A car is moving 10m/s and crashes into a tree and stops in 0.26s. The mass of the passenger is 70kg. Calculate the force the seatbelt exerts on a passenger in the car to an abrupt stop.
To calculate the force exerted on a passenger, we can use Newton's second law of motion, which states that force (F) is equal to mass (m) multiplied by acceleration (a).
First, let's calculate the acceleration of the car as it comes to an abrupt stop.
We are given that the car is moving at a speed of 10 m/s and comes to a stop in 0.26 s.
Using the formula for acceleration:
acceleration = change in velocity / time
Change in velocity = final velocity - initial velocity
= 0 - 10
= -10 m/s
acceleration = (-10 m/s) / (0.26 s)
= -38.46 m/s^2
The negative sign indicates that the car is decelerating.
Next, let's calculate the force exerted on the passenger using Newton's second law.
force (F) = mass (m) × acceleration (a)
mass of the passenger (m) = 70 kg
acceleration (a) = -38.46 m/s^2
force (F) = 70 kg × (-38.46 m/s^2)
= -2692.2 N
The force exerted by the seatbelt on the passenger to an abrupt stop is 2692.2 Newtons in the opposite direction of the car's motion.
Contributions of the Newton's law in seatbelts
Newton's laws of motion are fundamental principles in physics that describe the relationship between the motion of an object and the forces acting upon it. In the context of seatbelts, Newton's laws are highly relevant and provide valuable insights into their functioning and effectiveness.
1. Newton's First Law of Motion: Also known as the law of inertia, this law states that an object at rest will stay at rest, and an object in motion will stay in motion at a constant velocity unless acted upon by an external force. In the case of seatbelts, this law highlights the importance of keeping passengers restrained to prevent them from being propelled forward during a sudden deceleration (such as during a car crash). The seatbelt applies a force on the passenger to prevent them from continuing to move forward, in accordance with this law.
2. Newton's Second Law of Motion: This law relates the force exerted on an object, its mass, and the resulting acceleration. In the case of seatbelts, this law helps us understand the forces exerted on passengers during a crash. The seatbelt exerts a force on the passenger to stop their forward motion, as we calculated in the previous calculation. This force is directly proportional to the mass of the passenger and the acceleration experienced during the crash.
3. Newton's Third Law of Motion: This law states that for every action, there is an equal and opposite reaction. In the context of seatbelts, this law helps us understand that the force exerted by the seatbelt on the passenger is directly countered by an equal and opposite force exerted by the passenger on the seatbelt. This action-reaction pair of forces helps to restrain the passenger and prevent them from being thrown forward in a crash.
Overall, Newton's laws of motion provide a scientific foundation for understanding the importance of seatbelts and how they work to protect passengers during a car crash. They highlight the need to counteract the forces generated during sudden deceleration events and emphasize the role of seatbelts in preventing severe injuries by restraining passengers.
To calculate the force exerted by the seatbelt on the passenger, we can use Newton's second law of motion, which states that force is equal to mass times acceleration.
First, we need to determine the deceleration of the car. To do this, we can use the formula:
acceleration = (final velocity - initial velocity) / time
Given:
Initial velocity (u) = 10 m/s
Final velocity (v) = 0 m/s
Time (t) = 0.26 s
Using the formula, we can calculate the acceleration:
acceleration = (0 - 10) / 0.26
= -38.4615 m/s²
The negative sign indicates that the car is decelerating.
Now, we can calculate the force using Newton's second law:
force = mass * acceleration
Given:
Mass (m) = 70 kg
Acceleration (a) = -38.4615 m/s²
Calculating the force:
force = 70 kg * (-38.4615 m/s²)
= -2692.307 N
The force exerted by the seatbelt on the passenger is approximately 2692.307 Newtons. Since the force is negative, it indicates that the force is acting in the opposite direction of the car's motion, helping to stop the passenger.