A block of mass m is pushed against a wall by a force P that makes an angle ? =

Question

A block of mass m is pushed against a wall by a force P that makes an angle ? = 50 ?
with the horizontal. The coe?cient of static friction between the block and wall is 0.25.
(a) Determine the possible values for the magnitude of P that allow the block to remain stationary.
(b) Describe what happens if |P| has a larger value and what happens if it is smaller.

Explanation / Answer

Weight = 3.00x9.81 = 29.43 N down Vertical component of applied force = Psin50.0° up maximum frictional force = 0.250Pcos50.0° At a minimum value of P, friction will be up. 29.43 = Psin50.0° + 0.250Pcos50.0° 29.43 = P(sin50.0° + 0.250cos50.0°) P = 29.43/(sin50.0° + 0.250cos50.0°) P = 31.8 N At a maximum value of P, friction will be down. 29.43 = Psin50.0° - 0.250Pcos50.0° 29.43 = P(sin50.0° - 0.250cos50.0°) P = 29.43/(sin50.0° - 0.250cos50.0°) P = 48.6 N At a minimum value of P, friction will be up. 29.43 = Psin13° + 0.250Pcos13° 29.43 = P(sin13° + 0.250cos13°) P = 29.43/(sin13° + 0.250cos13°) P = 63 N At a maximum value of P, friction will be down. 0.250cos13° > sin13° Friction is greater than vertical component of P. There is no maximum value of P. The block will not slide up when the angle is 13°

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