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3 years ago

A box of mass 20kg is pulled up an inclined plane by a force of 285N. Given that the value of

Physics

1 answer:

lorasvet [3.4K]3 years ago

4 0

Answer:

19.6 m/s

Explanation:

The parameters given are:

Mass M = 20 Kg

Force F = 285 N

Angle Ø = 30 degree

Time t = 4 seconds

Coefficient of friction = 0.72

At the plane, the weight of the box will be mgsinØ

Resolving forces at the plane, we will have:

MgsinØ + Fr = F

Where Fr = frictional force.

Fr = F - mgsinØ

Substitute all the parameters into the formula

Fr = 285 - 20 × 9.8 sin30

Fr = 285 - 98

Fr = 187 N

But for the box moving toward the top of the plane,

F - Fr = ma

Where a = V/t

Substitute all the parameters involved into the formula

285 - 187 = 20 ( V/4)

98 = 5V

V = 98/5

V = 19.6 m/s

Therefore, the speed with which the box is moving is 19.6 m/s

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4 years ago

A horizontal 826 N merry-go-round of radius 1.17 m is started from rest by a constant horizontal force of 57.8 N applied tangent

Julli [10]

Answer:

The kinetic energy of the merry-go-round is $\bf{475.47~J}$ .

Explanation:

Given:

Weight of the merry-go-round, $W_{g} = 826~N$

Radius of the merry-go-round, $r = 1.17~m$

the force on the merry-go-round, $F = 57.8~N$

Acceleration due to gravity, $g= 9.8~m.s^{-2}$

Time given, $t=3.47~s$

Mass of the merry-go-round is given by

$m &=& \dfrac{W_{g}}{g}\\~~~~&=& \dfrac{826~N}{9.8~m.s^{-2}}\\~~~~&=& 84.29~Kg$

Moment of inertial of the merry-go-round is given by

$I &=& \dfrac{1}{2}mr^{2}\\~~~&=& \dfrac{1}{2}(84.29~Kg)(1.17~m)^{2}\\~~~&=& 57.69~Kg.m^{2}$

Torque on the merry-go-round is given by

$\tau &=& F.r\\~~~&=& (57.8~N)(1.17~m)\\~~~&=& 67.63~N.m$

The angular acceleration is given by

$\alpha &=& \dfrac{\tau}{I}\\~~~&=& \dfrac{67.63~N.m}{57.69~Kg.m^{2}}\\~~~&=& 1.17~rad.s^{-2}$

The angular velocity is given by

$\omega &=& \alpha.t\\~~~&=& (1.17~rad.s^{-2})(3.47~s)\\~~~&=& 4.06~rad.s^{-1}$

The kinetic energy of the merry-go-round is given by

$E &=& \dfrac{1}{2}I\omega^{2}\\~~~&=&\dfrac{1}{2}(57.69~Kg.m^{2})(4.06~rad.s^{-1})^{2}\\~~~&=& 475.47~J$

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