Chapter 5: Applying Newton's Laws

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?

w=490N a=2.2m/s*2 change in X=9.9m the apparent weight is larger than the actual weight - its positive acceleration so elevator is moving upward

A golfer putts a 46 g ball with a speed of 3.0 m/s. Friction exerts a 0.020 N retarding force on the ball, slowing it down. Will her putt reach the hole, 10 m away?

a=-.435m/s*2 Xf=10.3m

Weight

the gravitational force exerted on an object by a planet W=mg

Apparent Weight

the weight of an object is the force of the gravity on that object. your sensation of weight is due to contact forces supporting you. w(app)=magnitude of supporting contact forces Ex: a man feels heavier in an elevator when accelerating upward.

A 1.2 kg book lies on a table. The book is pressed down from above with a force of 15 N. What is the normal force acting on the book from the table below?

w=12N n=27N

An orangutan weighing 500 N hangs from a vertical rope. What is the tension in the rope?

500N = T

The box is sitting on the floor of an elevator. The elevator is accelerating upward. The magnitude of the normal force on the box is A. n > mg B. n = mg C. n < mg D. n = 0 E. Not enough information to tel

A. n > mg Upward acceleration requires a net upward force.

A box is being pulled to the right at steady speed by a rope that angles upward. In this situation: A. n > mg B. n = mg C. n < mg D. n = 0 E. Not enough information to judge the size of the normal force

C. n < mg

Static Friction

Force that a surface exerts on an object to keep it from slipping across the surface. Labeled as fs. Will point in the opposite direction of motion to prevent it.

Kinetic Friction

Has a nearly constant magnitude given by: fk=ukn. The magnitude of the fk force DOES NOT depend on how fast the object is sliding.

A 100-kg block with a weight of 980 N hangs on a rope. Find the tension in the rope if the block is accelerating upwards at 2 5 m/s .

T=1480N

Normal Forces on an Incline

When we rotate the x-axis to match the surface, the angle between w and the - y axis is the same as the angle theta of the slope. w can be decomposed into x and y components. (use cos and sin)

A 50-kg student (mg = 490 N) gets in a 1000-kg elevator at rest and stands on a metric bathroom scale. As the elevator accelerates upward, the scale reads A. > 490 N B. 490 N C. < 490 N but not 0 N D. 0 N

> 490N

Which of these objects is in equilibrium? A car driving down the road at a constant speed. A skydiver falling at a constant speed. A block sitting at rest on a table. All of the listed answers are correct.

All of the listed answers are correct

Static Equilibrium

When an object is at rest. No net force acting on the object If there is no net force acting on an object in xy plane, there is no net force in either the x- or y-components of the net force:

If you experience weightlessness, this means that

Your apparent weight is zero.

A box on a rough surface is pulled by a horizontal rope with tension T. The box is not moving. In this situation: A. fs > T B. fs = T C. fs < T D. fs = usmg

B. fs = T - Newton's 1st Law.

A box with a weight of 100 N is at rest. It is then pulled by a 30 N horizontal force. us=.4 uf=.2 Does the box move? A. Yes B. No C. Not enough information to say

No bc 30N < fs max - 40N

Static Equilibrium

When the static friction exactly balances the pushing force. Harder you push, the harder it will push back, if she pushes hard enough the box will slip and start to move.

A wooden box, with a mass of 22 kg, is pulled at a constant speed with a rope that makes an angle of 25° with the wooden floor. What is the tension in the rope?

fk=43.12 T=47.6N

Rules for Static Friction

-The direction of static friction is opposite to motion. -The magnitude of static friction adjusts itself so that the net force is zero and the object doesn't move. -The magnitude of static friction cannot exceed the maximum value given by the equation fmax=usn. If the friction force needed to keep the object stationary is greater than fsmax, the object will slip and move.

A 50-kg student (mg = 490 N) gets in a 1000-kg elevator at rest and stands on a metric bathroom scale. Sadly, the elevator cable breaks. What is the reading on the scale during the few seconds it takes the student to plunge to his doom? A. > 490 N B. 490 N C. < 490 N but not 0 N D. 0 N

0N The bathroom scale would read 0 N. Weight is reading of a scale on which the object is stationary relative to the scale.

Dynamics and Newton 2nd Law

1) Forces acting on an object determine its acceleration a=Fnet/m 2) Object's motion can be found by using a in the equations of kinematics Thus Fnet=ma, is sumFx=max=0 and sumFy=may=0

A car with a mass of 1500 kg is being towed at a steady speed by a rope held at a 20° angle from the horizontal. A friction force of 320 N opposes the car's motion. What is the tension in the rope?

340N

Two boxes are suspended from a rope over a pulley. Each box has weight 50 N. What is the tension in the rope?

50N

Are the objects described here in static equilibrium, dynamic equilibrium, or not in equilibrium at all? A. A girder is lifted at constant speed by a crane. B. A girder is lowered by a crane. It is slowing down. C. You're straining to hold a 200 Ib barbell over your head. D. A jet plane has reached its cruising speed and altitude. E. A rock is falling into the grand canyon. F. A box in the back of a trunk doesn't slide as the truck stops.

A. A girder is lifted at constant speed by a crane. - dynamic B. A girder is lowered by a crane. It is slowing down. - not equilibrium C. You're straining to hold a 200 Ib barbell over your head. - static D. A jet plane has reached its cruising speed and altitude. - dynamic E. A rock is falling into the grand canyon. - not in equilibrium bc accelerating d/t gravity F. A box in the back of a trunk doesn't slide as the truck stops. - not in equilibrium - when the truck is in motion then the box will also be in motion along with the truck and doesn't slide as the truck stops.

The top block is accelerated across a frictionless table by the falling mass m. The string is massless, and the pulley is both massless and frictionless. The tension in the string is A. T < mg B. T = mg C. T > mg

A. T < mg Tension has to be less than mg for the block to have a downward acceleration.

Dynamic Equilibrium

An object moving in a straight line at a constant speed (a=0) is in... No net force acting on the object If there is no net force acting on an object in xy plane, there is no net force in either the x- or y-components of the net force:

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.

Both 980N

Boxes A and B are being pulled to the right on a frictionless surface; the boxes are speeding up. Box A has a larger mass than Box B. How do the two tension forces compare? A. T1 > T2 B. T1 = T2 C. T1 < T2 D. Not enough information to tell

C. T1 < T2

A box is being pulled to the right over a rough surface. T > fk , so the box is speeding up. Suddenly the rope breaks. What happens? The box A. Stops immediately. B. Continues with the speed it had when the rope broke. C. Continues speeding up for a short while, then slows and stops. D. Keeps its speed for a short while, then slows and stops. E. Slows steadily until it stops.

E. Slows steadily until it stops.

Ropes

F-T=(mrope)(ax)=0 Generally, the tension in a massless string or rope equals the magnitude of the force pulling on the end of the string or rope. A massless string/rope "transmits" a force undiminished from one end to the other :If you pull on one end of a rope with force F, the other end of the rope pulls on what it's attached to with a force of the same magnitude F. The tension in a massless string or rope is the same from one end to the other.

Weightlessness

Having no apparent wright. A person in free fall has zero apparent weight.

Working with Ropes and Pulleys

If a force pulls on one end of a rope, the tension in the rope equals the magnitude of the pulling force. If two objects are connected by a rope, the tension is the same at both ends. If the rope passes over a pulley, the tension in the rope is unaffected

Problem Solving Equilibrium Problems

If an object is in equilibrium, the net force acting on it must be zero. -Does a=0? -Determine type of equilibrium: static or dynamic -Identify forces have and forces needed -Draw a free-body diagram -An object in equilibrium must satisfy Newton's 2nd law in component form.

Interacting Objects

Newton's 3rd law states: Every force occurs as one member of an actin/reaction pair of forces. The two members of the pair always act of different objects. The two members of an action/reaction pair point in the opposite directions and are equal in magnitude.

For the block sliding on the table in the video, the force of kinetic friction was __________ the maximum value of the static friction force; this is generally true.

Smaller than

A ball weighing 50 N is pulled back by a rope by an angle of 20°. What is the tension in the pulling rope?

T=53N

Pulleys

Tension in a massless string is unchanged by passing over a massless, frictionless pulley. Tension in the string is the same on both sides of the pulley

The drag force pushes opposite your motion as you ride a bicycle. If you double your speed, what happens to the magnitude of the drag force?

The drag force goes up by a factor of 4.

Objects in Contact

The forces on A and B are not independent: Forces F b on a acting on block A and Fa on b acting on block B are an action/reaction pair and thus have the same magnitude. Because the two blocks are in contact, their accelerations must be the same: aAx=aBx=ax We can't solve for the motion of one block without considering the motion of the other block.

Which of the following statements must be true if the net force on an object is zero? Choose all that apply. The object must have constant velocity. The object must have zero acceleration. The object must be at the origin. The object must be at rest.

The object must have constant velocity. The object must have zero acceleration.

When two objects are in contact, moving together, which of the following statements must be true? Choose all that apply. The objects must exert the same magnitude force on each other. The objects must have the same weight. The objects must have the same acceleration. The objects must have the same net force acting on them.

The objects must exert the same magnitude force on each other. The objects must have the same acceleration.

Problem Solving Approach to Dynamic Problems

Use Newton's 2nd law as the connection between forces and kinematics. If the forces are known: use 2nd law to find the acceleration, then from kinematics the objects position and velocity or vice versa. 1) sketch: list of values and what trying to find, force identification diagram and a free-body diagram. If using kinematics to find velocities or positions need a motion diagram for the accel direction and a pictorial representation that establishes a coordinate system. 2)write sumFx=max=0 and sumFy=may Solve for the acceleration, then use kinematics to find velocities and positions. Use kinematics to determine the acceleration, then solve for unknown forces.

Rolling Friction

Wheel rolling on a surface - portion of the wheel that contacts the surface is stationary with respect to the surface, not sliding. Treat it like another type of friction force that opposes the motion. Defined by fr=urn

Working with Objects in Contact

When two objects are on contact and their motion is linked, we need to duplicate certain steps in our analysis: 1) Draw each object separately and prepare a separate force identification diagram for each object 2)Draw a separate free-body diagram for each object 3)Write Newton's 2nd law in component form for each object The two objects in contact exert forces on each other: 4)Identify the action/reaction pairs of forces. If the obj A acts on obj B with force (Faonb), then identify the force Fbona that exerts on A 5)Newton's 3rd law says that you can equate the magnitude of the two forces in each action/reaction pair. The fact that the obj are in contact simplifies the kinematics: 6)Obj in contact will have the same acceleration.

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?

a=-.6m/s*2 Change in X=16.9m

A car with a mass of 1500 kg is being towed by a rope held at a 20° angle to the horizontal. A friction force of 320 N opposes the car's motion. What is the tension in the rope if the car goes from rest to 12 m/s in 10 s?

a=1.2m/s*2 T=2256N

Very small organisms, like paramecia or protozoa, moving around in water __________. almost immediately come to rest once they stop swimming experience inertia much like large objects do have quadratic drag forces acting on them take a long time to come to rest once they stop swimming

almost immediately come to rest once they stop swimming

Normal Force

an object at rest on a table is subject to an upward force due to the table. It will always be directed normal, or perpendicular, to the surface of contact.

Coefficient of Kinetic Friction.

fk.

Carol wants to move her 32 kg sofa to a different room in the house. She places "sofa sliders," slippery disks with 0.080, k on the carpet, under the feet of the sofa. She then pushes the sofa at a steady 0.40 m/s across the floor. How much force does she apply to the sofa?

fk=25N

Coefficient of Static Friction

fsmax=usn (maximum possible magnitude)

In general, the coefficient of static friction is __________. equal to the coefficient of kinetic friction greater than the coefficient of kinetic friction smaller than the coefficient of kinetic friction

greater than the coefficient of kinetic friction

You are riding in an elevator that is accelerating upward. Suppose you stand on a scale. The reading on the scale is __________. equal to your true weight greater than your true weight less than your true weight

greater than your true weight

Mass

is a quantity that describes an object's inertia. Tends to resist being accelerated