Can i geth help with this problem An object that weighs 68.0 N is pulled on a horizontal surface by a force of 82.6 N,at angle 36.0 degrees to the right. The coefficient of kinetic friction is 0.204.a) What is the acceleration of the object?b) how fast the object is moving after traveling 1.24 m, starting from rest?IVE

Answered: a) What is the acceleration of the…

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)...

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Can i geth help with this problem

An object that weighs 68.0 N is pulled on a horizontal surface by a force of 82.6 N,
at angle 36.0 degrees to the right. The coefficient of kinetic friction is 0.204.
a) What is the acceleration of the object?
b) how fast the object is moving after traveling 1.24 m, starting from rest?
IVE

Expert Solution

Step 1

Given data:

The weight of the object is: $W = 68 N$

The force on the object is: $F = 82.6 N$

The angle of force is: $θ = 36^{\circ}$

The kinetic friction's coefficient is: $μ_{k} = 0.204$

The acceleration of the object is: $a$

The initial velocity of the object is: $u = 0$

The final velocity of the object after traveling 1.24 m is: $v$

The distance traveled by an object is: $s = 1.24 m$

(a)The component of force is calculated as,

$\begin{array}{rcl} Horizontal force on the object & = & F \cos (θ) \\ Vertical upward force on the object & = & F \sin (θ) \\ The upward normal force & = & N \\ The vertical downward force & = & W = m g \end{array}$

Applying Newton's second law of motion along the horizontal direction,

$\begin{array}{rcl} F_{n e t} & = & m a \\ F \cos (θ) - μ_{k} (W - F \sin (θ)) & = & (\frac{W}{g}) a \\ 82.6 N \times \cos (36^{\circ}) - 0.204 \times (68 N - 82.6 N \times \sin (36^{\circ})) & = & \frac{68 N}{9.81 m / s^{2}} \times a \\ 66.82 - 3.96 & = & 6.93 \times a \\ a & = & 9.07 m / s^{2} \end{array}$

Thus, the acceleration of the object is 9.07 m/s².

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