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Lorico [155]
3 years ago
11

An ice cube with a mass of 0.0600 kg is placed at the midpoint of a 1.00-m-long wooden board that is propped up at a 49° angle.

The coefficient of kinetic friction between the ice and the wood is 0.160.
(a) How much time does it take for the ice cube to slide to the lower end of the board?
(b) If the ice cube is replaced with a 0.0600 kg wooden block, where the coefficient of kinetic friction between the block and the board is 0.385, at what angle should the board be placed so that the block takes the same amount of time to slide to the lower end as the ice cube does?
Physics
1 answer:
Bess [88]3 years ago
3 0

Answer:

Explanation:

distance covered by ice cube = 0.5 m

force acting downwards = mgsin49

force of friction acting along surface upwards

= mgcos49 x .16  ( reaction force of inclined surface R = mgcos49.)

net force acting downwards

mgsin49  - mgcos49 x .16

mg (sin49  - cos49 x .16 )

net acceleration downwards

g (sin49  - cos49 x .16 )

= (.7547 - .105 ) x 9.8

= 6.367 m / s²

s = ut + 1/2 at²

0.5 = 0 + 1/2 x 6.367 x t²

t² = .1570

t = .4 s

b )

Let required inclination be θ

in the second case net acceleration

a = g ( sin θ - .385 cosθ )

s = ut + 1/2 at²

0.5 = 0 + 1/2 x g ( sin θ - .385 cosθ ) x .4 x .4

( sin θ - .385 cosθ ) = .6377

sin θ  =  .385 cosθ +  .6377

θ  = 58 degree.

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Here it is given that an elevator is moving down with an acceleration of 3.36 m/s² . And we are interested in finding out the apparent weight of a 64.2 kg man . For the diagram refer to the attachment .

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From the Free body diagram ,

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\sf\longrightarrow Weight = 64.2( 9.8 - 3.36) N\\

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An object floats in a beaker as shown. when it was put into the beaker, it displaced an amount of water into the graduated cylin
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A box is placed on a 30o frictionless incline. What is the acceleration of the box as it slides down the incline
balandron [24]

Answer:

<em>2.78m/s²</em>

Explanation:

Complete question:

<em>A box is placed on a 30° frictionless incline. What is the acceleration of the box as it slides down the incline when the co-efficient of friction is 0.25?</em>

According to Newton's second law of motion:

\sum F_x = ma_x\\F_m - F_f = ma_x\\mgsin\theta - \mu mg cos\theta = ma_x\\gsin\theta - \mu g cos\theta = a_x\\

Where:

\mu is the coefficient of friction

g is the acceleration due to gravity

Fm is the moving force acting on the body

Ff is the frictional force

m is the mass of the box

a is the acceleration'

Given

\theta = 30^0\\\mu = 0.25\\g = 9.8m/s^2

Required

acceleration of the box

Substitute the given parameters into the resulting expression above:

Recall that:

gsin\theta - \mu g cos\theta = a_x\\

9.8sin30 - 0.25(9.8)cos30 = ax

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ax = 2.78m/s²

<em>Hence the acceleration of the box as it slides down the incline is 2.78m/s²</em>

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