Case Study
Passage with linked questions
Case Set 1
Case AnalysisPassage
Rahul is travelling in a bus when the driver suddenly applies the brakes. Rahul, who was standing in the aisle, lurches forward and nearly falls. His friend Priya, seated and wearing a seatbelt, remains safe. Later, when the bus starts again from rest with a jerk, Rahul is thrown backward. Priya explains to Rahul that both incidents are caused by the same fundamental property of matter. She tells him that this property was first formally described by Galileo and later incorporated by Newton into his laws of motion. The property explains why objects resist any change in their state of rest or uniform motion. Understanding this concept helps engineers design safer vehicles with headrests, seatbelts, and airbags to protect passengers during sudden changes in motion.
Question 1: Name the property of matter responsible for Rahul being thrown forward when the bus brakes suddenly, and state the law that describes this property.
- The property is inertia — the tendency of a body to resist any change in its state of rest or uniform motion.
- When the bus brakes, the floor decelerates rapidly, but Rahul's body continues to move forward with its original velocity due to inertia, making him lurch forward.
- Newton's First Law of Motion describes this property: every body continues in its state of rest or uniform motion in a straight line unless compelled by an external force to change that state.
Question 2: Why is Rahul thrown backward when the bus starts suddenly from rest, even though no one pushes him?
- When the bus accelerates forward, friction between the floor and Rahul's feet accelerates his feet forward along with the bus.
- However, the rest of Rahul's body remains at rest (in its original state) due to inertia, causing a relative backward displacement of the upper body relative to the bus.
- The human body is deformable, allowing relative displacement between feet and upper body; muscular forces then bring the whole body to the bus's velocity, but the initial backward jerk is due to inertia of the upper body.
Question 3: Priya's seatbelt exerts a force of 450 N on her (mass 50 kg) when the bus decelerates to rest from 54 km/h in 3 s. Verify using Newton's Second Law whether the seatbelt force is consistent with the deceleration, and identify the action-reaction pair involving the seatbelt.
- Initial speed u = 54 km/h = 15 m s⁻¹; final speed v = 0; time = 3 s; deceleration a = (0 − 15)/3 = −5 m s⁻².
- By Newton's Second Law, the net force needed = ma = 50 × 5 = 250 N; the seatbelt force of 450 N also has to overcome any additional forward tendency, and the net retarding force on Priya is 250 N backward — this is consistent since the seatbelt provides at least the required force.
- The action-reaction pair: the seatbelt exerts a backward force of 450 N on Priya (action); Priya exerts an equal and opposite forward force of 450 N on the seatbelt (reaction); these act on different bodies and cannot cancel each other.