Physics, 25.07.2019 14:30 Jmajano99

Asolid ball is released from rest and slides down a hillside that slopes downward at an angle 51.0 ∘ from the horizontal. what minimum value must the coefficient of static friction between the hill and ball surfaces have for no slipping to occur?

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In order for the object not to slip, the component of the weight parallel to the surface must be equal to the frictional force (which acts in the opposite direction):
$F_{//}= F_a$

The parallel component of the weight is:
$F_{//} = mg \sin \alpha$
where m is the object mass and $\alpha$ is the angle of the inclined plane.

The frictional force is
$F_a = \mu m g \cos \alpha$
where $\mu$ is the coefficient of static friction.

Equalizing the two forces, we have
$mg \sin \alpha = \mu m g \cos \alpha$
from which we find
$\mu = \tan \alpha$

and so, in our problem the coefficient of static friction must be
$\mu=\tan 51^{\circ} =1.23$

Answer from: Quest

1.state2.trash3.the earth

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.

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Asolid ball is released from rest and slides down a hillside that slopes downward at an angle 51.0 ∘...

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