Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 4: Problem 15

A car leaves the road traveling at \(110 \mathrm{km} / \mathrm{h}\) and hits a tree, coming to a stop in 0.14 s. What average force does a seatbelt exert on a \(60-\mathrm{kg}\) passenger during this collision?

Short Answer

Expert verified
The seatbelt exerts an average force of approximately \(13097.4 N\) on the passenger during the collision.

Step by step solution

01

Convert speed into m/s

First, convert the speed from kilometres per hour (\(km/h\)) to meters per second (\(m/s\)). This is done by multiplying the speed by \(1000/3600\). So, \(110 km/h = 110 \times \frac{1000}{3600} = 30.56 m/s.\)
02

Calculate acceleration

Next, calculate the acceleration of the passenger during the collision. Acceleration is defined as the change in velocity divided by the time it takes for the change to occur. In this case, the passenger's velocity changes from \(30.56 m/s\) to \(0 m/s\) in 0.14 seconds. So, acceleration (\(a\))= \(\frac{final velocity - initial velocity}{time}\) = \(\frac{0 - 30.56 m/s}{0.14 s}\) = \( -218.29 m/s^2\). The negative sign indicates that this is a deceleration.
03

Calculate force

Finally, calculate the force exerted on the passenger. According to Newton's second law of motion, force is the product of mass and acceleration. So, force (\(F\)) = mass (\(m\)) \times acceleration (\(a\)) = \(60 kg \times -218.29 m/s^2\)= \( -13097.4 N\). The negative sign indicates that the force is acted in the opposite direction to the movement of the car.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

You're asked to calibrate a device used to measure vertical acceleration in helicopters. The device consists of a mass \(m\) hanging from a massless spring of constant \(k .\) Your job is to express the acceleration as a function of the spring's stretch \(\Delta y\) from its equilibrium length. What's your expression?

A ball bounces off a wall with the same speed it had before it hit the wall. Has its momentum changed? Has a force acted on the ball? Has a force acted on the wall? Relate your answers to Newton's laws of motion.

An F-16 jet fighter has mass 12 Mg and engine thrust 132 kN. An Airbus \(A-380\) has mass \(560 \mathrm{Mg}\) and total engine thrust \(1.5 \mathrm{MN}\). Could either aircraft climb vertically with no lift from its wings? If so, what vertical acceleration could it achieve?

You step into an elevator, and it accelerates to a downward speed of \(9.2 \mathrm{m} / \mathrm{s}\) in \(2.1 \mathrm{s} .\) How does your apparent weight during this time compare with your actual weight?

In paddling a canoe, you push water backward with your paddle. What force actually propels the canoe forward?
See all solutions

Recommended explanations on Physics Textbooks

Medical Physics

Read Explanation

Space Physics

Read Explanation

Conservation of Energy and Momentum

Read Explanation

Force

Read Explanation

Torque and Rotational Motion

Read Explanation

Magnetism and Electromagnetic Induction

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free