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# Tutorial 4.pdf

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McMaster University

Physics

PHYSICS 1L03

Reza Nejat

Fall

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Phys 1L03 Tutorial session Set 4
Forth series: forces, equilibrium
Concept:
m m
Newton’s Law of Universal Gravitation: F ▯ G 1 2 G ▯ 6.67 ▯10 ▯11N m kg 2
r2
q1q 2 9 2 2
Coulomb’s Law: F ▯ k 2 k ▯ 8.99 ▯10 N m C
r
▯ Static friction f ▯ ▯ N
Force of friction▯ s s
▯ kinetic friction fk▯ ▯k N
▯ ▯ ▯ ▯ F ▯ 0
Equilibrium: F ▯ F ▯ 0 F ▯ ▯▯ i,x
net ▯ i net ▯ F ▯ 0
▯▯ i, y
Some Examples for drawing Free Body Diagram:
Drawing all external force acting on an object:
1. A three way tug-on-war:
Draw free body diagram
Hints for drawing:
▯ For the system: ▯ For the free body diagram:
▯ Identify the system ▯ Identify all forces acting on the object
▯ Draw a close curve around the system ▯ Draw a coordinate system
▯ Name and label each contact force ▯ Represent the object as a dot at the origin
▯ Name and label long range force of the coordinate
▯ Draw vectors for the identified forces.
1 2. A car is being towed up a 20 slope at constant velocity. Draw free body diagram:
3. A skier is pulls up a snow-covered hill by a tow rope at a constant speed. Draw free body diagram:
4. A file cabinet in the back of a dump truck. Draw free body diagram:
2 Phys 1L03 Tutorial session Set 4
Forth series: forces, equilibrium
1. A block of mass M rests on an inclined plane that makes an angle o▯ with the horizontal, as
shown in Fig 3.55. The static friction between the block and the inclined surface is:
a. s ▯ M g
b. f ▯ M gcos▯
s
c. s ▯ M gsin▯
d. s ▯ M gcos▯
e. Zero because the plane is inclined.
2. A spring is stretched by a certain amount and then released to return to its original length. Then it
is stretched twice that initial amount (without exceeding its elastic limit). Compare to the first
stretching, the second one needs
a. twice much force.
b. four times much force
c. half as much force
d. the same amount of force.
e. none of the above.
3. Suppose you drop two steel marbles in glycerin, a highly viscous liquid. The diameter of one
marble is twice the diameter of the second one, and both marbles move with constant velocity. If
the velocity of the larger marble is four times of the velocity of the smaller one, the viscose force
of the larger marble is
a. twice the viscose force of the smaller one.
b. four times the viscose force of the smaller one.
c. half the viscose force of the smaller one.
d. the same as the viscose force of the smaller one.
e. none of the above
4. Find the force of gravity between two uniform spheres as they touch each other. Each sphere has
a mass of m ▯ 15 kg and a radius of r ▯ 0.5 m . What is the force of gravity between them
when they stand?(rsurftoe ocsarfmoe) f2 m
5. A bowling ball of mass M = 7.2 kg and radius R = 0.11 m and a billiard ball of m = 0.38 kg and
r = 0.028 m may each be treated as uniform spheres. What is the magnitude of the maximum
gravitational force that each can exert on the other?
6. The sun is more massive than the moon, but the sun is further from the earth. Which one exerts a
greater gravitational force on a person standing on the earth? Give your answer as the ration of
F sunF moon of the magnitude of the gravitational force. Take :
30 22 24
m sun▯ 2.0▯10 kg m moon ▯ 7.35▯10 k

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