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Static Friction, Tension, and Equilibrium: Solving Acceleration and Force Problems

Explore the concepts of static friction, tension, and equilibrium through various examples and calculations involving acceleration and forces.

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Static Friction, Tension, and Equilibrium: Solving Acceleration and Force Problems

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  1. Sponge - A block is resting on a ramp. The coefficient of static friction between the two is µs = 1.00. What is the maximum angle of the ramp before the block starts sliding down?

  2. Tension - the force on a rope that would tend to pull the rope apart. A force on one end of a rope will be felt by the object to which it is attached. We will assume for our discussions that all ropes are massless.

  3. Equilibrium - An object is in equilibrium when it has zero acceleration. The x-component of the net force and the y-component of the net force must both be zero. ∑Fx = 0 ∑Fy = 0

  4. Ex. 11 - A tension is to be created in a rope by attaching the right end to a person’s head and attaching a weight to the other and hanging it over a pulley. If F and T are desired to have a magnitude of 34 N, how much mass should be suspended from the rope?

  5. Ex. 12 - This traction device is used with a foot injury. Ignoring the weight of the foot, what is the value of F?

  6. Ex. 14 - A jet plane is flying with a constant speed along a straight line, at an angle of 30.0° above the horizontal. The plane has a weight W whose magnitude is 86 500 N, and its engines provide a forward thrust T of 103 000 N. In addition, the lift force L (perpendicular to the wings) and the force R of air resistance (opposite to motion) act on the plane. Find L and R.

  7. If an object is accelerating, these new equations apply: ∑Fx = max ∑Fy = may

  8. Ex. 15 - A supertanker (mass = 1.50 x 108 kg) is being towed by two tugboats. The tensions in the towing cables apply the forces T1 and T2 at equal angles of 30.0° with respect to the tanker’s axis. In addition, the tanker’s engines produce a forward drive force D, whose magnitude is 75.0 x 103 N. Moreover, the water applies an opposing force R, whose magnitude is 40.0 x 103 N. The tanker move forward with an acceleration that points along the tanker’s axis and has a magnitude of 2.00 x 10-3 m/s2. Find the magnitudes of T1 and T2.

  9. Ex. 16 - An 8500-kg truck is hauling a 27 000-kg trailer along a level road. The acceleration is 0.78 m/s2. Ignoring the retarding forces of friction and air resistance, determine (A) the magnitude of the tension in the horizontal drawbar between the trailer and the truck and (B) the force D that propels the truck forward.

  10. Ex. 18 - A flatbed truck is carrying a crate up a 10.00° hill. The coefficient of static friction between the truck bed and the crate is µs = 0.350. Find the maximum acceleration that the truck can attain before the crate begins to slip backward relative to the truck.

  11. Ex. 19 - Block 1 (m1 = 8.00 kg) is moving on a frictionless 30.0° incline. This block is connected to block 2 (m2 = 22.0 kg) by a cord that passes over a massless and frictionless pulley. Find the acceleration of each block and the tension in the cord.

  12. Ex. 20 - A window washer on a scaffold is hoisting the scaffold up the side of a building by pulling downward on a rope which passes through a fixed pulley on the roof, through a movable pulley on the scaffold, and is attached to the roof. The magnitude of the pulling force is 540 N, and the combined mass of the person and the scaffold is 155 kg. Find the upward acceleration of the unit.

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