Equilibrium

When a system is equilibrium the net force on the object is zero.Strategy for Equilibrium Problems

Example 1

A 100 kg block with a weight of 980 N hangs on a rope. Find the tension in the rope if the block is stationary, then if it's moving upward at a steady speed of 5 m/s, and finally it it's accelerating upward at .

Example 2

Determine the resultant, or net force, exerted on the stationary elephant by the two clowns in the below figure. What is the tension in the rope attached to the elephant?

Example 3

In a two-dimensional tug-of-war, Alex, Betty, and Charles pull horizontally on an automobile tire at the angles shown in the figure. The tire remains stationary in spite of the three pulls. Alex pulls with a force of magnitude 220 N, and Charles pulls with a force of magnitude 170 N. The direction of is not given. What is the magnitude of Betty's force ?

Example 4

A ball weighing 60 N is pulled back by a rope by an angle of . What is the tension in the pulling rope?

Example 5

A car with a mass of 1500 kg is being towed at a steady speed by a rope held at a angle. A friction force of 320 N opposes the car's motion. What is the tension in the rope?

Dynamics and Newton's Second Law

Complete the activites 2.1 through 2.4.

Example 6

A sled with a mass of 20 kg slides along frictionless ice at 4.5 m/s. It then crosses a rough patch of snow that exerts a friction force of 12 N. How far does it slide on the snow before coming to rest? Macie pulls a 40 kg rolling trunk by a strap angled at from the horizontal. She pulls with a force of 40 N, and there is a 30 N rolling friction force acting on the trunk. What is the trunk's acceleration?

Example 7

Inclined Planes

When an object is on an inclined plane the normal force is only equal to part of the gravitational force . This is usually done with the use of sine and cosine.

To solve problems on an inclined plane the forces must be resolved into the components that are parallel and perpendicular to the plane.

Example 8

A 75 kg skier starts down a 50 m high, slope on frictionless skis. What is his speed at the bottom?

Example 9

Burglars are trying to push a 1000 kg safe up a frictionless slope with a horizontal force of 4000 N. Find an expression for the acceleration of the safe. Then find the acceleration for the information in the problem. Look at the two limiting cases for the angle.

Mass and Weight

Apparent Weight

Example 10

A 50 kg student gets in a 1000 kg elevator at rest. As the elevator begins to move, she has an apparent weight of 600 N for the first 3 s. How far has the elevator moved, and in which direction, at the end of 3 s?

Apparent Weight –

Friction

Static Friction

Kinetic Friction

Rolling Friction

Example 11

A crate of mass 20 kg is sliding across a wooden floor. The
coefficient of kinetic friction between the crate and the floor is 0.3.

(a) Determine the strength of the friction force acting on the crate.

(b) If the crate is being pulled by a force of 90 N (parallel to the floor),
find the acceleration of the crate.

Example 12

A crate of mass 100 kg rests on the floor. The coefficient of static friction is 0.4. If a force of 250 N (parallel to the floor) is applied to the crate, what's the magnitude of the static friction on the crate?

Example 13

A lawn roller is a heavy cylinder used to flatten a bumpy lawn, as in figure. Is it easier to push or pull such a roller? Which is more effective for flattening the lawn, pushing or pulling?

Example 14

A 50.0 kg steel file cabinet is in the back of a dump truck. The truck's bed, also made of steel, is slowly tilted. What is the size of the static friction force on the cabinet when the bed is tilted ? At what angle will the file cabinet begin to slide?

Example 15

The figure shows a coin of mass m at rest on a book that has been tilted at an angle with the horizontal. By experimenting, you find that when is increased to , the coin is on the verge of sliding down the book, which means that even a slight increase beyond produces sliding. What is the coefficient of static friction between the coin and the book?

Example 16

If a car's wheels are "locked" during emergency braking, the car slides along the road. Ripped-off bits of tire and small melted sections of road form the "skid marks" that reveal that cold-welding occurred during the slide. The record for the longest skid marks on a public road was reportedly set in 1960 by a Jaguar on the M1 highway in England–the marks were 290 m long! Assuming that and the car's acceleration was constant during the braking, how fast was the car going when the wheels became locked?

Drag

Example 17

Calculate the drag force on a missile 53 cm in diameter cruising with a speed of 250 m/s at low altitude, where the density of air is . Assume C = 0.75.

Terminal Speed

Example 18

If a falling cat reaches a first terminal speed of 97 km/h while it is tucked in and then stretches out, doubling A, how fast is it falling when it reaches a new terminal speed?

Example 19

A raindrop with a radius r = 1.5 mm falls from a cloud that is at height h = 1200 m above the ground. The drag coefficient C for the drop is 0.60. Assume that the drop is spherical throughout its fall. The density of water is , and the density of air is . (a)What is the terminal speed of the drop? (b)What would be the drop's speed just before impact if there were no drag force?