An object rests on an inclined surface thanks to the presence of static friction forces between the object and the surface.
The magnitude of the friction force that prevents the object from sliding is found to be 30 N. Now, the angle that the surface makes with respect to the horizontal is increased, and the object is found to be still at rest.The magnitude of the friction force that prevents the object from sliding is now ...
a) zero
b) larger than zero less than 30N
c) exactly equal to 30N
d) greater than 30N
I think it is greater than 30N
It could be larger, if someone has stuck a nail through the object. But barring that,
the normalforce is mg*CosTheta. What does CosTheta do as the angle gets larger?
but isn't costheta periodic?
Only if you got 180 degrees, but here in Texas, we only angle to ramp from zero to 89 degrees. At that point, all things not nailed fall off.
What does CosTheta do between zero and 90 deg?
costheta decreases so the answer is B? right
yes.
To find the magnitude of the friction force that prevents the object from sliding when the angle of the surface is increased, we need to consider the equation governing static friction on inclined surfaces.
The equation is given by:
$F_{\text{friction}} = \mu_s \cdot F_{\text{normal}}$
Where:
$F_{\text{friction}}$ is the friction force,
$\mu_s$ is the coefficient of static friction, and
$F_{\text{normal}}$ is the normal force.
The normal force is the force exerted by the surface on the object perpendicular to the surface. In this case, since the object is at rest, the normal force is equal to the weight of the object.
As the angle of the surface increases, the component of the weight perpendicular to the surface decreases, leading to a decrease in the normal force.
Since the object is still at rest, the friction force must be equal to or greater than the force required to prevent sliding.
Considering that the friction force was initially found to be 30 N, the possible options are:
a) zero: If the friction force becomes zero, the object will start sliding down the incline, which contradicts the statement that it is still at rest.
b) larger than zero and less than 30 N: It is possible for the friction force to be smaller than 30 N, but it cannot be greater than the original value, as there is no additional force applied.
c) exactly equal to 30 N: This is a possibility, as it maintains the balance and prevents sliding.
d) greater than 30 N: This is not possible, as there is no additional force applied to increase the friction force.
Since the question states that the object is still at rest, and there is no additional force applied, the correct answer is:
c) exactly equal to 30 N
The friction force remains at 30 N to prevent the object from sliding down the inclined surface.