A toy chest filled with toys has a weight of 180 N. The coefficients of static a

Question

A toy chest filled with toys has a weight of 180 N. The coefficients of static and kinetic friction between the chest and the floor are 0.68 and 0.56, respectively. A child attempts to move the chest across the floor by pulling on a rope attached to the chest with a force of 100 N at an angle of 38 degree above the horizontal.

a) What is the acceleration of the chest? Show all work
b) If the chest were initially sliding acorss the floor, would the acceleration of the chest increase, decrease, or remain the same? Explain

Explanation / Answer

The box feels two horizontal forces: the force of the child pulling on the rope, which I will call F, and the force of friction. However, F is made with an angle t (for theta = 38 degrees) above the horizontal, so the net force in the x direction is Net F_x = Fcost - f The friction will depend upon the normal force acting on it. The normal force plus F_y (which is equal to Fsint) equals the weight mg, or N = mg - Fsint So, friction will be equal to f = mu*N = mu(mg - Fsint) First and foremost, the x component of the force F must be larger than static friction for there to be an acceleration. The x component of the force F is F_x = Fcost = (100N)cos(38) = 78.8N and maximum static friction is f_s = mu*(mg - Fsint) = (0.68)*(180N - (100N*sin38)) = 80.5N Since the force F_x is not enough to overcome static friction, the acceleration will be ZERO. b) If the object were already moving, the frictional force would be kinetic, in which case Net F_x = Fcost - mu_k(mg - Fsint) = 12.5N Since the box weighs 180N, the mass is 180N/9.8m/s^2 = 18.4kg and a = 0.68 m/s^2 So it would increase.

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