/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 81 A car of mass \(400 \mathrm{~kg}... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 81

A car of mass \(400 \mathrm{~kg}\) and travelling at \(72 \mathrm{kmph}\) crashes into a truck of mass \(4000 \mathrm{~kg}\) and travelling at \(9 \mathrm{kmph}\), in the same direction. The car bounces back at a speed of \(18 \mathrm{kmph}\). The speed of the truck after the impact is (a) \(9 \mathrm{kmph}\) (b) \(18 \mathrm{kmph}\) (c) \(27 \mathrm{kmph}\) (d) \(36 \mathrm{kmph}\)

Short Answer

Expert verified
The speed of the truck after the impact is approximately \(16.2 \mathrm{kmph}\). So the closest answer is (b) \(18 \mathrm{kmph}\).

Step by step solution

01

Identify Initial momenta

Consider the masses and initial velocities of the car and the truck. The car has mass \(400 \mathrm{~kg}\) and travels at \(72 \mathrm{kmph}\) and the truck has mass \(4000 \mathrm{~kg}\) and is at \(9 \mathrm{kmph}\). Let's convert the speeds from \(kmph\) to \(\frac{m}{s}\) by dividing by \(3.6\). Thus, the momentum of the car before collision is \(400*72/3.6 \mathrm{~kg \cdot m/s}\) and for the truck it's \(4000*9/3.6 \mathrm{~kg \cdot m/s}\). Calculating these gives approximately \(8000 \mathrm{~kg \cdot m/s}\) for the car and \(10000 \mathrm{~kg \cdot m/s}\) for the truck.
02

Identify Final momenta of the car

The car's mass is \(400 \mathrm{~kg}\) and after collision, its speed is \(18 \mathrm{kmph}\) but in opposite direction. Convert this speed to \(\frac{m}{s}\). Therefore, momentum of the car after collision is \(400 * 18/3.6 \mathrm{~kg \cdot m/s}\) but in opposite direction, giving approximately \(-2000 \mathrm{~kg \cdot m/s}\).
03

Calculate Final momentum of the truck

Since the initial total momentum equals the final total momentum (conservation of momentum), and the truck's after-impact momentum is the only unknown, calculation is straightforward. Thus for truck, find the difference of initial total momentum and car's final momentum. Doing this calculation gives approximately \(18000 \mathrm{~kg \cdot m/s}\).
04

Find Final speed of the truck

We now know that the final momentum of the truck is \(18000 \mathrm{~kg \cdot m/s}\). As momentum = mass * velocity, we can find the velocity (or speed, as it's a scalar quantity) by dividing the total momentum by the mass of the truck. The mass of the truck is \(4000 \mathrm{~kg}\), and putting these in equation gives the speed of approximately \(4.5 \mathrm{m/s}\). Convert this back to \(kmph\) by multiplying by \(3.6\).

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.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Collision Mechanics
When two objects collide, a fascinating interplay of forces begins. **Collision mechanics** focuses on the interaction between these colliding bodies. In this exercise, we've a car and a truck heading in the same direction at different speeds.
These kinds of collisions are common in everyday life and are described by the principles of momentum and energy. For this exercise, we primarily leverage momentum conservation - meaning the total momentum before the collision is equal to the total momentum after the collision.
Key aspects of collision mechanics include:
  • Determining whether the collision is elastic or inelastic.
  • Preserving the law of conservation of momentum regardless of the type of collision.
  • Analyzing how speed and direction can affect the post-collision motion.
Understanding these mechanics assists in predicting how the truck and car move after their crash.
Initial and Final Velocity
In physics, velocity is the speed of an object concerning a direction. **Initial and final velocity** refers to the object's speed at the beginning and end of an event, such as our collision example.
Before the collision, the car and truck have specific initial velocities: 72 kmph and 9 kmph, respectively. After the crash, these velocities change due to interaction.
Key elements to grasp about initial and final velocity:
  • Initial velocity determines the momentum each object carries into the collision.
  • Final velocity is influenced by the forces exerted during the crash and the conservation of momentum.
  • The final velocity can differ in direction, as evidenced by the car bouncing back at 18 kmph.
Understanding these velocities helps in assessing the effects of collisions regarding speed and motion direction.
Mass and Speed Conversion
In dealing with collision exercises, knowing how to handle units for **mass and speed conversion** is crucial. Often, mass is in kilograms, while speed may initially be given in kilometers per hour (kmph).
For calculations involving momentum, it's practical to convert these speeds to meters per second (m/s).
Here's why and how:
  • Physics equations typically use m/s for speed to maintain unit consistency with other measurements, like acceleration.
  • Convert kmph to m/s by dividing the speed by 3.6. So, 72 kmph becomes 20 m/s.
  • Perform reverse conversion when needed: multiply m/s by 3.6 to revert to kmph.
Mastering these conversions ensures accurate calculations and deeper understanding of the forces at play during collisions.
Physics Problem Solving
Solving a physics problem, like the truck and car collision, involves applying logical steps meticulously. **Physics problem solving** requires unpacking the scenario and utilizing the appropriate laws and equations successfully.
Follow these steps for effective problem solving:
  • Identify and understand all given data, like mass and velocities.
  • Apply relevant physics laws, such as the conservation of momentum in this instance.
  • Convert units when necessary, ensuring consistency across calculations.
  • Perform calculations accurately, checking and rechecking observance of physical laws.
Through this structured process, solutions are clarified, leading to deeper comprehension of complex interactions, like our car and truck collision.

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

A sphere of mass \(0.1 \mathrm{~kg}\) is attached to a cord of \(1 \mathrm{~m}\) length. Starting from the height of its point of suspension this sphere hits a block of same mass at rest on a frictionless table, If the impact is elastic, then the kinetic energy of the block after the collisio (a) \(1 J\) (b) \(10 J\) (c) \(0.1 J\) (d) \(0.5 \mathrm{~J}\)

A smooth sphere of mass \(M\) moving with velocity \(u\) directly collides elastically with another sphere of mass \(m\) at rest. After collision their final velocities are \(V\) and \(v\) respectively. The value of \(v\) is (a) \(\frac{2 u M}{m}\) (b) \(\frac{2 u m}{M}\) (c) \(\frac{2 u}{1+\frac{m}{M}}\) (d) \(\frac{2 u}{1+\frac{M}{m}}\)

The ratio of masses of two balls is \(2: 1\) and before collision the ratio of their velocities is \(1: 2\) in mutually opposite direction. After collision each ball moves in an opposite direction to its initial direction. If \(e=(5 / 6)\), the ratio of speed of each ball before and after collision would be (a) \((5 / 6)\) times (b) Equal(c) Not related (d) Double for the first ball and half for the second ball

Two protons are situated at a distance of 100 fermi from each other. The potential energy of this system will be in \(\mathrm{eV}\) (a) \(1.44\) (b) \(1.44 \times 10^{3}\) (c) \(1.44 \times 10^{2}\) (d) \(1.44 \times 10^{4}\)

One sphere collides with another sphere of same mass at rest inelastically. If the value of coefficient of restitution is \(\frac{1}{2}\), the ratio of their speeds after collision shall be (a) \(1: 2\) (b) \(2: 1\) (c) \(1: 3\) (d) \(3: 1\)
See all solutions

Recommended explanations on Physics Textbooks

Electric Charge Field and Potential

Read Explanation

Waves Physics

Read Explanation

Torque and Rotational Motion

Read Explanation

Fields in Physics

Read Explanation

Astrophysics

Read Explanation

Solid State Physics

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.