USE VECTOR NOTATIONIn a physics laboratory class, three massless strings are tied together at a point. A tensile force is applied along each rope: F_1 = 150 N at 60°, F_2 = 200. N at 100°. F_3 = 100. N at 190° What is the magnitude of a fourth force and the angle at which it acts to keep the point at the center of the system stationary? (All angles are measured from the positive x-axis counterclockwise.)

a) Cables AC and BC are connected to lifting points A & B, and joined together at C as shown in Figure Q1a. The angle = 200 and angle B = 50°. If the tension in each cable is 3.75 KN, calculate the force (F) and the angle a required to maintain point C in static equilibrium. Give your answers for F in kilonewtons (kN) and the angle a in degrees to two decimal places. A 3 F α B O

Consider the following force vectors: A =-3î + ĵ + 2k (N) B = 2î – ĵ – k (N) 1. Vectors Á, B , and C maintain a body in equilibrium. What is vector C (in unit vector form)? Answer 1: 2. Evaluate: Bx A - (B. A)

The system in the figure is in a stationary state in its original state. Determine the required P force and T tensile force in the rope to activate the system under the following conditions. (The friction coefficients between blocks and between block and ground are given in the figure.) (a) When the force P is applied to a 5 kg block only (b) When the force P is applied only to a 10 kg block 5 kg = 0.50 10 kg = 0.60

Figure below shows an overhead view of 0.0250 kg lemon half and two of the three horizontal forces that act on it as it is on a frictionless table. Force −→F1 has a magnitude of 6 N and is at θ1 = 30◦. Force −→F2 has a magnitude of 7 N and is atθ2 = 30◦. In unit-vector notation, what is the third force if the lemon half (a) is stationary, (b) has the varying velocity−→v = 13t ˆi − 14t ˆj m/s2, where t is time?

You are a bully.  You pin a 48 kg dweeb to a wall so that his feet aren't touching the ground.  Your arm is extended so that it makes an angle 28 degrees with the horizontal.  The dweeb's back is so sweaty with fear that there is no friction between his back and the wall.  What is the magnitude of the force , in N, you must apply to keep the dweeb in equilibrium? (Use g = 10 m/s2) This scenario is represented schematically below.  Unfortunately for you, years later the dweeb is your boss and he makes your life miserable. (Please answer to the fourth decimal place - i.e 12.3445)

Students are performing an experiment with the setup shown above, where a block of mass M sits on a horizontal table. The coefficient of kinetic friction between the block and the table is uk. The block is connected to a hanging object over a pulley. The pulley has negligible mass and friction. The string connecting the two is very light and does not stretch. The students add mass to the hanging object so that its mass is mm, where m < M, and the block-hanging object system is released from rest. The hanging object falls for a distance h, at which point it collides with the ground and comes to rest. The block on the table keeps sliding and travels a total distance d before coming to rest. It does not reach the pulley, and d > h. If the experiment were repeated where the height hh above the floor was increased, would the distance that the block slides after the hanging object hits the floor increase, decrease, or remain the same? Justify your answer without using or manipulating…

You are working in an ice skating rink and have been asked to hang a new banner on the wall. Your friend is helping you so that the ladder does not collapse by exerting a force F→AL at an angle phi relative to the horizontal. See the diagram below. The ladder has a length L and makes an angle of theta with respect to the vertical wall. You have a mass, m_Y, and are a horizontal distance x from the wall. The ladder has a mass of m_L. Because the wall is slick, and the ice on the floor is slick, the frictional forces acting on the ladder are negligible.  Part One: Find a formula for the magnitude of the force that your friend must exert to keep the ladder from falling, in terms of the following variables: x,L,m_Y,m_L,theta,phi. Then use the following values to get a number for the magnitude of F→AL. theta = 29.5 degrees phi = 23.305 degrees x= 2.204 meters L = 7.6 meters m_Y= 82 kg m_L = 34.44kg

You are working in an ice skating rink and have been asked to hang a new banner on the wall. Your friend is helping you so that the ladder does not collapse by exerting a force F→AL at an angle phi relative to the horizontal. See the diagram below. The ladder has a length L and makes an angle of theta with respect to the vertical wall. You have a mass, m_Y, and are a horizontal distance x from the wall. The ladder has a mass of m_L. Because the wall is slick, and the ice on the floor is slick, the frictional forces acting on the ladder are negligible.  Part Three: Find the magnitude of the normal force that the floor exerts on the ladder. F→AL = 307.77N Normal Force wall exterts on ladder = 282.6634N Theta = 29.5 degrees phi = 23.305 degrees x= 2.204 meters L = 7.6 meters m_Y= 82 kg m_L = 34.44kg

A solid cube with fifteen cm long sides has a uniform density p=4250 kg/m³. The cube travels on a frictionless horizontal surface in the x-direction under the influence of two external forces, F, pushing and F, pulling. F, and F, are in the x-y plane, and are represented in the figure by arrows with 10.0 cm of arrow length corresponding to a magnitude of 30.00 N. Note that the arrows start or end either at mid-points between grid intersections or at grid intersections. 40 30 20 10 10 20 30 40 50 60 70 80 90 100 110 Horizontal, x (cm) A. Calculate the size of N, the normal force which the surface applies on M. Use g=9.81 m/s2. Submit Answer Tries 0/10 B. Calculate the magnitude of the total force acting on M. Submit Answer Tries 0/10 C. A third external force F3 is now applied to the mass, and it is observed that the velocity of the mass stops changing and then remains constant. What is the horizontal (x) component of F3? Submit Answer Tries 0/10 D. In the form below, give the value(s)…