# PHYHSICS QUESTIONS

**Chapter 3 – Translational MotionTop of Form**

**Question 1**

The average speed of a horse that gallops 10 kilometers in 30 minutes is

1. **15 km/h.**

2. **30 km/h.**

3. **40 km/h.**

4. **20 km/h.**

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**Question 2**

If a car increases its velocity from zero to 60 m/s in 10 seconds, its acceleration is

1. **3 m/s2.**

2. **60 m/s2.**

3. **600 m/s2.**

4. **6 m/s2**Bottom of Form

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**Question 3**

A mosquito flying at 3 m/s that encounters a breeze blowing at 3 m/s in the opposite direction has a speed of

a**4 m/s.**

b0 m/ms

c. **6 m/s.**

**3 m/s.**Bottom of Form

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**Question 4**

A mosquito flying at 3 m/s that encounters a breeze blowing at 3 m/s in the same direction has a speed of

1. **4 m/s.**

2. **0 m/s.**

3. **3 m/s.**

4. 6 m/s

Top of Form**Question 5**

You cannot exert a force on a wall

5. **unless you put your mind to it.**

6. **if the wall resists.**

7. Bottom of Form**unless the wall simultaneously exerts the same amount of force on you.**

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**Question 6**

When you walk at an average speed of 4 m/s, in 5 s you’ll cover a distance of

8. **15 m.**

9. **2 m.**

10. **10 m.**Bottom of Form

11. **20 m.**

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**Question 7**

A car’s speed 3 seconds after accelerating from rest at 2 m/s2 is

12. **2 m/s.**

13. **4 m/s.**

14. **3 m/s.**

15. **6 m/s.**Bottom of Form

**Question 8**

Explain the difference between rotational and translational motion.

**Question 9**

During vertical jump (no running), which are the forces acting on the jumper, and their directions?

What is the net force (include the direction of the net force)?

If the Weigh of the jumper is greater than the force exerted on the feet of the jumper, can be the jump be executed?

**Question 10**

When the body of a jumper leave the ground, what is the only force acting on the jumper?

**Question 11**

During running High Jump, the jumper use the Kinetic Energy of the run to pass over the bar. What conversion of energy occur during the jump (KE to ?)?

**Question 12**

During standing broad jump, to reach the maximum range, the jumper needs a Resultant Force with angle of 45 degrees (respect the ground). Which are the forces on the jumper, that are the origin of that resultant force?

Can the jumper change the direction or magnitude of his weigh?

**Question 13**

During standing broad jump, a jumper with mass 67 kg, exerts a force, with his feet, of 1.8 times his weight at an angle of 70 degrees respect the horizontal. Find the magnitude and direction of the Resultant force Fr?

**Question 14**

Read the paper: https://www.tsijournals.com/articles/survey-and-analysis-for-sport-injuries-of-long-jumpers.pdf

Write with less than 500 words a summary of this articles, including: Common injuries and prevention.

**Question 15**

Find the air resistance acting on a parachuter that jumps from a plane. The mass of the parachuter is 85 kg, the coefficient of shape is 0.88 kg/m^3, and the velocity is 25 m/s. The area facing the direction of the motion is 0.30m^2.

Compare the magnitudes of the air resistance and the weight of the parachuter. What is the magnitude and direction of the net force?

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1

A note on Head Acceleration During Low Speed

Rear-End Collisions

Oren Masory Mechanical Engineering Department, Florida Atlantic University

Sylvian Poncet IFMA – Institut Francais De Mechanique Advancee, Les Cezeaux

ABSTRACT

The purpose of this paper is to find a relationship between vehicle’s acceleration and the occupant’s head acceleration during low speed rear end collision. It is based on experimental data obtained from tests performed on live human volunteers. It was found that the head acceleration, on the average, is at least two and a half times larger than vehicle’s acceleration.

INTRODUCTION Low speed, 5-10 mph, rear end collisions (LSREC) represent an important percentage of car accidents (7 out 1000 people will involve in such accident). Even though these collisions usually do not cause any visible damage, they might cause neck and upper back injuries. In spite of many years of research and testing, it is still difficult to determine the value of the impact force in these accidents and consequently the related injuries. A dynamic model for LSREC, which considers the bumper as a spring/damper combination, was proposed in [1]. This assumption is based on the fact that there is very little, if at all, permanent damage to the car and therefore very little energy is absorbed during the collision. Thus the impact can be considered as an elastic one. The model predicts the acceleration of both vehicles (bullet and target) after the collision. In [2] tests were conducted to determine whether the linear model proposed in [1] could be adapted to simulate low-speed impacts for vehicles with various combinations of energy absorbing bumpers (EAB). The types of bumper used in these tests included, in various combinations; foam, piston and honeycomb systems. Impact speeds varied between 4.2 and 14.4 km/h (2.6 and 9.0 mph) and a total of 16 tests in 6 different combinations were conducted. The results of this study reveal that vehicle accelerations vary approximately linearly with impact velocity for a wide variety of bumper systems and that a linear mass-spring-damping model may be used to efficiently model each vehicle/bumper system for low-speed impacts.

However, the cause of injuries is the acceleration of the occupants’ heads, in particular those of the occupants in target vehicle. The motion of the head due to the impact is called whiplash and is demonstrated in Figures 1 and 2.

Figure 1: Motion of the target vehicle occupant.

Figure 2 : Head motion in LSREC.

The severity of the injuries in this case depends of the range of motion and the head acceleration. While the above model can predict the target vehicle acceleration, this is not sufficient since there is a large difference between the vehicle’s acceleration and the occupant’s head acceleration as shown in Figure 3. Although many LSREC tests were performed using dummies and cadavers, very few were performed on volunteers, and even fewer were fully instrumented. The purpose of this note is to collect data obtained by tests on volunteers and to determine a relationship between the target vehicle’s and its occupant head accelerations.

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Figure 3: Vehicle, shoulder, neck and head accelerations of a target vehicle’s occupant (V-Vehicle, S-Shoulder, H-N-Neck & Head).

SOURCES OF DATA The first test on human occupant is described in [3]. In this test a 1941 Plymouth was used to rear end a 1947 Plymouth with impact velocities ranging from 7-20 mph. The tests used dummies and volunteers as occupants. It should be noted that these are very old vehicles and their bumpers are by far more rigid than current ones. In [4], human volunteers were exposed to 10 mph LSREC tests. These tests were conducted with 1981 and 1984 ford escort with both men and women between 27 and 58 years old. It was concluded that: “In spite of the fact that human volunteers in the present study differed in sex, age, height, weight and initial spinal condition, kinematics for all occupants were similar”. Also, “head acceleration multiplication factor” was defined as the ratio of the peak head acceleration to the peak vehicle acceleration. This factor was used to evaluate cervical injury and it was determined that in cases where this ratio exceeds the value of 2, it usually indicates cervical injuries. In [5] tests were conducted with male and female occupants between the age of 22 and 54 years old with impact speeds up to 16 Km/h (10 mph). In this work, in which 2 mid 1970’s Volvos were used, two different head restraints were tested. Rear end collisions tests are reported in [6], two 1979 Plymouth where used. In these tests the impact speeds ranging from 1.8Km/h (1.1Mph) to 11.6Km/h (7.2Mph). The results of rear end collisions with higher impact speeds, 30 mph, are reported in [7]. The test vehicles in this case were two standard Audi 80s. The use of the data obtained from these tests is limited since the speed too high for considering as low speed. However, the data will be presented here for comparison purpose.

EXPERIMENTAL DATA COMPILATION Figure 4 plots the experimental data collected from all the above tests. To obtain a better insight to the experimental results, the data was regrouped according to the Impact speed and it is shown in Figure 5. It is clear that for high speed impact (>40 [km/h]) the occupant’s head acceleration is almost constant and independent of the vehicle acceleration. These cases are not considered to be low speed impact since large plastic deformations are involved. The data for the mid-range speeds (10-20 [km/h]) are not conclusive. However, the data for the low speed (0-10 [km/h]) experiments do show trend which need exploration.

Peak Head Acceleration versus Peak Vehicle Acceleration

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2.00

4.00

6.00

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14.00

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18.00

20.00

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00

Peak Vehicle Acceleration [g]

Pe ak

H ea

d ac

ce le

ra tio

n [g

]

Ref. [6] Ref. [5] Ref. [3] Ref. [4] Ref. [7]

Figure 4: Experimental raw data.

Head Acceleration versus Vehicle’s acceleration for different Impact speeds

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6.00

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0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00 16.00

Vehicle’s Acceleration

H ea

d’ s

A cc

el er

at io

n

0-10 [km/h] 5-10 [km/h] >40 [km/h]

Figure 5: Vehicle and head accelerations for different impact speeds.

The data related to slow speed impact (0- 10 [km/h]) are redrawn in Figure 5 and a simple linear regression of the data yielded: 89.075.2 −= vh AA (1)

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where: Ah – Head acceleration Av — Vehicle acceleration with a correlation index of R2=0.80.

Head Acceleration versus Vehicle Acceleration at low Impact Speeds

y = 2.7482x – 0.8972 R2 = 0.8023

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1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

9.00

10.00

0.50 1.00 1.50 2.00 2.50 3.00 3.50

Vehicel Acceleration [g]

H ea

d A

cc el

er at

io n

[g ]

Figure 6: Linear regression for the low speed data.

Having in mind that the repeatability of the above experiments is relative low, due to difficulty in controlling all the experimental parameters, the high value of the correlation index indicates that that this phenomena where the head acceleration is amplified, is real. CONCLUSIONS

Low speed rear end collision happen very

frequently. In most cases there is no damage to the vehicles and as a result, it is assumed that to injury occurred. However, in some cases occupants later complain about neck and back pain which is characterized as “whiplash” injury. The reason for this pain is the exposure of the head to high acceleration.

Experimental results from low speed rear

end collisions, which involved live human subjects, have shown that the peak head acceleration is at least two and a half times larger than peak acceleration of the struck vehicle. This assessment is correct for impact speed below 10 [km/h] (6.8 mph).

This fact can explain why injuries are reported although no vehicle damage was observed.

REFERENCES 1. Ojalvo, I. U., Cohen, E. C., “An Efficient Model

for Low Speed Impact of Vehicles”, SAE 970779 and SP-1226, pp.193-199.

2. Ojalvo I.O., Weber B. E., D. A. Evenson, T. J. Szabo, J. B. Welcher, “Low-Speed Car Impacts With Different Bumper Systems: Correlation of Analytical Model With Tests”, SAE Technical paper 980365, 1998.

3. D.M. Severy, J.H. Mathewson and C.O. Bechtol, M.D., “Controlled automobile rear- end collisions, an investigation of related engineering and medical phenomena”, Can Serv Med J. 1955,11(10):727-59.

4. T.J. Szabo and J.B. Welcher, “Human subject kinematics and electro myographic activity during low speed rear impacts”, SAE Technical paper 962432, 1996.

5. T.J. Szabo, J.B. Welcher, R.D. Anderson, M.M. Rice, J.F. Ward, L.R.Paulo, and N.J. Carpenter, “Human occupant kinematic response to low speed rear-end impacts”, SAE Technical paper 940532, 1994.

6. D. H. West, P.E; J.P. Gough, P.E; G.T.K. Harper, P.E., “Low speed rear-end collision testing using human subjects”, Accident Reconstruction Journal, May/June 1993.

7. R. Wagner,”A 30mph front/rear crash with human test persons”, SAE Technical paper 791030, 1979.

8. G.P. Siegmund, D.J. King, and J.M. Lawrence, “Head/Neck kinematic response of human subjects in low-speed rear-end collisions”, SAE Technical paper 973341, 1997.

**Chapter 5 – Elasticity 10 questions**

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**Question 1**

What is Elasticity (formal definition)?Bottom of Form

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**Question 2**

If a body, under the action of a force, is distorted beyond its elastic limit, will the original shape restored after removal of the force?Bottom of Form

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**Question 3**

A bar of steel. with radius 12 mm, is under the action of an axial force of 130 N.

a. Find the normal stress, Sn (express your answer in MPa, given that: 1 N/mm^2 = 1 MPa)

b. If the Tensile Strength of the steel is 350 MPa (yield limit), is this bar going to fail?

**Question 4**

A bar under the action of an axial force F, suffer a variation in length as is represented below:

a. Find the normal Strain

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**Question 5**

When a force is considered an “impulsive Force”?Bottom of Form

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**Question 6**

A car with a mass of 1100 kg at 50 mph, driving toward the East, have collision and rebound (toward West) with a velocity of 7 mph. Find the Average Value of the Impulsive Force (F av) If the duration of the collision is 4 × 10^-3 seconds. (Convert the mph to m/s)

1mph = 0.447 m/s

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**Question 7**

The average impulsive force due to a fall is:

If a person with mass 67 kg, fall from a roof with height 2.9 m, and the impact time is estimated in 2 x 10 ^ -2 seconds.

a. Find the Average Impulsive Force

If the combined area of his 2 leg bones is 5.8 cm^2 (convert in m^2).

b. Find the Compressive normal stress acting in his legs

If the rupture strength of the bones is 1.0 x 10^8 Pa (1 Pa = 1 N/m^2)

c. Should the bones of his legs fracture due to the fall? Explain.

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**Question 8**

What is the role of the airbags during a car collision?Bottom of Form

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**Question 9**

The force acting on a person due to the deceleration of a car (from initial velocity v = v0 to final velocity v = 0, is given by the formula:

If the mass of a person is 90 kg, the velocity of the car is 60 mph and the stopping distance of the person when move forward due to the Inertia is 28 cm.

a. Find the Average Force of the Impact

b. If the force is uniformly distributed over an area of 900 cm^2. What is the Normal Stress on the person/s body?

c. If the Compressive Strength of Human Tissue is 6 x 10^5 Pa, is the person going to survive the impact without severe damage?

1 mph = 0.447 m/s

1m = 100 cm

1 N/m^2 = 1 Pa

1 m^2 = 10,000 cm^2Bottom of Form

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**Question 10**

Read the article:

https://pdfs.semanticscholar.org/66bd/c547daa2e5597dbfda723caa3232f671ed7e.pdf?_ga=2.41604513.249990383.1591109343-1781856615.1591109343

Write a summary of less than 500 words of the findings by the Authors

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**Chapter 7 Fluids. Chapter 8. Motion of fluids**

**Question 1**

A container consists of two vertical cylindrical columns of different diameter connected by a narrow horizontal section, as shown in the figure. The open faces of the two columns are closed by very light plates that can move up and down without friction. The tube diameter at A is 35.0 cm and at B it is 10.2 cm. This container is filled with oil of density 0.820 g/cm3. If a 125-kg object is placed on the larger plate at A, how much mass should be placed on the smaller plate at B to balance it?

**Question 2**

As shown in the figure, water (density 1000 kg/m^3) is flowing in a pipeline. At point 1 the water speed is 5.90 m/s. Point 2 is 5.20 m above point 1. The cross-sectional area of the pipe is0.0800 m^2 at point 1 and 0.0200 m^2 at point 2. What is the pressure difference P1 – P2 between points 1 and 2? Treat the water as an ideal incompressible fluid.

**Question 3**

Calculate the pressure exerted on the ground due to the weight of person standing on one foot. if the bottom of the person’s foot is 13cm wide and 28cm long.

Hint: Pressure = Force/ Area

1. **4.8 × 104 Pa**

2. **2.1 × 104 Pa**

3. **2.2 × 103 Pa**

4. **5.3 × 104 Pa**

**Question 4**

A block of metal weighs 40 N in air and 30 N in water. What is the buoyant force on the block due to the water? The density of water is 1000 kg/m3.

Hint: Archimedes’s Principle

1. **10 N**

2. **30 N**

3. **70 N**

4. **40 N**

**Question 5**

A plastic block of dimensions 2.00 cm × 3.00 cm × 4.00 cm has a mass of 30.0 g. What is its density?

Hint: Density = mass / volume

1. **1.25 g/cm3**

2. **1.60 g/cm3**

3. **0.80 g/cm3**

4. **1.20 g/cm3**

**Question 6**

Under standard conditions, the density of air is 1.29 kg/m3. What is the mass of the air inside a room measuring 4.0 m × 3.0 m × 2.0 m?

Hint: mass = density x volume

1. **3.1 kg**

2. **31 kg**

3. **19 kg**

4. **0.32 kg**

5. **1.9 kg**

**Question 7**

Fluid flows at 2.0 m/s through a pipe of diameter 3.0 cm. What is the volume flow rate of the fluid?

Hint: Volume flow rate = velocity x area

1. **5.7 × 10-3 m3/s**

2. **57 m3/s**

3. **14 m3/s**

4. **1.4 × 10-3 m3/s**

**Question 8**

A fluid is flowing with an average speed of 1.5 m/s through a tube that has a radius of 2.0 mm and is 18 cm long. The drop in pressure is 967 Pa. What is the viscosity of the fluid?

Hint: Use Poiseuille’s Equations

1. **0.028 N ∙ s/m2**

2. **0.0034 N ∙ s/m2**

3. **0.0056 N ∙ s/m2**

4. **0.013 N ∙ s/m2**

5. **0.0018 N ∙ s/m2**

**Question 9**

Water flows through a pipe. The diameter of the pipe at point B is larger than at point A. Where is the water pressure greatest?

Hint: Remember that: P + g(density)h + 0.5(density)v^2 = constant

1. **at point A**

2. **at point B**

3. **It is the same at both A and B.**

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Is the object represented below in stable equilibrium or not? Explain

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*Top of FormQuestion 2Bottom of FormTop of Form*

Why the person below is bending his torso and extending his arm, while carrying an uneven load?

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**Question 3**

Complete the sentence with the correct phrase:

A body is in static equilibrium if the vectorial sum of both the forces and the torques acting on the body is ______________________

1.

*zero*

2.

**different of zero**

3.

**100 N**

4. **equal to body’s weight**Bottom of Form

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**Question 4**

Write the equation of equilibrium of the forces along the y-axis for the forces acting on the person below

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**Question 5**

Find the magnitude of the force Fa, apply to the shoulder, needed to topple the person below, if the mass of this person is 115 kg (the pivot point is point A)

**Question 6**

If a force Fa of 125 N is applied to the shoulder of the person below. What is the minimum mass needed to avoid the force Fa topple the person (pivot point is point A).

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**Question 7**

Why spreading the legs, a person increases his stability?

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**Question 8**

Define “a lever” in Physics.

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**Question 9**

Calculate the force F needed to keep the lever below in balance:

a. What class is this lever?

b. Find its Mechanical Advantage.

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**Top of FormQuestion 10**

Calculate the force F needed to keep the lever below in balance:

a. What class is this lever?

b. Find its Mechanical Advantage.

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**Question 11**

Calculate the force F needed to keep the lever below in balance:

a. What class is this lever?

b. Find the Mechanical Advantage

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**Question 12**

Find the magnitude of the displacement L1:

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**Question 13**

Write the equations of translational equilibrium, and rotational equilibrium respect point A, for the model of the arm represented below.

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**Question 14**

Write the equations of translational equilibrium, and rotational equilibrium respect point A, for the model of the

hip represented below.

a. What represents the letters W and WL?

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**Question 15**

Find the force in the Achilles Tendon, if the weight W of the person is 700 N