Answered: An object of mass M= 25 kg is being…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

See similar textbooks

Related questions

Concept explainers

Topic Video

Question

An object of mass M= 25 kg is being pulled by two forces as shown in the image:

a) Determine the x and y component of each force.

b) Find the magnitude and direction of the total force acting on the object.

c)what is the magnitude and direction of its acceleration?

d) What third force would you need so that the object does not accelerate?(give magnitude and direction and show it in the diagram)

Expert Solution

Step 1

(a)

Givens
The magnitude of $\vec{F_{1}} i s F_{1} = 25 N$
The magnitude of $\vec{F_{2}} i s F_{2} = 35 N$
The vector $\vec{F_{1}}$ has two rectangular components
along x-axis
$F_{1} c o s 30^{o} = 25 c o s 30^{o} = 21.65 N$
along y-axis
$F_{1} s i n 30^{o} = 25 s i n 30^{o} = 12.5 N$
The vector $\vec{F_{2}}$ has two rectangular components
along the x-axis
$F_{2} c o s 40^{o} = 35 c o s 40^{o} = 26.8 N$
along negative y-axis
$- F_{2} s i n 40^{o} = - 35 s i n 40^{o} = - 22.5 N$
The net force along the x-axis is given by
$\vec{F_{x}} = F_{1} c o s 30^{o} + F_{2} c o s 40^{o} = 21.65 + 26.8 = 48.45 N$
The net force along the y-axis is given by
$\vec{F_{y}} = F_{1} s i n 30^{o} - - F_{2} s i n 40^{o} = 12.5 - 22.5 = - 10 N$

(b)

The net force is given by
$\vec{F} = \vec{F_{x}} + \vec{F_{y}} \vec{F} = (48.45 \hat{i} - 10 \hat{j}) N . . . . . . . . . . . . . (1)$
The magnitude of the vector $\vec{F}$ is given by
$F = \sqrt{(48.45)^{2} + (- 10)^{2}} F = 49.5 N$

Let us suppose that the resultant vector $\vec{F}$ makes an angle $θ$ w.r.t x-direction then
$t a n θ = (10 / 48.45) θ = \arctan (10 / 48.45) θ = 11.7 ° c l o c k w i s e w i t h t h e p o s i t i v e x - a x i s$

Step by step

Solved in 3 steps with 1 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.

Similar questions