The figure shows a mobile of toys hanging from a ceiling. The black vertical lines represent wires from which crossbars are hung. The red crossbar has its left and right arms in equal length while the blue crossbars have right arms that are twice the length of their left arms. The crossbars are all horizontal and they themselves as well as the wires have negligible toy 1 toy 2 toy3 toy4 toy5 mass. Toy 1 has mass m, = 1 kg. What are the masses m2, m3, m4, and ms of toys 2, 3, 4, and 5, respectively?

Lizzy is training on the trapeze when a slight accident occurs. As a result, she is now hanging from the middle of a 60 m safety rope connected to the ceiling on one end and held by a strongwoman from the circus on the other end. She has a mass of 50 kg and the part of the rope connected to the ceiling makes an angle of 55° with the vertical. The part of the rope that connects Lizzy to her fellow circus artist makes an angle of 20° above the horizontal (the strongwoman is above Lizzy). As long as Lizzy remains stationary, what is the tension in both parts of the rope?

The L1 and L2 re the lengths of the rope that supports the masses M1₁ and M2, respectively. The hanging masses are placed at the end of a horizontal bar whose length is R₁ + R₂, as shown. R₁ R₂ L₁ M₁ R1L1= R242 L₁ L2 and R₁ = R₂ L₁ L2 and M₁ = M2 R₂ and M₁ = M2 L₂ The horizontal bar in the figure will remain horizontal if: OR₁ M₂

The drawing shows two identical systems of objects; each consists of the same three small balls connected by massless rods. In both systems the axis is perpendicular to the page, but it is located at a different place, as shown. The same force of magnitude F is applied to the same ball in each system (see the drawing). The masses of the balls are m1 = 9.0 kg, m2 = 6.1 kg, and m3 = 7.9 kg. The magnitude of the force is F = 441 N. (a) For each of the two systems, determine the moment of inertia about the given axis of rotation. (b) Calculate the torque (magnitude and direction) acting on each system. (c) Both systems start from rest, and the direction of the force moves with the system and always points along the 4.00-m rod. What is the angular velocity of each system after 5.35 s?

Three ropes are tied to a small metal ring. At the end of each rope three students are pulling, each trying to move the ring in theirdirection. If we look down from above, the forces and directions they are applying are shown in the figure below. Find the netforce on the ring due to the three applied forces.

The system shown consists of 3 cables. For instance; cable C12 joins points 1 and 2. The coordinates of point 1 are (7.79, 0, 0) m, those of point 2 are (0, 7.58, 9.77) m, and those of point 3 are (0, 7.58, -9.77) m. The force P = 99 kN. Determine the force in cable C14.

A lamp of mass m is hung from from a series of short massless wire segments to a horizontal ceiling and a vertical wall as shown in the figure. The lamp is not moving. T₂ 2 60° T₁ Lamp T3 m 60° The wire segments create angles 60° with respect to the horizontal ceiling and 60° with respect to the vertical wall as shown and the mass creates tensions in the segments of the wire of magnitude T₁, T2, and T3, as labeled in the diagram. (A) Draw a free-body diagram for the hanging mass system showing (and labeling) all forces acting on the hanging lamp system. Then draw x and y axes for your free-body diagram. (B) Use Newton's second law to write equations for forces in component forms (x and y, separately) acting on the lamp in terms of: tension magnitudes T2 and T3, the angles shown, the mass of the object m and the gravitational constant g. You do not need to solve the equations but simplify as possible. (C) The weight of the lamp is determined to be 250 Newtons. Solve for magnitudes of…

The figure below shows two boxes connected to each other by a light cord that passes over a pulley with negligible friction. The box of mass  m1 = 3.80 kg  lies on a horizontal table with negligible friction, while the box of mass  m2 = 10.3 kg  hangs vertically. Two boxes labeled m1 and m2 are attached together by a cord. Box m1 lies on a horizontal table with the cord extending horizontally from its right side. The cord extends horizontally from the right side of m1 then goes over a pulley and then straight down to m2. Box m2 hangs from the cord. (a) What is the magnitude of the acceleration of each box (in m/s2)? (Here,  a1  is the acceleration of  m1,  and  a2  is the acceleration of  m2.) a1 = m/s2 a2 = m/s2 (b) What is the tension in the cord (in N)?  N

The mass M_1 slides on a 45 degree incline surface with a height of H, as shown in the figure . The mass is connected by a flexible rope, over a small pulley (its mass is neglected) and connected to another mass M_2 whose mass is equal to the previous block and is vertically hanging as shown below. The rope is long enough for two blocks to be at rest at height H/2 . The dimensions of the two blocks and the pulley are neglected compared to the height H, the blocks were left to move freely at time t=0 1- At time t> 0 find the vertical acceleration of the mass m_2 2- Which of the two blocks moves down? Calculate the time when it will hit the ground? 3- If the block stopped in the previous paragraph when it hit the ground, but the other block continued to move, clarify whether or not it will hit the pulley. Why?

The drawing shows two identical systems of objects; each consists of the same three small balls connected by massless rods. In both systems the axis is perpendicular to the page, but it is located at a different place, as shown. The same force of magnitude F is applied to the same ball in each system (see the drawing). The masses of the balls are m₁ = 9.4 kg, m₂ = 6.2 kg, and m3 = 7.8 kg. The magnitude of the force is F = 493 N. (a) For each of the two systems, determine the moment of inertia about the given axis of rotation. (b) Calculate the torque (magnitude and direction) acting on each system. (c) Both systems start from rest, and the direction of the force moves with the system and always points along the 4.00-m rod. What is the angular velocity of each system after 5.79 s? (b) A TB (c) WA WB = i II m₁ Axis 3.00 m 5.00 m System A m₂ 4.00 m m3 m₁ 3.00 m 5.00 m Axis System B m₂ 4.00 m m₂