Applying Newton's laws to traveling car

In summary, a 46 kg passenger in a car traveling at 62 km/h hits a bridge abutment and moves forward 57 cm before being brought to rest by an inflated air bag. Using the constant acceleration formula, the magnitude of force acting on the passenger's upper torso can be calculated as F = m*a.
  • #1
iamkristing
33
0
1. A car traveling at 62 km/h hits a bridge abutment. A passenger in the car moves forward a distance of 57 cm (with respect to the road) while being brought to rest by an inflated air bag. What magnitude of force (assumed constant) acts on the passenger's upper torso, which has a mass of 46 kg?




Homework Equations



F= m*a



The Attempt at a Solution



I know its the force of the car= - the force of the bridge. But I am not exactly sure how to put into that equation the distance the person traveled and the velocity of the car
 
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  • #2
Forget the car, forget the bridge, hell, even forget the person. All you need to know is that a mass of 46Kg was decelerated from 62 Km/h to 0 over a distance of 57cm.

You can use constant acceleration formulae to determine the acceleration, then from that determine the force with F = ma.
 
  • #3
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To solve this problem, we can use Newton's second law, which states that the force acting on an object is equal to its mass multiplied by its acceleration. In this case, the force acting on the passenger's upper torso is the force of the airbag pushing back against the passenger to bring them to a stop.

First, we need to convert the car's velocity from km/h to m/s, since the unit of acceleration is meters per second squared (m/s^2). We can do this by dividing 62 km/h by 3.6, which gives us a velocity of 17.22 m/s.

Next, we need to calculate the acceleration of the passenger. We can do this by using the equation v^2 = u^2 + 2as, where v is the final velocity (0 m/s in this case), u is the initial velocity (17.22 m/s), a is the acceleration, and s is the distance traveled (0.57 m in this case). Rearranging the equation, we get a = (v^2 - u^2) / 2s. Plugging in the values, we get a = (-17.22^2) / (2*0.57) = -528.86 m/s^2.

Now, we can use Newton's second law to calculate the force acting on the passenger's upper torso. F = m*a, where m is the mass of the passenger (46 kg) and a is the acceleration we just calculated (-528.86 m/s^2). Plugging in the values, we get F = 46 kg * (-528.86 m/s^2) = -24337.56 N.

Therefore, the magnitude of the force acting on the passenger's upper torso is approximately 24337.56 N. This force is negative because it is in the opposite direction of the passenger's motion. This force is also assumed to be constant, as stated in the problem.
 

Related to Applying Newton's laws to traveling car

What are Newton's laws?

Newton's laws are three fundamental principles of physics that describe the behavior of objects in motion. The first law states that an object will remain at rest or in uniform motion in a straight line unless acted upon by an external force. The second law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. The third law states that for every action, there is an equal and opposite reaction.

How do Newton's laws apply to traveling cars?

When a car is in motion, it is subject to all three of Newton's laws. The first law explains why a car will continue moving in a straight line at a constant speed unless acted upon by a force. The second law explains how a car accelerates when the gas pedal is pressed, as the force from the engine overcomes the car's mass. The third law explains the equal and opposite forces involved in braking, as the car's brake pads exert a force on the wheels to slow down the car.

Why is it important to understand Newton's laws when driving a car?

Understanding Newton's laws can help drivers make informed decisions while on the road. For example, knowing that a car will continue moving forward unless acted upon by a force can help drivers maintain a safe braking distance. Understanding the relationship between force, mass, and acceleration can also help drivers adjust their speed and braking to avoid collisions.

How do Newton's laws apply to different types of cars?

Newtons's laws apply to all types of cars, regardless of their size, speed, or model. However, certain factors such as the car's weight, aerodynamics, and engine power may affect how these laws manifest in the car's movement. For example, a heavier car will have a greater mass and therefore require more force to accelerate or decelerate compared to a lighter car.

Can Newton's laws be used to improve car design?

Yes, Newton's laws are often used in the design and engineering of cars. Engineers use these laws to calculate and optimize factors such as engine power, weight distribution, and aerodynamics to improve a car's performance. For example, understanding how different forces act on a car can help engineers design more efficient braking systems or reduce drag to improve a car's speed and fuel efficiency.

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