2- A box with mass M=2000 Kg is on the ground. Two boys are trying to pull the box using two ropes as shown in the figure. The boy on the left pulls the box with a rope which makes angle L=30 degrees with horizon and has tension TL=10 N. The boy on the right pulls the box with a rope that makes angle R=45 degrees with horizon. (grade: 20) a) If there is no friction between the box and the ground, what is the minimum required tension in the rope on the right (TR=?) such that the box starts moving toward right? b) If the tension in the right rope is TR=100 N, what will be the acceleration of the box? c) In this part we want to assume that there is friction between the box and the ground with coefficient of friction equal to u=0.01. What is the minimum required tension in the right rope such that the box moves toward right? d) What is the minimum required tension in the right rope (TR=?) such that the box takes off from the ground?
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You are lowering two boxes, one on top of the other, down a ramp as shown, by pulling on a taut cable that is parallel to the surface of the ramp. The lower box has mass m1 = 20.0 kg, and the upper box has mass m2 = 10.0 kg. The two boxes move together at constant speed 0.125 m/s: the upper box does not move with respect to the lower box. The coefficient of kinetic friction between the ramp and the lower box is ̄̄̄k = 0.250, and the coefficient of static friction between the two boxes is ̄̄̄s = 0.900. (a) Find the magnitude of the force that the cable exerts on the lower box. (b) Find the magnitude of the static frictional force that the lower box exerts on the upper box. Keep in mind that it is static friction that prevents the upper box from slipping off of the lower box. *Check* that your calculated value is smaller than the maximum possible value for static friction. (c) Draw a free-body diagram for the upper box, showing the direction and numerical magnitude of each force. Decompose the gravitational force into components, as a check that your calculated force values add up as expected. Please label your forces G=gravity, S=static, N=normal, E=Earth, L=lower, U=upper. (d) Draw a free-body diagram for the lower box, showing the direction and numerical magnitude of each force. Again decompose the gravitational force into components, as a check that your calculated force values add up as expected. Please label your forces G=gravity, S=static, K=kinetic, N=normal, E=Earth, L=lower, U=upper, R=ramp, T=tension (in Cable).
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