Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 4: Problem 497

A force of \((2 \mathrm{i} \wedge+3 j \wedge-\mathrm{k} \wedge) \mathrm{N}\) acts on a body for 5 second, produces a displacement of $(3 i \wedge+5 j \wedge+k \wedge)$. What was the power used? (A) \(4 \mathrm{~W}\) (B) \(20 \mathrm{~W}\) (C) \(21 \mathrm{~W}\) (D) \(4.2 \mathrm{~W}\)

Short Answer

Expert verified
The power used by the force is 4 W.

Step by step solution

01

Calculate dot product of force and displacement vectors

To calculate the dot product of the force and displacement vectors, multiply the respective components and add them together: Dot product = (Force in x) × (Displacement in x) + (Force in y) × (Displacement in y) + (Force in z) × (Displacement in z) Dot product = (2)(3) + (3)(5) + (-1)(1) = 6 + 15 - 1 = 20 J
02

Calculate power used by the force

Now that we have the work done by the force (20 J), we can divide that by the time (5 seconds) to calculate the power: Power = \(\frac{\text{Work done}}{\text{Time}}\) Power = \(\frac{20 \text{ J}}{5 \text{ s}}\) Power = 4 W So, the correct answer is (A) 4 W.

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

A ball dropped from a height of \(4 \mathrm{~m}\) rebounds to a height of $2.4 \mathrm{~m}$ after hitting the ground. Then the percentage of energy lost is (A) 40 (B) 50 (C) 30 (D) 600

A \(60 \mathrm{~kg}\) JATAN with \(10 \mathrm{~kg}\) load on his head climbs 25 steps of \(0.20 \mathrm{~m}\) height each. What is the work done in climbing ? \(\left(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}\right)\) (A) \(5 \mathrm{~J}\) (B) \(350 \mathrm{~J}\) (C) \(100 \mathrm{~J}\) (D) \(3500 \mathrm{~J}\)

A ball of mass \(5 \mathrm{~kg}\) is striding on a plane with initial velocity of \(10 \mathrm{~m} / \mathrm{s}\). If co-efficient of friction between surface and ball is \((1 / 2)\), then before stopping it will describe \(\ldots \ldots\) \(\left(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}\right)\) (A) \(12.5 \mathrm{~m}\) (B) \(5 \mathrm{~m}\) (C) \(7.5 \mathrm{~m}\) (D) \(10 \mathrm{~m}\)

The mass of a car is \(1000 \mathrm{~kg}\). How much work is required to be done on it to make it move with a speed of \(36 \mathrm{~km} / \mathrm{h}\) ? (A) \(2.5 \times 10^{4} \mathrm{~J}\) (B) \(5 \times 10^{3} \mathrm{~J}\) (C) \(500 \mathrm{~J}\) (D) \(5 \times 10^{4} \mathrm{~J}\)

A bullet of mass \(0.10 \mathrm{~kg}\) moving with a speed of $100 \mathrm{~m} / \mathrm{s}\( enters a wooden block and is stopped after a distance of \)0.20 \mathrm{~m}$. What is the average resistive force exerted by the block on the bullet ? (A) \(2.5 \times 10^{2} \mathrm{~N}\) (B) \(25 \mathrm{~N}\) (C) \(25 \times 10^{2} \mathrm{~N}\) (D) \(2.5 \times 10^{4} \mathrm{~N}\)
See all solutions

Recommended explanations on English Textbooks

Synthesis Essay

Read Explanation

English Grammar

Read Explanation

Argumentative Essay

Read Explanation

Cues and Conventions

Read Explanation

5 Paragraph Essay

Read Explanation

Email

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