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A block of mass m sits at rest on a rough inclined ramp that makes an angle θ with the horizontal. What must be true about force of static friction f on the block?
A) f > mg
B) f = mgsin(?)
C) f > mgcos(?)
D) f = mgcos(?)
E) f > mgsin(?)

Respuesta :

opudodennis

Answer:

Option B

Explanation:

For a system of block on inclined ramp shown in the attached image. From the attached image, the Normal force N, weight mg and frictional force f act on the block.  The sum of vertical forces should be zero just as sum of vertical forces should be zero when the system is in equilibrium condition.

Taking sum of forces along the inclined plane we deduce that  

[tex]f=mgsin \theta [tex]

Therefore, option B is the correct option.

Ver imagen opudodennis
onyebuchinnaji

When the block is at rest, the static frictional force is equal to the horizontal component of the block's weight (F = mgsin(θ)).

The static frictional force on the body at rests is determined by applying Newton's second law of motion.

F = ma

where;

  • F is applied force on a body
  • m is the mass of the body
  • a is the acceleration of the body

If the block is at rest, then the net horizontal force on the block is zero.

[tex]\Sigma F_x = 0\\\\mg sin(\theta ) - F_s = 0\\\\F_s = mg sin(\theta)[/tex]

Thus, when the block is at rest, the static frictional force is equal to the horizontal component of the block's weight.

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