If the rod shown has a weight of 150 N, calculate the magnitude of the reactions at A (horizontal and vertical) and B. Hint: A is a pin support 60° A 6 m
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- Let A⃗ =(9,78∘) and B⃗ =(2,289∘), where the angles are measured counterclockwise from the positive x-axis. What is C⃗ =4A⃗ +B⃗ ? Give your answer in component form. x component: y component:The temperature at a point (x, y) on a rectangular metal plate is given byT(x, y) = 100 6x2 + y2 (a) Find the rate of change of T at the point (3, 4) in the direction of the vector (−3, −4) (b) At the point (3, 4), find a unit vector in the direction in which the temperature increases the fastest. (c) What is the maximum rate of change of T at the point (3, 4)?A bricklayer hits a screw with a hammer and drives it into a ceiling. If the hammer hits the nail with three times the speed, how much deeper will the nail be driven?... Please explain MCQ choice (with calculations where needed) in the Rationale section! A. three times deeper B. the same depth C. nine times deeper. D. four times deeper
- When rebuilding his car's engine, a physics major must continuously exert 4.02 ✕ 102 N of force to insert a dry steel piston as it slides into a steel cylinder. What is the normal force (in N) between the piston and cylinder? (Enter the magnitude.)The figure shows Superhero and Trusty Sidekick hanging motionless from a rope. Superhero’s mass is 82 kg, while Trusty Sidekick’s is 65 kg, and the mass of the rope is negligible. Randomized Variables m1 = 82 kgm2 = 65 kg a) Find the tension in the rope above Superhero in Newtons. b)Find the tension in the rope between Superhero and Trusty Sidekick in Newtons.How do the values of µs compare to the values of µk? (Of course, you can only compare them for the same pairs of materials.) Is the relationship between µs and µk what you expected? Explain. What are three reasons why friction is needed? Does the coefficient of friction change with mass? How can we reduce friction? What would happen if there was no friction? Does frictional force depend on mass? What are 3 factors that affect friction? Is friction affected by surface area? Can humans live without friction? Why is the coefficient of friction less than 1? Explain.
- Explorers in the jungle find an ancient monument in the shape of a large isosceles triangle as shown. The monument is made from tens of thou- sands of small stone blocks of density = 800 kg/m3 . The monument is 15.7 m high and 64.8 m wide at its base and is everywhere 3.60 m thick from front to back. Before the monument was built many years ago, all the stone blocks lay on the ground. (a) Choosing a coordinate system with x = 0 at the center of the pyramid, y = 0 at the base of the pyramid, and z = 0 at the face of the pyramid shown in the diagram, determine the coordinates of the center of mass of the pyramid in the x, y, and z directions. (b) How much work did laborers do on the blocks to put them in position while building the entire monument? Note: The gravitational potential energy of an object–Earth system is given by Ug = MgyCM, where M is the total mass of the object and yCM is the elevation of its center of mass above the chosen reference level.A sphere is placed over the three closely packed identical spheres on a horizontal plane. All the spheres are identical both in weight and size. If one sphere weights 100-N, determine the contact reaction between the upper and bottom spheres in N.The answer key to this problem is stated as follows: x(t) = (4.0 cm)cos[(2π/8.0 s)t - π/3.0] Did they get the answer wrong? How you solved the problem landed with 'pi/6' In the answer key, it is with 'pi/3). Can you please explain?
- A car with two passengers and fuel weighs 1000 kg. It has wings with an area of 16 m^2 that are designed such that air moving over them must travel 1.05 times as far as air moving under them. How fast must this plane be moving so that wings generate enough lift to offset the plane's weight? The wings are thick. Please give answer in m/sA round trunk duct fitting has a branch that forms an angle of 30° with themain duct. The main duct is straight. The main duct and the branch form a Y.How far apart are the centers of the ducts 25 feet from the Y along the centerof the branch? Round the answer to the nearer hundredth foot.A cup is a cylinder with a diameter of 9.87cm and is 30cm tall. The hole is 1.44 from the bottom of the cup and has a diameter of 0.254cm. The cup sits at the edge of a 0.912m tall table. A.) Find the velocity of the water leaving the hole when the cup is full. B.) How far away from the table does the water hit the floor?