FREE BODY DIAGRAMS: RESULTANT FORCE
1. Calculate the missing values in the following free body diagrams. Don't forget to include direction.
100 N
20 N
75 N
100N
20 N
150 N
50 N
96 N
43.6 N
98.4 N
75 N
100 N
FR =
FR =
FR =
m = 5 kg
m =
m = 9.5 kg
a =
a = 4.356 m/s2 [left]
a =
57 N
120 N
70 N
80 N
120 N
140 N
??
80 N
65 N
??
70 N
??
FR =
FR =
FR =
m = 14.2 kg
m =
m = 12.7 kg
a = 3.68 m/s2 [up]
a = 4.25 m/s2 [left]
a =
80 N
45 N
67 N
85.3 N
20 N
200 N
80 N
53 N [right]
200 N
?? N
?? N
67 N
123 N
FR =
FR =
FR =
m = 4.23 kg
m =
m = 32 kg
a =
a = 3.5 m/s2 [down]
a = 2.5 m/s2 [right]
answers: 1. 50 N [u], 10 m/s2 [up] 2. 54 N [left], 12.40 kg 3. 54.8 N [right], 5.768 m/s2 [right], 4. 4.744 N [down], 52.26 N [up] 5. 80 N [down], 60 N [left]
14.12 kg 6. 118 N [right], 4.173 m/s2 [right] 7. 25 N [left], 5.910 m/s2 [left] 8. 37.7 N [down], 10.77 kg 9. many combinations, 80 N [right]
2. Calculate the missing values in the following free body diagrams. Don't forget to include direction.
100 N
70 N
75 N
100N
70 N
78 N
150 N
90 N 50 N
99 N
96 N
28 N
98.4 N
43.6 N
30 N 45 N
100 N
FR =
FR =
FR =
m =
m = 14.25 kg
m = 9.5 kg
a = 2.36 m/s2 [down]
a =
a =
57 N ??
120 N
70 N
80 N
120 N
140 N
45 N
?? N
??
20 N
65 N
65 N
70 N
FR =
40 N 40 N
FR = 25 N [left]
FR =
m = 5.67 kg
m =
m = 9.75 kg
a = 4.59 m/s2 [up]
a = 4.25 m/s2 [left]
a =
80 N
38 N
32 N
29 N 36 N
42 N
150 N
45 N 35 N
28 N [right]
75 N
150 N
45 N
?? N
?? N
75 N
123 N
FR =
FR =
FR =
m = 6.92 kg
m =
m = 22 kg
a =
a = 12.5 m/s2 [down]
a = 3.75 m/s2 [left]
answers: 1. 40 N [down], 16.95 kg
2. 33 N [left], 2.316 m/s2 [left] 3. 82.8 N [right], 8.716 m/s2 [right] 4. 34.02 N [up], 26.02 N [up]
5. 160 N [right], 5.882 kg 6. 73 N [right], 2.872 m/s2 [right] 7. 28 N [left], 4.046 m/s2 [left] 8. 58 N [down], 4.64 kg 9. many combinations, 82.5 N [left]
Dynamics Problems
1.
The net force on a 5 kg bowling ball is 20 N [E]. What is the bowling ball’s acceleration? (4 m/s2)
2.
A baseball hit by a bat with an average force of 1000 N [W] accelerates at 4000 m/s 2. What is the baseball’s
mass? (0.25 kg)
3.
What unbalanced force is needed to accelerate a 30 000 kg spacecraft at 2.5 m/s 2 [182o mark 28]?
(75 000 N [182o mark 28])
4.
How much applied force is needed to accelerate a 2 kg block of wood at 4 m/s 2 along a rough table, against a 10
N force of friction? (18 N)
5.
A jet plane pilot decides to accelerate horizontally. If the thrust of the engines is increased to 50 000 N at a time
when the air resistance (or drag) acting on the 4000 kg plane amounts to 30 000 N, what will be the plane’s
acceleration? (5 m/s2)
6.
Two children are arguing over a toy. One pulls on the toy with a force of 32 N [N]. The other pulls with a force of
30 N [S]. If the toy has a mass of 500 g, what will be its resulting acceleration? (4 m/s 2)
7.
A tennis player is practising by hitting a ball against a brick wall. The ball has a mass of 84 g and is traveling at 32
m/s [E] when it hits the racquet. It leaves the racquet 0.085 s later with a velocity of 40 m/s [W]. Determine the
average force exerted by the racquet on the ball during this phase of its motion? (71.15 N [W])
8.
A swimmer releases a 20 kg rock from rest under the water. If the resistance and buoyancy provided by the water
is 150 N while the force of gravity on the rock is 200 N [down], how long will it take to fall 1 m? (0.8944 s)
9.
A little girl has a toy of mass 312 g on the end of a string. She holds the string so that the toy hangs below her
hand. She then exerts a force upward on the string of 3.8 N. The force of gravity on the toy is 3.12 N [down].
What will be the toy’s velocity after it has been raised 10 cm? (0.6602 m/s)
Physics 11 Dynamics Unit Questions
Qualitative force and fbd’s
P54 1,2 55 4-6
Inertia 60 1,2
63 6,7
65 1,2
F=ma
73 1-6 74 1-3
56 7,8
57 9
58 1-3
net force 61 3,4
third law 77 3-5 77 blue 1,2
Review 80 1-17
Gravity 86 1-5
87 9,10
89 1-9
Universal gravitation 93 3-7
95 1-3
Friction 103 1-6 105 7,8 107 1-6
110 13-16
110 6-12
Gravity Problems
1.
A hockey player who weighs 800 N comes to rest from 10.0 m/s [W] in 1.00s.
a) What is his mass? [81.55 kg]
b) What is his average acceleration? [10 m/s2]
c) What force is required to provide this acceleration? [816 N [E]]
2.
A 500g ball is dropped from a tall building. An observer measures the ball’s acceleration to be 5.0 m/s 2
downwards. What must the force of air resistance be? [2.4 N upward]
3.
A parachutist jumps out of airplane with an initial speed of 2.0 m/s downwards. There is a force of air resistance
equivalent to 305 N. Determine the parachutist’s mass if it takes a total of 3 seconds for him to travel 30 m
downwards. [68 kg]
4.
An elevator of mass 900kg accelerates upwards at 3.00 m/s2. What is the tension in the cable where it is attached
to the elevator? [1.15 x 104 N upward]
5.
A 60.0 kg man hangs from a lightweight cable suspended from a helicopter. Find the tension in the cable if the
acceleration of the box is
a) 5.00 m/s2 upward [889 N]
b) 5.00 m/s2 downward [289 N]
6.
A man in an elevator at rest stands on a scale and reads his weight as being 490.0 N. The elevator then begins to
accelerate downwards at 4.210 m/s2. When this acceleration occurs, what does the Newton scale now read?
[279.5 N]
7.
When an elevator accelerates upwards at 2.70 m/s2, a woman standing on a scale reads a weight of 750 N.
Determine the woman’s weight when at rest. [588 N]
Friction Problems
1.
A 20 kg toboggan is pulled along at a constant speed by a horizontal force of 30 N.
a) What is the force of gravity on the toboggan? (196.2 N [down])
b) What is the coefficient of friction? (0.1529)
c) How much force is needed to pull the toboggan if two 60 kg girls are sitting on it? (210.0 N)
2.
It takes a 5 N horizontal force to pull a 2 kg object along the ground at a constant speed. What is the coefficient of
friction? (0.2548)
3.
How much horizontal force does it take to pull a 100 kg packing crate along a rough floor at a constant speed,
given each of the following coefficients of friction?
a) 0.1 b) 0.2 c) 0.5 (98.1 N, 196.2 N, 490.5 N)
4.
If the coefficient of friction is 0.25, how much horizontal force is needed to pull each of the following masses along
a rough desk at a constant speed?
a) 25 kg
b) 15 kg
c) 200 g
(61.31 N, 36.79 N, 0.4905 N)
5.
A force of 40 N is required to start a 5 kg box moving across a horizontal concrete floor.
a) What is the coefficient of static friction between the box and the floor? (0.8155)
b) If the 40 N force continues, the box accelerates at 0.7 m/s 2. What is the coefficient of kinetic friction? (0.7441)
6.
The police measure the skid marks of a car to be 80 m. The coefficient of kinetic friction between the rubber and
the pavement is 0.8. Estimate the initial speed of the car assuming a level road. (127.6 km/h)
7.
A box is given a push so that it slides across the floor. How far will it go, given that the coefficient of kinetic friction
is 0.2 and the push imparts an initial speed of 4 m/s? (4.077 m)
8.
A coffee cup on the dashboard of a car slides forward on the dash when the driver decelerates from 40 km/hr to
rest in 3.5 s or less, but not if he decelerates in a longer time. What is the coefficient of static friction between the
cup and the dash? (0.3236)
9.
A flatbed truck is carrying a heavy crate. The coefficient of static friction between the crate and the bed of the
truck is 0.75. What is the maximum rate at which the driver can decelerate and still avoid having the crate slide
against the cab? (7.358 m/s2)
10.
Show that the minimum stopping distance for an automobile traveling at a speed v is equal to v 2
sg. If a 1200
kg car were traveling at 95 km/hr, what would the stopping distance be if the coefficient of static friction were
0.45? What would it be if the car was on the Moon but all else stayed the same? (78.87 m, g moon = 1.619 m/s2,
477.9 m)
11.
A 70 kg climber is supported in a chimney by the friction forces exerted on his shoes and back, which are in
contact with the vertical walls. The coefficients of static friction between his shoes and the wall and his back and
the wall, are 0.8 and 0.6 respectively. What is the minimum normal force he must exert? The normal force he
exerts is the same for both walls. (490.5 N)
12.
Drag race tires in contact with an asphalt surface probably have on the highest coefficients of static friction in the
everyday world. Assuming a constant acceleration and no slipping of tires, estimate the coefficient of static friction
for a drag racer that covers the quarter mile in 6 s. (1 mile is 5280 ft) (2.283)
Normal Problems
1.
A 15 kg object rests on a horizontal surface.
a) What is the normal force exerted by the surface? (147.2 N [up])
b) If the object is pushed down with a force of 50 N (and remains at rest) what is the normal force?
(197.2 N [up])
c) If the object is pulled upward with a force of 100 N (and remains at rest) what is the normal force?
(47.2 N [up])
d) If the object is lifted with a force of 300 N what is the normal force. What is the acceleration of the object?
(0, 10.19 m/s2 [up])
2.
A 2 kg ball is dropped from a height of 5 m onto the ground below. After the ball first touches the ground it takes
0.106 s for the ball to come to rest (it then begins its rebound).
a) Draw an fbd of the ball in the air?
b) What velocity did the ball hit the ground with? (9.905m/s [down])
c) Draw an fbd of the ball in contact with the ground?
d) What was the normal force of the ground that brought the ball to rest? (206.5 N [up])
3.
Ian throws Alex (60 kg) into a soft ceiling so that Alex hits the ceiling with a velocity of 7.8 m/s [up]. The ceiling
compressed 54 cm at which point Alex was stuck in the ceiling.
a) Draw an fbd of Alex in contact with the ceiling.
b) What was the normal force that ceiling imparted to Alex? (2791.4 N [down])
4.
Husna (50 kg) goes skydiving but a hole developed in her parachute that allowed her to go a bit faster than she
wished. She landed with a constant velocity in some mud, which compressed 78 cm in 0.268 s during her landing.
a) Draw Husna's fbd while in the mud?
b) What was Husna's acceleration while in the mud? (21.72 m/s2 [up])
c) What was the normal force of the mud on Husna? (1576 N [up])
d) What velocity did Husna hit the ground with? (5.821 m/s [down])
5.
Douglas (60 kg) dives into the water from a height of 20 m with his favourite floaties on. He reaches a depth of 4
m before he comes to a stop. The floaties provide an upward force of 300 N (due to buoyancy).
a) What velocity did Douglas hit the water with? (19.81 m/s [down])
b) Draw an fbd for Doug in contact with the water.
c) What was the normal force of the water on Douglas (buoyancy is not the normal force)?
(3232 N [up])
Newton's Third Law Problems
1.
Mr. Moors pulls 2 sleds connected with ropes with a force of 250 N. The first sled has a mass of 50 kg while the
second sled has a mass of 36 kg. Assume the snow is frictionless.
a) Draw fbd's for the two sleds.
b) What was the acceleration of the two sleds? (2.907 m/s 2)
c) What was the tension in both connecting ropes? (250 N, 104.7 N)
d) Redo this question with friction present (coefficient of kinetic friction is 0.085). (2.073 m/s2, 250 N, 104.6 N)
2.
A 5 kg mass rests on a 10 kg mass, which rests on 25 kg mass, which rests on the ground.
a) Draw fbd's for each mass.
b) What is the net force acting on each mass? (0)
c) What is the normal force acting on each mass? (49.05 N [up], 147.2 N [up], 392.4 N [up])