Physics, 13.02.2020 02:03 jose477

A copper block rests 44.4 cm from the center of a steel turntable. The coefficient of static friction between the block and the surface is 0.60. The turntable starts from rest and rotates with a constant angular acceleration of 0.60 rad/s2 . After what time interval will the block start to slip on the turntable? The acceleration of gravity is 9.81 m/s 2 . Answer in units of s.

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Answer from: 120175

4.041 sec

Explanation:

Let

m = mass of the block

r = Radius of circle in which the block moves = 44.4 cm = 0.444 m

μ = coefficient of friction =0.60

We know

Foprce of friction

Fs= coefficient of friction × Normal reaction force = μ×weight of block =μ mg=0.6×9.81 m =5.886 m

We are given angular acceleration = 0.6 rad / $sec^{2}$

The block will slip when centripetal force on block will become equal or greater than force of friction

Centripetal Force = Force of friction

But centripetal force F= m× $\frac{v^{2} }{r}$

and Force of friction Fs = 5.886 m

==> m× $\frac{v^{2} }{r}$ = 5.886 m

cancelling mass m on both sides;

==> $\frac{v^{2} }{r}$ = 5.886

==> $v^{2}$ = 5.886 × $0.444^{2}$ = 1.16 $(meter/sec)^{2}$

==> v =1.077 meter /sec

Now we can get angular velocity using

v= ω×r

From this formula we have;

ω = $\frac{v}{r}$ = 1.077 / 0.444=2.43 rad / sec

But we know that

angular acceleration = ω / t

==> 0.6 = 2.43 / t

==> t= 4.04 sec

Answer from: Quest

force is based upon mass and acceleration.the statement is not always true.

it can be explained from newton's second law of motion.

as per newton's second law of motion the rate of change of momentum is directly proportional to the applied force and takes place along the direction of force.

mathematically it can be written as -

$f\alpha \frac{dp}{dt}$

⇒ $f= k \frac{dp}{dt}$

here k is the proportionality constant whose value is 1.

$f=\frac{dp}{dt}$

$f= \frac{d[mv]}{dt}$

$f= m\frac{dv}{dt} +v\frac{dm}{dt}$

$f=ma+v\frac{dm}{dt}$ [a is the acceleration=dv/dt]

hence we see that force not only depends on mass and acceleration but also on velocity and rate of change of mass. force f will depend on mass and acceleration only when mass is constant.

hence the statement that force is based upon mass and acceleration is false.

Answer from: Quest

use photo math tells u all the answers thats what i use

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