conserved in an isolated system? (Yes or No)
Answer: Yes - What is the SI unit of momentum?
Answer: Kilogram-metre-per-second - What type of collision conserves both momentum and kinetic energy?
Answer: Elastic - What is the name of the quantity calculated as mass times velocity?
Answer: Momentum - What does impulse change in a moving object?
Answer: Momentum
📝 10 Examination-Style 2-Mark Questions on Momentum with 1-Sentence Answers
- What is the formula for momentum?
Momentum is calculated using the formula p = mv, where p is momentum, m is mass, and v is velocity. - What are the units of momentum?
Momentum is measured in kilogram metres per second (kg·m/s). - If an object’s mass doubles while its velocity remains the same, what happens to its momentum?
The momentum doubles because momentum is directly proportional to mass. - Define the principle of conservation of momentum.
The total momentum before a collision is equal to the total momentum after the collision in a closed system with no external forces. - How does increasing the time of impact affect the force during a collision?
Increasing the impact time decreases the force experienced, according to the impulse-momentum relationship. - What is meant by ‘impulse’ in physics?
Impulse is the change in momentum caused by a force acting over a period of time. - How would you calculate the change in momentum of an object?
Change in momentum is calculated by subtracting the initial momentum from the final momentum. - Why do safety features like airbags increase the time of collision in a car crash?
Airbags increase collision time to reduce the force on passengers by decreasing the rate of change of momentum. - How does velocity affect momentum if mass remains constant?
Momentum increases proportionally as velocity increases when mass is constant. - During a perfectly inelastic collision, what happens to the two colliding objects?
They stick together and move with a common velocity after the collision.
📝 10 Examination-style 4-Mark Questions on Momentum with Detailed 6-Sentence Answers
Question 1: Define momentum and state its unit.
Answer:
Momentum is a measure of the quantity of motion an object has. It depends on both the mass and velocity of the object. The formula for momentum (p) is p = mass (m) × velocity (v). Momentum is a vector quantity, meaning it has both magnitude and direction. The unit of momentum in the SI system is kilogram metres per second (kg·m/s). This unit shows how much mass is moving and how fast.
Question 2: A car of mass 800 kg is moving at 20 m/s. Calculate the momentum of the car.
Answer:
To calculate momentum, use the formula p = m × v. The mass (m) is 800 kg, and velocity (v) is 20 m/s. So, p = 800 × 20 = 16,000 kg·m/s. This shows the car has a momentum of 16,000 kg·m/s in the direction it is moving. Momentum tells us how hard it is to stop the car. The higher the momentum, the harder it is to change the car’s motion.
Question 3: Explain why momentum is conserved in a closed system during a collision.
Answer:
In a closed system, no external forces act on the objects involved. According to the law of conservation of momentum, the total momentum before a collision equals the total momentum after the collision. This happens because forces internal to the system occur in pairs that are equal and opposite. These forces change individual momenta but not the total momentum. Therefore, the total momentum remains constant. This principle is very useful for analysing collisions in physics.
Question 4: Two ice skaters, one of mass 50 kg and another of mass 70 kg, push each other apart on frictionless ice. If the 50 kg skater moves away at 3 m/s, find the velocity of the 70 kg skater.
Answer:
Before pushing, both skaters are at rest, so total momentum is zero. After pushing, the total momentum must still be zero (conservation of momentum). The momentum of the 50 kg skater is 50 × 3 = 150 kg·m/s. Let the velocity of the 70 kg skater be v m/s. Their momentum is 70 × v. Since total momentum is zero, 150 + (70 × v) = 0. Solving gives v = -150/70 = -2.14 m/s, meaning the 70 kg skater moves in the opposite direction at 2.14 m/s.
Question 5: A ball of mass 0.5 kg moving at 8 m/s collides with a stationary ball of mass 0.5 kg. After collision, the first ball stops. What is the velocity of the second ball?
Answer:
Using conservation of momentum, total momentum before = total momentum after. Before collision, the first ball’s momentum is 0.5 × 8 = 4 kg·m/s, and the second ball is stationary so its momentum is 0. After collision, the first ball stops so its momentum is zero. Therefore, the second ball must have the total momentum, 4 kg·m/s. Since its mass is 0.5 kg, velocity = momentum ÷ mass = 4 ÷ 0.5 = 8 m/s. The second ball moves at 8 m/s after the collision.
Question 6: A stationary object explodes into two pieces of masses 3 kg and 2 kg. If the 3 kg piece moves at 4 m/s to the right, find the velocity of the 2 kg piece.
Answer:
Since the object was stationary before the explosion, total momentum was zero. The total momentum after the explosion still equals zero. The 3 kg piece has momentum 3 × 4 = 12 kg·m/s to the right. Let the velocity of the 2 kg piece be v, moving left. Its momentum is then 2 × v. Using conservation of momentum: 12 + 2v = 0. Solving for v gives v = -12/2 = -6 m/s. So, the 2 kg piece moves left at 6 m/s.
Question 7: Why is a momentum-changing event that happens over a longer time less forceful than one that happens over a shorter time?
Answer:
Force is related to the change in momentum over time (Force = change in momentum ÷ time). If the same change in momentum happens over a longer time, the divisor is bigger. This makes the force smaller. So, when a momentum change occurs slowly, the force involved is less. This explains why wearing seat belts and airbags helps reduce injury. They increase the time over which momentum changes, decreasing the force on the body.
Question 8: A cyclist of mass 70 kg is moving at 5 m/s and applies brakes to stop in 4 seconds. Calculate the average braking force applied.
Answer:
First, calculate the change in momentum: initial momentum = 70 × 5 = 350 kg·m/s, final momentum = 0. Change in momentum = 350 kg·m/s. Using Force = change in momentum ÷ time, force = 350 ÷ 4 = 87.5 N. The force is applied opposite to the cyclist’s motion to slow them down. This average force brings the cyclist to rest safely. It shows how braking force relates to change in momentum.
Question 9: Explain how airbags help to reduce injuries in a car crash using the concept of momentum.
Answer:
During a crash, a person’s momentum changes very quickly. This sudden change causes a large force on the person. Airbags inflate quickly and increase the time taken for the person to stop. This longer stopping time reduces the force on the person, according to Force = change in momentum ÷ time. By reducing the force, airbags lower the risk of serious injury. This shows the importance of momentum change and time in safety devices.
Question 10: What is meant by an inelastic collision, and how does momentum behave during it?
Answer:
An inelastic collision is when objects collide and stick together or deform, losing kinetic energy. However, the total momentum before and after the collision is conserved. This is because external forces are negligible during the collision. The kinetic energy is not conserved, but momentum is always conserved in closed systems. In inelastic collisions, you use conservation of momentum to find final velocities. This principle helps us solve many physics problems involving collisions.
📝 10 Examination-style 6-Mark Questions on Momentum with 10-Sentence Answers
Question 1: Explain what is meant by momentum and how it relates to mass and velocity.
Answer:
Momentum is a measure of the quantity of motion that an object has. It is defined as the product of an object’s mass and its velocity, which means momentum depends directly on both these factors. The formula for momentum is p = m × v, where p is momentum, m is mass, and v is velocity. A larger mass or a higher velocity will produce a greater momentum. Momentum is a vector quantity, so it has both magnitude and direction. This means the direction of the velocity affects the momentum direction. For example, two objects with the same mass but moving in opposite directions will have momenta in opposite directions. Momentum helps to predict how objects behave in collisions. It is conserved in closed systems, meaning total momentum before and after a collision stays the same. Understanding momentum is important because it explains how forces affect the motion of objects during impacts.
Question 2: Describe the principle of conservation of momentum and give an example of where it applies.
Answer:
The principle of conservation of momentum states that the total momentum before an event is equal to the total momentum after the event, as long as no external forces act on the system. This means momentum can be transferred from one object to another but the overall amount stays the same. An example is a collision between two ice skaters pushing off each other on a frictionless surface. Before pushing, their total momentum is zero because they are both stationary. After pushing, one skater moves forward and the other moves backward, but the momentum of one skater is equal and opposite to the other. This shows how momentum is conserved. The law is a key concept in understanding collisions and helps explain outcomes without needing to know all the forces involved. Conservation of momentum applies in everyday events like car crashes or playing pool. It helps engineers design safer vehicles by understanding how momentum transfers during impacts. This principle also plays a critical role in physics problems involving multiple objects interacting.
Question 3: How do you calculate the change in momentum and why is it important in physics?
Answer:
The change in momentum is calculated by subtracting the initial momentum from the final momentum of an object. The formula for change in momentum is Δp = m(v_f – v_i), where v_f is the final velocity and v_i is the initial velocity. It is important because it shows how much an object’s motion has been altered. A larger change means a bigger effect on the object’s motion. Change in momentum is closely related to the force applied, as described by Newton’s second law in its momentum form: force equals the rate of change of momentum. This means a greater force or longer time applying the force results in a bigger change in momentum. In practical terms, it explains why airbags in cars reduce injuries – they increase the impact time, reducing the force. Understanding change in momentum helps scientists and engineers control motions and impacts. It is vital in designing helmets, sports equipment, and vehicle safety systems. By calculating change in momentum, we can predict effects of collisions and improve safety.
Question 4: Explain the difference between elastic and inelastic collisions in terms of momentum.
Answer:
In both elastic and inelastic collisions, the total momentum of the system is conserved. However, the main difference lies in how kinetic energy behaves. In an elastic collision, both momentum and kinetic energy are conserved. This means the objects bounce off each other without losing kinetic energy as heat or deformation. Examples include billiard balls hitting each other. In contrast, an inelastic collision conserves momentum but not kinetic energy. Some kinetic energy is transformed into other forms like heat, sound, or deformation energy. A car crash is a common example where vehicles deform, losing kinetic energy. Although kinetic energy decreases, the total momentum before and after the collision is the same, obeying conservation of momentum. Understanding this difference is important for predicting outcome and damage in collisions. It also helps in calculating speeds after impact. Elastic collisions are easier to model but less common in real-life scenarios.
Question 5: Why is momentum considered a vector quantity? Give an example to support your answer.
Answer:
Momentum is considered a vector quantity because it has both magnitude and direction, just like velocity. The direction of momentum is always the same as the velocity of the object. This means if an object moves in a certain direction, its momentum points that way too. For example, if a car is moving east at a certain speed, its momentum vector points east. If the same car reverses direction and moves west at the same speed, the momentum vector points west. This directional property is crucial when adding momenta of different objects. For instance, two cars moving in opposite directions will have momenta in opposite directions, which can cancel out partially when calculating the total momentum. This vector nature helps in solving problems involving collisions and forces in more than one dimension. It also explains why an object reversing direction experiences a change in momentum. Without direction, it would be impossible to fully describe motion and interactions.
Question 6: How does increasing the impact time affect the force experienced during a collision?
Answer:
Increasing the impact time during a collision reduces the force experienced by the objects involved. This is because force is related to the change in momentum divided by the time taken for that change, shown by the equation F = Δp / Δt. If the change in momentum remains the same but the impact time is longer, the force must be smaller. For example, when a car crashes, airbags increase the time over which the driver’s momentum changes, reducing the force on the driver and lowering injury risk. Similarly, sports helmets extend the impact time, lessening force and protecting the head. Conversely, if the impact time is very short, the force can be very large, causing more damage. This principle is key in safety design to minimise injury. Understanding impact time helps in choosing materials and devices that absorb impact efficiently. Increasing impact time is a practical safety measure based on momentum principles.
Question 7: Calculate the momentum of a 2 kg ball moving at 5 m/s to the right.
Answer:
Momentum is calculated using the formula p = m × v, where m is the mass and v is the velocity. For the 2 kg ball moving at 5 m/s, the momentum is:
p = 2 × 5 = 10 kg m/s.
Since the velocity is to the right, the momentum direction is to the right as well. Therefore, the momentum of the ball is 10 kg m/s to the right. This value tells us how much motion the ball has and in which direction. Higher momentum means it will be harder to stop the ball. This calculation assumes the velocity is constant and the mass does not change. Momentum can be positive or negative depending on direction chosen as positive. Here, right is positive. Understanding this helps predict how objects behave when forces act on them.
Question 8: Describe what happens to momentum in a two-object collision when one object is stationary before the collision.
Answer:
When one object is stationary before a collision, its initial momentum is zero because velocity is zero. The total momentum before collision is therefore just the momentum of the moving object. When the collision happens, momentum is transferred from the moving object to the stationary one. The moving object slows down, losing some momentum, while the stationary object gains velocity and momentum. The total momentum after the collision equals the total before, showing conservation of momentum. How the momentum is shared depends on the masses and whether the collision is elastic or inelastic. In an elastic collision, both objects might move off with different speeds but total momentum stays constant. In an inelastic collision, objects could stick together and move as one. This concept is important in understanding impacts and sports interactions. It shows how motion can be transferred between objects.
Question 9: Explain why external forces affect whether momentum is conserved in a system.
Answer:
Momentum is only conserved in a system if no external forces act on it. External forces, such as friction, air resistance, or applied pushes, add or remove momentum from the system. This means the total momentum can change because momentum is not isolated inside the system. For example, a football rolling on grass slows down because friction opposes its motion, reducing momentum. In contrast, in space where almost no external forces act, momentum stays constant for objects moving freely. When external forces act, they cause acceleration or deceleration, changing velocity and thus momentum. The concept of conservation of momentum applies best to closed or isolated systems with no external interference. This idea helps physicists idealise problems to understand natural laws. Identifying external forces is crucial in experiments and calculations. Without considering external forces, predictions about momentum would be inaccurate.
Question 10: How can the concept of momentum help in designing safer cars?
Answer:
The concept of momentum helps engineers design cars that reduce injuries during crashes. Understanding momentum shows that stopping a car suddenly involves a large change in momentum. To reduce the force felt by passengers, cars are designed to increase the time over which the momentum changes, decreasing impact force. Features like crumple zones deform in collisions, absorbing energy and extending the impact time. Seat belts stretch slightly to increase stopping time for the passengers. Airbags inflate to cushion impact, also increasing impact time. By controlling momentum change, safer car designs minimise injury. Momentum principles guide materials choice and structural design. Engineers simulate crashes to measure momentum changes and forces involved. Safer cars are an application of physics concepts protecting lives. This makes momentum a key topic in vehicle safety engineering.
