A wood block sits on an angled concrete ramp. A person stands at the bottom of the ramp and pushes on the block so that a non-zero force is applied parallel to the angled surface of the ramp. Assume that we can neglect air resistance. For this scenario, which of the following statements about friction is false?
A. If the block is moving, then the force due to friction is independent of how hard the person is pushing.
B. The force due to friction depends on the mass of the block, regardless of whether the block is moving or stationary.
C. If the block is not moving, then the force due to friction depends on how hard the person is pushing.
D. If the block is not moving, then the force due to friction must be zero.
E. The force due to friction depends on the angle of the ramp, regardless of whether it is moving or stationary

If the block is not moving , it does not mean that friction on the block is not acting . Friction acts both in case when the body is moving on a rough surface or it tends to move on a rough surface . When a body tends to move on a rough surface due to a force acting on it , friction force is equal to applied force . This friction force is known as static friction .

All other given statements are correct . Static friction depends upon force applied on the body and kinetic friction does not depend on force applied when the force acts parallel to the surface .

onyebuchinnaji onyebuchinnaji · Answer 2 · 2021-11-05T23:26:02+01:00

The force due to friction depends on the angle of the ramp, regardless of whether it is moving or stationary.

The normal force on the block is calculated as follows;

[tex]F_n = mgcos \theta[/tex]

The frictional force on the block is calculated as follows;

[tex]F_k = \mu_k F_n\\\\F_k = \mu_k mg cos(\theta)[/tex]

The net horizontal force on the block is calculated as follows;

[tex]mgsin(\theta) - F_k = ma[/tex]

[tex]mgsin(\theta) - \mu_k mgcos(\theta) = ma\\\\mg(sin\theta - \mu_k cos\theta) = ma\\\\sin\theta - \mu_k cos\theta = \frac{a}{g} \\\\ \mu_k cos\theta = sin\theta -\frac{a}{g}\\\\\mu_k = \frac{sin\theta}{cos \theta} - \frac{a}{gcos\theta }\\\\\mu_k = tan\theta - \frac{a}{gcos\theta }\\\\if \ the \ block \ is \ not \ moving, \ the \ new \ equation \ becomes;\\\\\mu_s = tan(\theta)[/tex]

where;

[tex]\mu_k[/tex] is the coefficient of kinetic friction

[tex]\mu_s[/tex] is the coefficient of static friction

Frictional force depends on coefficient of friction (kinetic or static), and coefficient of friction depends on the angle of the ramp.

Thus, we can conclude that the force due to friction depends on the angle of the ramp, regardless of whether it is moving or stationary.

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