Physics Homework Assignment: Mechanics, Energy, and Safety Features

This physics assignment presents a comprehensive exploration of various physics concepts. It begins with questions on converting angles to radians and angular velocity, followed by problems involving torque calculations and ranking forces. The assignment delves into mechanics, including calculating gravitational force and applying Newton's laws. It then addresses energy concepts, such as work done by jet engines, gravitational potential energy, and kinetic energy calculations. Additionally, the assignment explores spring constants and pendulum periods. The document concludes with a detailed essay on car safety features, explaining how seat belts, crumple zones, and airbags reduce injury in collisions by manipulating momentum, impulse, interaction time, and force. The assignment provides a complete understanding of core physics principles.

Use complete sentences and details to answer all but the quantitative questions.
Mathematical calculations are recommended on your answer sheet for
quantitative problems (questions with numbers).
1. Convert the following into radians
360 °=2 π rad1 °= π
180 rad
a. 2.0°
¿ 2 × π
180 = π
90 rad
b. 20.0°
¿ π
180 ×20= π
9 rad
c. 40.0°
¿ π
180 × 40= 2 π
9 rad
d. 100°
π
180 ×100=5 π
9 rad
e. 200°
π
180 ×200=10 π
9 rad
2. Convert the following into angular velocity in radians per second?
1 rpm= 1
60 revolution per second= π
30 rad / s
a. 33 rpm
¿ 33 × π
30 =11 π
10 rad / s
b. 78 rpm
¿ 78 × π
30 =13 π
5 rad /s
c. 120 rpm
¿ 120 × π
30 =4 π rad / s
d. 1 rotation per second
¿ 1 × π
30 ÷ 1
60 =2 π rad /s
e. 30 rotations per second
¿ 30 × π
30 ÷ 1
60 =60 π rad / s

3. Look at the overhead diagram of the door on a hinge. Force A, B and C are all
equal. Rank each force from highest to lowest torque on the hinge of the door.
τ =rF sinθ τ is the Torque ; r distance ¿ the hinge τ A =rF sin ( 0 ) =0 τ B=rFsin ( 90 ) =rB F
τC =rF sin ( 90 ) =rC F But rB >r C Thus : τB >τC B>C> A
4. A force of 100 N is applied to a wrench as shown in the diagram below. What
is the torque is the force is applied 0.500 m from the pivot point of the nut? Is
the torque positive or negative?
τ =dF sinθ τ is the Torque ; d distance ¿ the pivot point τ =0.500 m× 100 N =50 Nm The force is
acting on anticlockwise direction. Thus the torque is Positive

5. In the diagram below a 30.0 lb weight is supported by the bicep muscle. What
is the torque (in units of Nm) on the elbow joint due to the 30 lb weight?
. 30 lb=13.6078 kg=13.6078× 9.81 N =133.4925 N
The free body diagram is shown below
τ =dF sinθ ¿ 0.35 ×133.4925 ¿ 46.7224 Nm
6. What is the force (in units of N) of the bicep muscle to support the weight?
From the free body diagram shown below, upward moment equal to
downward moment
Thus:
0.04 m× FB =0+ ( 0.35 ×133.4925 ) FB= 0.35 ×133.4925
0.04 N ¿ 1168.0594 N
7. According to Newton’s Universal Law of Gravitation, any object with mass
exerts a force on any other object with mass. Calculate the gravitational force
between two people (both mass of 80 kg), 1 meter away from each other.

Does this explain why we don’t feel the gravitational force from all but the
Earth?
FGrav=G m1 m2
d2 FGrav is gravitational force , G=6.673 x 10−11 N m2
k g2 Gravitational constant
FGrav=6.673 x 10−11 × 80 ×80
12 ¿ 4.27072 ×10−7 N
The gravitational force between the two people is very small, thus it
explains why we don’t feel the gravitational force from all but the Earth
8. Explain why Saturn is almost 100 times more massive than the Earth,
however, the acceleration of gravity on the top of Saturn’s clouds (no solid
surface) is about the same as the gravity at the surface of the Earth.
Saturn and Earth have nearly the same surface gravitational acceleration though
Saturn is much larger and more massive than earth, this is because Saturn, is
composed mostly of hydrogen, helium, and ices of low-mass volatiles. Earth is
made principally of silicon, carbon, iron and other metals which are many, many
times denser.
9. In 2014, a pair of astronomers offered proof of a distant planet orbiting the
Sun using the orbits of Pluto-like bodies at the edge of the Solar System.
The hypothetical well beyond the orbit of Neptune, 700 times further from
the Sun than the Earth. What would the approximate period of this orbit be
according to Kepler’s third law?

It will take 700 Earth years to make one full orbit around the sunplanet
nine may orbit

10.Type equation here .The Boeing 777-300ER uses two of the largest jet engines
ever built (GE-90) to generate thrust? It’s massive GE-90 has been able to
generate 569 kN (5.69 x 105 N) of force during a “red-line” test. Normally
maximum thrust is 500 kN (5.00 x 105 N). If the Jet has two of these engines,
how much work do these engines do as it accelerates 1.2 km (1200 m) down
the runway?
Work done=Force × Distance E=Fd¿ 2 ×5.69 ×105 ×1200 ¿ 1365600000 J
¿ 1.3656 ×109 J ∨1.3656 GJ
11.The 777 has a cruising altitude of 43,000 ft (13,100 m) at a speed of 560 mph
(250 m/s). The operational mass of the 777 is 168,000 kg. What is the
gravitational potential energy and the kinetic energy of this aircraft at
cruising altitude? Type equation here .

Type equation here . PE=mgh¿ 168000 ×9.81 ×13100¿ 2.1589848 ×1010 J KE= 1
2 m v2
¿ 1
2 ×168000 ×2502
¿ 5.25 ×109 J
12. A scale is used to measure the weight of an object. The scale can measure
weights up to a maximum of 200 N. If the spring compresses 5.0 cm (0.050
m) at this maximum weight, what is the spring constant of the spring in this
scale?
K=−F
x ¿− 200
0.05 ¿ 4000 N /m

13.A pendulum on a mechanical clock is designed to have a period of precisely
0.50 seconds to keep time. How long should this pendulum be to have a
period of 0.50 s?
It will have a period 0.5
2 =0.25 s

14.A cannon used by Napoleon’s forces had a mass of 1,200 kg and could fire a
4.0 kg shell with a velocity of 440 m/s (nearly the speed of sound). What is
the momentum and kinetic energy of the shell?
Momentum=mass × velocity P=mv=4.0 × 440¿ 1760.0 kg . m/sKE= 1
2 m v2 ¿ 1
2 × 4 × 44 02
¿ 387200 kg . m2 /s2
15. If the cannon above were not secured to the ground, what would its recoil
velocity be for these conditions?
m2 v2=mv=1760 v2=mv
m2
=−1760
1200 ¿−1.46667 m/s
Negative because recoil velocity acts on opposite direction
Essay (2 paragraph minimum): Car Safety and Momentum (25 points) –
Please reread the chapter on momentum and impulse. Explain how safety
features such a seat belts, crumple zones and air bags can reduce injury. Do

this in the context of momentum, impulse, interaction time and force. If
you need to draw diagrams or graphs, please feel free to include them in
your discussion.
A moving vehicle have momentum. Forces cause changes in momentum. In case a
vehicle comes to a sudden stop, each mass (passage or body of the vehicle) loses
all their momentum. To ensure that the force on the passengers are as small as
possible, it is significant that they stop gradually. This is accomplished by:
i) Use of seat belts. Seat belts are designed to stretch a bit in a collision.
This increases the time taken for the body's momentum to reach zero,
and so reduces the forces on it.
ii) Use of air bags. Air bags increase the time taken for the head's
momentum to reach zero, and so reduce the forces on it. They also act a
soft cushion and prevent cuts.
iii) Use of Crumple zones. These is an area of a vehicle that is designed to
crush in a controlled way in a collision. It increase the time taken to
change the momentum of the passengers in a crash, which reduces the
force involved.