PROBLEM -SOLVING

FrictionNewton’s Second law of motion

Free body diagramFree-body diagrams are diagrams

used to show the relative magnitude and direction of all forces acting upon an object in a given situation.

FrictionKinetic friction- The least amount of force necessary to make an initially moving object remain moving at constant speed.

Static friction- least amount of force necessary to make an object at rest move.

Coefficients of frictionDepends on the materials used

s = coefficient of static friction

k = coefficient of kinetic friction

FrictionEx. 3.4A 70 kg cross-country skier is on level

ground in wet snow wearing waxed wooden skis. A) What is the maximum force that can be exerted on the skier in a horizontal direction without causing her to move? B) Once the skier is moving, what horizontal force is necessary to keep her moving at a steady velocity? s =0.14, k = 0.1

Example 3.7 see figure 3.15, p. 48Calculate the acceleration of the

cart with a total mass of 25 kg if a 2.0 N frictional force opposes the motion. Calculate the magnitude of the normal force ?

Problem 3.11

An orderly exerts a horizontal force of 50 N on a gurney with a patient on it. The gurney and patient have a total mass of 90 kg. If the gurney and patient accelerate at 0.35 m/s2 , what is the magnitude of the frictional force opposing the motion?

Problem 3.14.

Two workers push horizontally in the same direction on a 250 kg wooden crate that is on a wooden floor. A) What total force must they exert to start the crate moving? B) Once moving, one worker exerts a force of 500 N and the other exerts a force of 600 N. Calculate the acceleration of the crate? s = 0.3 k = 0.25

FIRST CONDITION OF EQUILIBRIUM

To improve the acoustics in an auditorium, a sound reflector with a mass of 200 kg is suspended by a chain from the ceiling. What is the weight of the reflector? What is the tension in the chain?

Problem-solving

A car engine with weight of 2200 N hangs from a chain that is linked at point O, to two other chains, one fasted to the ceiling and the other to the wall. Find the tensions in these three chains assuming the weights of the chains are negligible.

Try this!

Free body diagrams

P. 3.12

A 70 kg gymnast climbs a rope. Calculate the tension in the rope. A) If the gymnast climbs at a steady speed; b) if the gymnast accelerates upward at 0.29 m/s2 .

P. 3.20

Two movers push horizontally on a refrigerator. One pushes due north with a force of 150 N and the other pushes due east with a force 200 N. Find the direction and magnitude of the resultant force on the refrigerator.

P. 3.23

Figure 3.26, p. 59, shows a sled viewed from above being pulled by two children and experiencing a frictional force. Find the acceleration of the 9.0 kg sled.

P. 3.25

An extremely large tension can be created in a rope by pulling on it perpendicular to its length. This technique can be used to pull a stuck car out of the mud by tying a rope to the bumper of the car and nearby tree and pulling on the rope as shown in figure 3.27, p. 59. Find the magnitudes of the tensions in the rope.

P. 3. 29

When reading, the head is normally held as shown in figure 3.31 p. 60. The forces acting are the weight of the head, w, the force of the neck muscles, Fm and the force supplied by the upper vertebrae, Fv. These forces add to zero when the head is stationary. Calculate the magnitude and direction of Fv needed to accomplish this.

Inclined planeA wooden plank is raised at one end

until an angle of 300 is achieved. A box is placed on the incline 1.0 m from the lower end and given a slight tap to overcome static friction. The coefficient of kinetic friction between the box and plank is 0.20. Determine the a) rate of acceleration of the box down the incline. B) speed of the box at the bottom assume that the initial speed of the box is zero.

Atwood’s machineIn a device known as an Atwood

machine, a massless, unstretchable rope passes over a frictionless pulley. One of the rope is connected to an object m = 1.0 kg while the other end is connected to an object m = 2.0 kg. The system is released from rest A) Calculate the acceleration and b) tension in the rope.

Elevator A student of mass 50 kg decides to

test Newton’s laws of motion by standing on a bathroom scale placed on the floor of an elevator. Assume that the scale reads in Newtons. Determine the scale reading when the elevator is a) accelerating upward at 0.50 m/s2 , b) traveling upward with a constant speed of 3.0 m/s and c) traveling downward with an acceleration of 1.0 m/s2 ?

F(scale ) – F (mg) = maIf velocity is constant a = 0Ans( 515 N, 490 N, 440 N)

An object with a mass of 10.0 kg is connected by a massless, unstretchable string to an object with a mass of 7.0 kg. The 10 kg load rests on a table. The coefficient between the object and incline is 0.10. Determine the a)rate of acceleration of the system b) tension in the rope that connects the boxes.

SEATWORKA child and basket with a total mass of

10 kg are suspended from a scale by a cord, as shown in fig. 3.6 p. 42. Calculate the tension in the cord.

A guy exerts a horizontal force of 110 N on a 20 kg cart. If the cart accelerates at a rate of 0.25 m/s2 , what is the magnitude of the frictional force opposing the motion?

A car pulling a 1500 kg trailer produces an acceleration of 0.50 m/s2 . a) The frictional force in the wheels of the trailer is 125 N. What force is the car exerting on the trailer?

SEATWORK

Calculate the total force exerted on a gurney by two orderlies who exert forces shown in figure. If the total mass is 100 kg, what will be the acceleration of the gurney?

P. 3.27

Two muscles in the back of the leg pull upward on the Achilles tendon as shown in figure 3.29 p. 59. These muscles are called the medial and lateral heads of the gastrocnemius muscle. Find the magnitude and direction of the total force on the Achilles tendon.

The skier has just begun descending the 30- degree slope. Assuming the coefficient of friction is 0.10, calculate her acceleration.

Two masses 2.2 kg and 3.2 kg are attached to the Atwood’s machine. Compute for the Tension in the string and the acceleration of each mass.

An 80 kg man is inside an elevator which accelerates downward at a rate of 1.2 m/s2 . What will be the normal force acting on the man?