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Determine the force \( P \) required to push a 15° wedge under a 94-kg uniform crate, which rests against a small stop at point \( A \). The coefficient of friction for all surfaces is 0.49.

Answer :

Final answer:

The force required to move the crate is 433.5 N.

Explanation:

To determine the force P required to move the crate, we need to consider the forces acting on the crate. The gravitational force acting on the crate can be calculated using the formula: Fg = mg, where m is the mass of the crate and g is the acceleration due to gravity (approximately 9.8 m/s2).

The normal force exerted by the wedge can be calculated using the formula: N = mg cos(θ), where θ is the angle of the wedge.

The frictional force between the crate and the wedge can be calculated using the formula: Ff = μN, where μ is the coefficient of friction.

Since the crate is at rest, the force required to move the crate is equal to the frictional force: P = Ff.

Substituting the values into the equations:

  1. Fg = (94 kg)(9.8 m/s2) = 921.2 N
  2. N = (94 kg)(9.8 m/s2) cos(15°) = 885.6 N
  3. Ff = (0.49)(885.6 N) = 433.5 N
  4. P = Ff = 433.5 N

Therefore, the force P required to move the crate is 433.5 N.

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