PHY 2311

PHYSICS 231Lecture 14: revision

Remco ZegersWalk-in hour: Monday 9:15-10:15 am

Helproom BPS 1248

PHY 2312

Chapter 4: Newton’s Laws

First Law: If the net force exerted on an object is zero the object continues in its original state of motion; if it was at rest, it remains at rest. If it was moving with a certain velocity, it will keep on moving with the same velocity.

Second Law: The acceleration of an object is proportional to the net force acting on it, and inversely proportional to its mass: F=ma

If two objects interact, the force exerted by the first object on the second is equal but opposite in direction to the force exerted by the second object on the first: F12=-F21

PHY 2313

Important equationsNewton’s second law: F=maGravitational Force: F=mg F=Gm1m2/r2

Earth: m1=mearth

r=rearth

g=Gm2/r2=9.8 m/s2

Equilibrium: Fx=0 Fy=0 (object not moving) FL=0 F//=0

normal force: force perpendicular to surface the objectis resting on, and balancing the component ofthe gravitational force perpendicular to the surface

friction: F=sn (s: coef. of static friction)F=kn (k: coef. of kinetic friction) s>k

Hooke’s law: Fs=-kx (k: spring constant)

PHY 2314

example 1To lift a patient, 4 nurses grip the sheet on which the patientis lying and lift upward. If each nurse exerts an upward force of 240 N and the patient has an upward accelerationof 0.504 m/s2 what is the weight of the patient?

PHY 2315

example 2

A 5.0 kg bucket of water is raised from a well by a rope.If the upward acceleration of the bucket is 3.0 m/s2, findthe force exerted by the rope on the bucket.

PHY 2316

example 3A 1000-kg car is pulling a 300 kg trailer. Their accelerationis 2.15 m/s2. Ignoring friction, find:a) the net force on the carb) the net force on the trailerc) the net force exerted by the trailer on the card) the resultant force exerted by the car on the road

PHY 2317

example 4

2 kg

Aq=20o

Is there a value for the staticfriction of surface A for whichthese masses do not slide?If so, what is it? And what if the 2-kg mass is only0.5 kg?

1 kg

PHY 2318

example 5

F A force F (10N) is exerted on the red block (1 kg). The coef.of kinetic friction between the red block and the blue one is 0.2.If the blue block (10kg)rests on a frictionless surface, what willbe its acceleration?

PHY 2319

example 6

A rocket is fired from a launching pad. The velocity ANDacceleration of the rocket increase with time even thoughthe thrust of the engine is constant. Why?a)The gravitational force becomes smaller because the mass of the rocket becomes smaller (losing fuel)b) The gravitational constant g becomes smaller if the rocket travels away from the earthc) While traveling away from earth, the gravitational pull from other planets/sun becomes stronger supporting the further accelerationd) Because the density of air becomes small, the friction becomes less

PHY 23110

Revision: chapter 5 Work: W=Fcos()x Energy transfer Power: P=W/t Rate of energy transfer Potential energy (PE) Energy associated with

position. Gravitational PE: mgh Energy associated with

position in grav. field. PE stored in a spring: 1/2kx2 x is the compression of the spring

k is the spring constant Kinetic energy KE: 1/2mv2 Energy associated with

motion Conservative force: Work done does not depend on path Non-conservative force: Work done does depend on path Mechanical energy ME: ME=KE+PE

Conserved if only conservative forces are present KEi+PEi=KEf+PEf

Not conserved in the presence of non-conservative forces (KEi+PEi)-(KEf+PEf)=Wnc

PHY 23111

example 7

k=100 N/m

m=1 kg

1 cm

A pendulum is pushed with initialvelocity 0.1 m/s from a height of1 cm. How far does it compress thespring? (assume m does not risesignificantly after hitting the spring)

PHY 23112

example 8

A ‘smart’ student decides to save energy by connecting his exercise treadmill to his laptop battery. If it takes 70 J to move the belt on the treadmill by 1 meter and 50% of the generated energy is stored in the battery, how‘far’ must the student run to use his 100 W laptop for freefor 2 hours?

PHY 23113

example 9

450

A block of 1 kg is pushed up a 45o

slope with an initial velocity of 10 m/s.How high does the block go if:a) there is no frictionb) if the coefficient of kinetic friction is 0.5.

h

PHY 23114

example 10A crate of 50kg is starting to slide from a slope. When it reaches the bottom, it is caught by a spring with a springconstant of 1000 N/m. a) If the crate was originally at a heightof 10 m and friction can be ignored, how much is the springmaximally compressed? b) if the frictional force is 100N and the length of the slope is 15m, what is the maximal compression?

PHY 23115

example 11

A car (A) can accelerate from 0 to 10 m/s in 5 s. Anothercar (B) of the same mass as A can reach 8 m/s in 5 s seconds. What is the ratio of the power of car A to car B ( PA/PB)?

A) 10/8B) 8/10C) 1D) 10/5E) 8/5F) 100/64

PHY 23116

example 12

A 70-kg diver steps of a 10-m tower and drops, from reststraight down into the water. If he comes to rest 5.0 mbelow the water surface, determine the average resistive force exerted by the water.