The drawing shows a 25 kg crate that is initually at rest. Two forces, F1 and F2

Question

The drawing shows a 25 kg crate that is initually at rest. Two forces, F1 and F2 are applied to the crate, and it begins to move (F1 is 50 degrees north of east and equals 88.0N, F2 is due east and equals 54.0N). The coefficient of kinetic friction between the crate and the floor is 0.350. Determine the magnitude and direction (relative to the x axis) of the acceleration of the crate. The drawing shows a 25 kg crate that is initually at rest. Two forces, F1 and F2 are applied to the crate, and it begins to move (F1 is 50 degrees north of east and equals 88.0N, F2 is due east and equals 54.0N). The coefficient of kinetic friction between the crate and the floor is 0.350. Determine the magnitude and direction (relative to the x axis) of the acceleration of the crate.

Explanation / Answer

The drawing shows a 25 kg crate that is initually at rest. Two forces, F1 and F2 are applied to the crate, and it begins to move (F1 is 50 degrees north of east and equals 88.0N, F2 is due east and equals 54.0N). The coefficient of kinetic friction between the crate and the floor is 0.350. Determine the magnitude and direction (relative to the x axis) of the acceleration of the crate.
Determine the force on the object: 1) The force due to gravity, the weight: Fw=mg=25kg(9.8m/s^2)=245N 2) The normal force: The crate lie on a horizontal surface and is neither accelerating upward or downward, so we know from newton's third law that the normal force will equal the force due to gravity:Fn=245N 3) The force due to friction:Ff=Fnk=(245N)(.350)=85.75N. 4) F2 acts to the east at 54N 5) F1 acts 50 degrees north of east at 88N. We are only concerned with the x component of this force, as stated in the question, so we need to break up 88N: F1x=cos50(88N)=56.57N east. Now, use this equation: F=ma We are pushing the crate to the right with F1 and F2, so these will be positive. To the left, we have the force of friction opposing these forces, so it will be negative. So, F=ma= F1+F2-Ff=ma 56.57N+54N-85.75N=(25kg)a 25N=25kg(a) We want the acceleration, a=25N/25kg=1m/s^2 This is a positive number, so F1 and F2 overcame the Ff, and the object is moving east on the x axis at 1m/s^2

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