Topic 6: Newtons Laws
● 1st law – intertia concept – only mass determines inertia, speed doesn’t matter
● 2nd law – F=ma concept – plus and chug values, net force = zero  constant speed, proportional changes to
variable (ex: double mass = ½ acceleration)
● 3rd law – action reaction – forces are always equal when action reaction
● FBD’s - identify proper force directions
● Friction and coeff of friction questions – find friction force with u, given surface types (wood-wood) get µ from
reference table, force needed to move object, force to move at constant v, variations in masses and angles
affects on friction forces and µ (µ never changes for given surface)
Key Points:
● Fnet(X) = max
Fnet(Y) = may = 0 in almost all cases
X and Y direction forces should never both be in the same Fnet equation, use components when necessary
● Equilibrium – a=0, Fnet=0
WATCH FOR CONSTANT SPEED:
● The Normal Force – The normal force is a supporting force that comes from a surface. It is most often equal to
the weight but in some scenarios is not.
● Friction – Keep in mind that the coefficients of friction for given surfaces are listed on the reference table.
If a problem does not specify frictionless, you must assume that there is friction.
● Incline Problems – Rotate the axis so the x direction is aligned parallel with surface. After drawing Fg, always
draw Fgx and Fgy and find them with Fgx = mg sin θ (sine slides) … and Fgy = Fg cos θ
● Watch signs +/- always. Always draw your axis on the page and set the direction you are moving in as +
Topic 7 A/B: Centripetal Acceleration/Force, Gravity
● Fg = Gravitational force of attraction between any two masses
Fg = G m m / r2
- remember that “r” is not radius, it is the separation of the two mass centers
- be aware of #’s on reference table for planets
● When an object is on the surface of a planet, you can use the above formula or FG=mg
● Recall changing factors problems where m is doubled and r is tripled and how is Fg changed. Start with all
variable equal to “1” then make the changes to see what the new value is
●
●
●
●
●
Fnet(c) = Centripetal force and acceleration always act towards the center
Velocity is tangent to the circular path at a given spot (things that leave the circle follow the tangent line)
Things are moving in circles, so in 1 revolution, d= 2 π r  v = 2 π r / T
ac is caused by direction changes, a is caused by speed changes
Fc does not push you out from circle center rather it pushes in to the center to make the circle happen;
inertia makes you “feel like” you are pushed to the outside
Physics Regents Review HW #2 – Newtons, Centripetal, Gravitation
Wells
Name: ___________________________
THIS HW WILL COUNT AS A DOUBLE HW GRADE. THAT MEANS YOU GET TWO ZEROS IF YOU DON’T DO IT.
ANSWER SHEET. Place your answers to the attached assignment on this first sheet. Standard class homework
policies apply.
MULTIPLE
CHOICE
PROBLEMS
1.)
1.)
(a)
2.)
(b) ON SHEET
3.)
(c)
4.)
(d) ON SHEET
5.)
6.)
2.)
7.)
8.)
9.)
10)
3.)
11)
(a)
12)
(b) ON SHEET
13)
(c)
14)
Questions 4,5,6
15)
ON SHEET
16)
17)
18)
19)
20)
21)
7.)
22)
23)
24)
25)
26)
27)
8.)
MULTIPLE CHOICE
1.) A ball having mass m is struck by a bat having mass 9 m. Compared to the magnitude of the force exerted by
the bat on the ball, the magnitude of the force exerted by the ball on the bat is
(1) less
(2) greater
(3) the same
2.) A 1.5-kilogram lab cart is accelerated uniformly from rest to a speed of 2.0 meters per second in
0.50 second. What is the magnitude of the force producing this acceleration?
(1) 0.70 N (3) 3.0 N
(2) 1.5 N (4) 6.0 N
3.) Which graph best represents the motion of an object that is not in equilibrium as it travels
along a straight line?
4.) When a 12-newton horizontal force is applied to a box on a horizontal tabletop, the box remains at rest. The
force of static friction acting on the box is
(1) 0 N
(2) between 0 N and 12 N
(3) 12 N
(4) greater than 12 N
5.) Which person has the greatest inertia?
(1) a 110-kg wrestler resting on a mat
(2) a 90-kg man walking at 2 m/s
(3) a 70-kg long-distance runner traveling at 5 m/s
(4) a 50-kg girl sprinting at 10 m/s
6.) A 60-kilogram skydiver is falling at a constant speed near the surface of Earth. The magnitude
of the force of air friction acting on the skydiver is approximately
(1) 0 N (3) 60 N
(2) 6 N (4) 600 N
7.) A 70.-kilogram astronaut has a weight of 560 newtons on the surface of planet Alpha. What is the
acceleration due to gravity on planet Alpha?
(1) 0.0 m/s2 (3) 9.8 m/s2
(2) 8.0 m/s2 (4) 80. m/s2
8.) Three forces act on a box on an inclined plane as
shown in the diagram below. [Vectors are not
drawn to scale.] If the box is at rest, the net force acting
it is equal to
(1) the weight (3) friction
(2) the normal force (4) zero
on
9.) A man standing on a scale in an elevator notices that the scale reads 30 newtons greater than his
normal weight. Which type of movement of the elevator could cause this greater-than-normal
reading?
(1) accelerating upward
(2) accelerating downward
(3) moving upward at constant speed
(4) moving downward at constant speed
10.) If the sum of all the forces acting on a moving object is zero, the object will
(1) slow down and stop
(2) change the direction of its motion
(3) accelerate uniformly
(4) continue moving with constant velocity
11.) The diagram below shows a block sliding down a plane inclined at
angle with the horizontal. As angle is increased, the coefficient of kinetic
friction between the bottom surface of the block
and the surface of the incline will
(1) decrease
(2) increase
(3) remain the same
12.) The diagram below shows a 10.0-kilogram mass held at rest on a
frictionless 30.0° incline by force F. What is the approximate magnitude of
force F?
(1) 9.81 N (3) 85.0 N
(2) 49.1 N (4) 98.1 N
13.) An apple weighing 1 newton on the surface of Earth has a mass of approximately
(1) 1 x 10–1 kg (3) 1 x 101 kg
0
2
(2) 1 x
kg (4) 1 x
kg
14.) In which situation is the net force on the object equal to zero?
(1) a satellite moving at constant speed around Earth in a circular orbit
(2) an automobile braking to a stop
(3) a bicycle moving at constant speed on a straight, level road
(4) a pitched baseball being hit by a bat
15.) Compared to the force needed to start sliding a crate across a rough level floor, the force needed to keep
it sliding once it is moving is
(1) less
(2) greater
(3) the same
16.) The diagram below shows a 5.00-kilogram block at rest on a horizontal, frictionless table.
Which diagram best represents the force exerted on the block by the table?
17.) A 1.0-newton metal disk resting on an index card that is balanced on top of a glass.
When the index card is quickly pulled away from the glass in a horizontal direction, the disk falls straight
down into the glass. This action is a result of the disk’s
(1) inertia (3) shape
(2) charge (4) temperature
18.) Gravitational force F exists between point objects A and B separated by distance R. If the mass of A is
doubled and distance R is tripled, what is the new gravitational force between A and B?
(1) 2F/9
(2) 2F/3
(3) 3F/2
(4) 9F/2
19.) An object weighs 100 newtons on Earth’s surface. When it is moved to a point one Earth radius above
Earth’s surface, it will weigh
(1) 25.0 N (3) 100. N
(2) 50.0 N (4) 400. N
20.) A child is riding on a merry-go-round. As the speed of the merry-go-round is doubled, the
magnitude of the centripetal force acting on the child
(1) remains the same (3) is halved
(2) is doubled (4) is quadrupled
The diagram represents two satellites of equal mass, A and B, in
circular orbits around a planet.
21.) Compared to the magnitude of the gravitational force of
attraction between satellite A and the planet, the magnitude of the
gravitational force of attraction between satellite B and the planet is
(1) half as great
(2) twice as great
(3) one-fourth as great
(4) four times as great
22-23) A roller coaster cart starts from rest and accelerates, due to gravity, down a track. The cart starts at a
height that enables it to complete a loop in the track. [Neglect friction.]
22.) The magnitude of the centripetal force keeping the cart in circular motion would be greatest at point
(1) A
(2) B
(3) C
(4) D
23.) 10 Which diagram best represents the path followed by an object that falls off the cart when the cart is at
point D?
24.) In the diagram, a cart travels clockwise at constant speed in a
horizontal circle.
At the position shown in the diagram, which arrow indicates the
direction of the centripetal acceleration of the cart?
(1) A (3) C
(2) B (4) D
The diagram shows a student seated on a rotating circular platform, holding a 2.0-kilogram block with a
spring scale. The block is 1.2 meters from the center of the platform. The block has a constant speed of 8.0
meters per second. [Frictional forces on the block are negligible.]
25.) Which statement best describes the block’s movement as the platform rotates?
(1) Its velocity is directed tangent to the circular path, with an inward acceleration.
(2) Its velocity is directed tangent to the circular path, with an outward acceleration.
(3) Its velocity is directed perpendicular to the circular path, with an inward acceleration.
(4) Its velocity is directed perpendicular to the circular path, with an outward acceleration.
26.) The reading on the spring scale is approximately
(1) 20. N (3) 110 N
(2) 53 N (4) 130 N
27) In the diagram below, S is a point on a car tire rotating at a constant rate.
Which graph best represents the magnitude of the centripetal acceleration of point S as a function of time?
Problems
1.) A force of 10. newtons toward the right is exerted on a wooden crate initially moving to the right on a
horizontal wooden floor. The crate weighs 25 newtons.
(a) Calculate the magnitude of the force of friction between the crate and the floor. [Show all work,
including the equation and substitution with units.] [2]
(b) Draw and label all horizontal and vertical forces acting on the crate. [2]
(c) What is the magnitude of the net force acting on the crate? [1]
(d) Is the crate accelerating? Explain your answer. [1]
2) The gravitational force of attraction between Earth and the Sun is 3.52 × 1022 newtons. Calculate the mass of
the Sun. [Show all work, including the equation and substitution with units.] [2]
3) The combined mass of a race car and its driver is 600. kilograms. Traveling at constant speed, the car
completes one lap around a circular track of radius 160 meters in 36 seconds.
(a) Calculate the speed of the car. [Show all work, including the equation and substitution with units.] [2]
(b) On the diagram draw an arrow to represent the direction of the net force acting on the car [1]
(c) Calculate the magnitude of the centripetal acceleration of the car. [Show all work, including
the equation and substitution with units.] [2]
4) Base your answers on the information and diagram below.
In an experiment, a rubber stopper is
attached to one end of a string that is
passed through a plastic tube before
weights are attached to the other
end. The stopper is whirled in a
horizontal circular path at constant
speed.
(a) On the diagram of the top view draw the path of the rubber stopper if
the string breaks at the position shown.
(b) Describe what would happen to the radius of the circle if the student
whirls the stopper at a greater speed without changing the balancing
weights.
(c) List three measurements that must be taken to show that the magnitude of the centripetal force is equal to
the balancing weights. [Neglect friction]
(d) The rubber stopper is now whirled in a vertical circle at the same speed. On the diagram draw and label
vectors to indicate the direction of the weight (Fg) and the direction of the centripetal force (Fc) at the position
shown.
5.) An airplane is moving with a constant velocity in level flight. Compare the magnitude of the forward force
provided by the engines to the magnitude of the backward frictional drag force, explain.
6.) A box of mass m is held motionless on a frictionless inclined plane
by a rope that is parallel to the surface of the plane. On the diagram
provided on your answer paper, draw and label all of the force
vectors acting on the box. The diagram below is provided for practice
purposes only. Be sure your final answer appears on your answer
paper. [3]
7.) The coefficient of kinetic friction between a 780.-newton crate and a level warehouse floor is 0.200. Calculate
the magnitude of the horizontal force required to move the crate across the floor at constant speed. [Show all
work, including the equation and substitution with units.] [2]
8.) A skier on waxed skis is pulled at constant speed across level snow by a horizontal force of 39 newtons.
Calculate the normal force exerted on the skier. [Show all work, including the equation and substitution with
units.] [2]