Question

The magnitude of each force is 259 N, the force on the right is applied at an angle 33◦ and the mass of the block is 20 kg. The coefficient of friction is 0.239. The acceleration of gravity is 9.8 m/s 2 . 20 kg µ = 0.239 259 N 33◦ 259 N What is the magnitude of the resulting acceleration? Answer in units of m/s 2 .

Answer 1

Answer:

A=23.15m/s

Explanation:

Our data are,

$m =20 kg\\\mu = 0.239 \\F = 259 N \\\theta=33\°$

First we calculate the Total Force in Y of the Block, that is

$\sum F_y=0$

$F_{Ty}=F_N-F_y\\F_{Ynet}=mg-sin\theta\\F_{Ynet}=(20)*9.8-259sin(33)=54.93N$

We calculate the Frictional Force,

$F_f=\mu*F_{net}=54.93*0.239=13.13N$

We can now calculate the aceletarion,

$F_{Xnet}=ma$

clearing A,

$A=\frac{F_{Xnet}}{m}= \frac{259cos(33)+259-13.13}{20}$

$A=23.15m/s$

Answer 2

The acceleration depends on the mass and velocity of the block. The acceleration in this case is found out by mass and net force applied on the block in the x-direction.

The magnitude of the acceleration of the block is 23.15 m/s^2.

How do you calculate the acceleration?

Given that the force on the block is 259 N, the mass m of the block is 20 kg, the force on the right is applied at an angle of 33 degrees, the coefficient of friction µ is 0.239. The acceleration of gravity g is 9.8 m/s 2.

The net force on the block is calculated as given below.

$F _{net}= F - F_y$

Here Fy is the force applied on the block in the vertical direction.

$F_{net} = mg - F sin \theta$

$F_{net} = 20\times 9.8 - 259\times sin 33^\circ$

$F_{net}= 54.93 \;\rm N$

The frictional force is calculated as given below.

$F_f = \mu F_{net}$

$F_f = 0.239\times 54.93$

$F_f = 13.12\;\rm N$

The net force in x-direction is calculated as given below.

$F_x = F + Fcos\theta - F_f$

$F_x = 259+259cos 33^\circ - 13.12$

$F_x = 463.1\;\rm N$

The acceleration of the block is calculated as given below.

$F_x = ma$

$463.1 = 20\times a$

$a = 23.15\;\rm m/s^2$

Hence we can conclude that the acceleration of the block is 23.15 m/s^2.

To know more about force and acceleration, follow the link given below.

https://brainly.com/question/1046166.