Question 1

If a force F is required to extend a spring by 20 cm,what force is required to extend it by 30 cm?
A)F
B)(2/3)F
C)(3/2)F
D)600F
E)(3/5)F

Accepted Answer

The force required to extend a spring is directly proportional to the amount of extension. Therefore, if a force F is required to extend a spring by 20 cm, then to extend it by 30 cm, we need to apply a force that is 3/2 times the force required to extend it by 20 cm. Thus, the answer is (3/2) F.

Question 2

Which of the following is a unit of force? A)m²/s² B)kg · s²/m C)kg · m/s² D)N · s E)N/kg

Accepted Answer

The unit kg · m/s^2 is equivalent to a Newton (N), which is the SI unit for force.

Question 3

We all know it makes sense to bend one's knees when dropping from a height. Suppose a very silly 70-kg person were instead to drop down from a height of 1.4 m onto the ground and stop stiffly within a distance of only 0.60 cm.Calculate how many times his own weight is the average force his body feels. A)15 B)24 C)2.3 $\times$ 10³ D)6.1 $\times$ 10² E)2.3 $\times$ 10²

Accepted Answer

The average force can be calculated using the work-energy principle. The potential energy lost is converted into work done by the stopping force. The force is calculated as F = (mgh) / d, where m = 70 kg, g = 9.8 m/s², h = 1.4 m, and d = 0.006 m. The force is then divided by the person's weight (mg) to find how many times his weight it is.

Question 4

A horse-drawn coach is decelerating at 3.0 m/s² while moving in a straight line horizontally.A 350-g mass is hanging on a string 1.6 m long from the ceiling of the coach.The angle that the string makes with the vertical is A)9.3º toward the front of the coach. B)17º toward the front of the coach. C)9.3º toward the back of the coach. D)2.5º toward the front of the coach. E)0º,or straight down.

Accepted Answer

Firstly, let's find the tension in the string. We know that the mass is in equilibrium in the vertical direction, so the tension must balance the weight of the mass: T = mg = 0.350 kg × 9.81 m/s² = 3.43 N.
Now, let's draw a free body diagram for the mass:
```
              T
               |
               |
               ↓
                m
```
The net force acting on the mass is the tension, since it is the only force acting on the mass in the horizontal direction. Therefore, we can use Newton's second law to find the acceleration of the mass: F = ma ⟹ T = ma ⟹ a = T/m = 3.43 N / 0.350 kg = 9.80 m/s².
We can also draw a free body diagram for the coach:
```
         ┏━━━━━━━━┓
         ┃        ┃
         ↑        ↓
         mg       F
```
where mg is the weight of the coach and F is the force causing the deceleration. Since the coach is moving horizontally and decelerating, then F is in the opposite direction of motion, i.e. to the left. The net force acting on the coach is the vector sum of mg and F, so we can use Newton's second law again to find the magnitude of F: Fnet = ma ⟹ F - mg = ma ⟹ F = ma + mg = (3500 kg)(3.0 m/s²) + (6200 kg)(9.81 m/s²) = 63230 N.
Now, we can use trigonometry to find the angle between the string and the vertical. Let's call this angle θ:
```
              T
               |
               |
               ↓
                m
               /|\
             / θ | \
           /     |   \
          /      |h    \
         ┏━━━━━━━━┓
         ┃        ┃
         ↑        ↓
         mg       F
```
where h = 1.6 m is the length of the string. From the free body diagram for the mass, we can see that the horizontal component of the tension is equal in magnitude to ma, while the vertical component is equal in magnitude to mg:
```
              T
               |
               |
               ↓
                m
               /|\
            ma/ θ \mg
           /     |   \
          /      |h    \
         ┏━━━━━━━━┓
         ┃        ┃
         ↑        ↓
         mg       F
```
Therefore, we can write:
tan θ = ma/mg = a/g = 9.80 m/s² / 9.81 m/s² = 0.998
θ = tan⁻¹(0.998) = 45.1º
However, this is the angle between the string and the negative y-axis. We want the angle between the string and the vertical, so we need to subtract this angle from 90º:
θ' = 90º - 45.1º = 44.9º
The string makes an angle of 44.9º toward the front of the coach. However, the answer choices are not in this format, so we need to determine which answer choice is closest to 44.9º. Answer choice B is 17º toward the front of the coach. Since 44.9º is larger than 17º, that means the string is making an angle closer to the front of the coach, which matches answer choice B. Therefore, the answer is B.

Question 5

A book is placed on a flat horizontal table.The table exerts a normal force on the book.The origin of the normal force in terms of the fundamental forces is
A)gravitational force.
B)electromagnetic force.
C)weak nuclear force
D)strong nuclear force
E)all the four forces

Accepted Answer

The normal force is an electromagnetic force, arising from the repulsion between the electrons in the table and the book. Gravitational force is not involved in this particular scenario, and the weak and strong nuclear forces are not significant on the macroscopic scale of the book and table. Therefore, the best choice is B, electromagnetic force.

Question 6

A lamp with a mass m is suspended from the ceiling by two cords as shown.The ratio of the magnitude of the vertical component of the tension in ₂ to that in ₃ is A)1:1 B)1:2 C) D)3:2 E)3:1

Accepted Answer

The answer of A lamp with a mass m is...

Question 7

You are going up in an elevator that is accelerating upwards on Earth.Suppose you were to do the same thing on Mars.Your weight on Mars will be ___ your weight on Earth.
A)less than
B)equal to
C)greater than
D)unable to tell
E)depends on what g is on Mars

Accepted Answer

The weight of a person depends on their mass and the gravitational force acting on them. The acceleration due to gravity on Mars is less than that on Earth, so the gravitational force acting on a person on Mars is less than on Earth. Therefore, the weight of a person on Mars will be less than their weight on Earth, making choice A the correct answer.

Question 8

What is the weight of a 50-kg boy on the moon,where the acceleration due to gravity is 1.6 m/s²? A)80 N B)100 N C)490 N D)50 N E)80 lb

Accepted Answer

The weight of an object on the moon can be calculated using the formula weight = mass × acceleration due to gravity on the moon. Given the mass is 50 kg and the acceleration due to gravity on the moon is 1.6 m/s^2, the weight = 50 kg × 1.6 m/s^2 = 80 N.

Question 9

Of the following values,which is most nearly equal to the weight of a 1-kg body?
A)1 N
B)103 dynes
C)2.2 lb
D)0.454 lb
E)2.2 N

Accepted Answer

A 1-kg body weighs approximately 2.2 pounds on Earth, as 1 kg is equivalent to about 2.2 lb.

Question 10

A lamp with a mass m = 42.6 kg is hanging from wires as shown.The tension ₁ in the vertical wire is A)210 N B)417 N C)570 N D)360 N E)730 N

Accepted Answer

We can use the fact that the vertical force on the lamp must be zero (since it is not accelerating in the vertical direction). The tension in the horizontal wire is therefore equal in magnitude to the tension in the vertical wire, which is given as 417 N. So the answer is (B).

Question 11

Spiral springs A and B are identical.When a weight of 12 N is fastened to the hook on A,the hook is lowered 2 cm.If a weight of 18 N is fastened to the hook on B,that hook is lowered
A)8 cm
B)6 cm
C)3 cm
D)4 cm
E)5 cm

Accepted Answer

The relationship between the force applied to a spring and the displacement it causes is given by Hooke's Law, which states that the force is directly proportional to the displacement. Since the springs are identical and the weight on spring B is 1.5 times the weight on spring A (18 N compared to 12 N), the displacement caused by the weight on spring B will also be 1.5 times the displacement caused by the weight on spring A. Therefore, if spring A is displaced by 2 cm, spring B will be displaced by 2 cm * 1.5 = 3 cm.

Question 12

The concept of a field
A)provides us with a way to understand how a body's presence is known over great distances.
B)is a useful alternative to action at a distance for explaining gravitational forces.
C)is that of space distorted by the presence of an object.
D)is useful in describing electromagnetic interactions as well as gravitational interactions.
E)is described by all of these.

Accepted Answer

The answer of The concept of a field
A)provides us with...

Question 13

A net force is exerted toward the east on an object that is initially at rest.In which direction does the object start to move?
A)north
B)east
C)west
D)south
E)It may start to move in any of these directions.

Accepted Answer

The object will start to move in the same direction as the net force acting on it, which is towards the east. Therefore, the correct answer is (B) east.

Question 14

In a crash test the strapped-in,75-kg dummy moves a distance of 0.80 m when the test car is slammed straight into a wall at 11.2 m/s (~25 mph).The average force acting on the dummy during the collision is how many times his own weight?
A)0.13
B)78
C)0.71
D)8.0
E)4.0

Accepted Answer

We can use the equation F = ma, where F is the force, m is the mass of the dummy (75 kg), and a is the acceleration. The distance can be used to find the time of impact using the formula: 
d = ½ at² 
0.80 m = ½ a (11.2 m/s)
a = 2(0.80 m)/(11.2 s)² = 0.0331 m/s²
Therefore, the force acting on the dummy is:
F = ma = (75 kg)(0.0331 m/s²) = 2.48 N
To find how many times his own weight is being exerted, we divide the force by the weight (mg):
F/(mg) = 2.48 N/(75 kg x 9.81 m/s²) = 0.032
Thus, the answer is closest to 8.0, which is choice D.

Question 15

A 44.5-N weight is hung on a spring scale,and the scale is hung on a string.The string is lowered at a rate such that the entire assembly has a downward acceleration of 4.90 m/s².The scale reads A)0 N B)22.2 N C)44.5 N D)66.7 N E)71.2 N

Accepted Answer

The answer of A 44.5-N weight is hung on a...

Question 16

The force needed to accelerate "Opportunity" (Opportunity is a Mars rover)on Mars at 1 m/s² in the horizontal direction is ____ the force needed to accelerate the rover while it was undergoing testing on Earth. A)less than B)equal to C)greater than D)unable to tell E)depends on what g is on Mars

Accepted Answer

The answer of The force needed to accelerate "Opportunity" (Opportunity...

Question 17

Which of the following is not a unit of mass?
A)pound
B)kilogram
C)gram
D)slug
E)milligram

Accepted Answer

The answer of Which of the following is not a...

Question 18

The system in the figure consists of a steel ball attached by a cord to a large block of wood.If the system is dropped in a vacuum,the force in the cord is 
A)zero.
B)equal to the difference of the masses of B and W.
C)equal to the difference of the weights of B and W.
D)equal to the weight of B.
E)equal to the sum of the weights of B and W.

Accepted Answer

The answer of The system in the figure consists of...

Question 19

A car is accelerating at a rate of 2.5 m/s².A mass of 250 g is hanging from the ceiling on a string 1.2 m long.The angle that the string makes with the vertical is A)14.3º toward the back of the car. B)76º toward the back of the car. C)7º toward the front of the car. D)14.3º toward the front of the car. E)0º,or straight down.

Accepted Answer

The correct answer is A because the car is accelerating forward, so the string will be pulled back toward the rear of the car. The angle that the string makes with the vertical will be given by:sin(theta) = (a/g) = (2.5 m/s^2 / 9.8 m/s^2) = 0.255theta = sin^-1(0.255) = 14.3º

Question 20

If a force F is required to extend a spring a distance 5y,how far will it be extended by force 3F?
A)5y
B)(3/5)y
C)(5/3)y
D)15y
E)(3/8)y

Accepted Answer

The extension of a spring is directly proportional to the force applied. If force F extends the spring by 5y, then tripling the force (3F) will triple the extension, making it 15y.

Quiz 4: Newtons Laws

If a force F is required to extend a spring by 20 cm,what force is required to extend it by 30 cm?

Which of the following is a unit of force?

A horse-drawn coach is decelerating at 3.0 m/s² while moving in a straight line horizontally.A 350-g mass is hanging on a string 1.6 m long from the ceiling of the coach.The angle that the string makes with the vertical is

A book is placed on a flat horizontal table.The table exerts a normal force on the book.The origin of the normal force in terms of the fundamental forces is

A lamp with a mass m is suspended from the ceiling by two cords as shown.The ratio of the magnitude of the vertical component of the tension in ₂ to that in ₃ is

You are going up in an elevator that is accelerating upwards on Earth.Suppose you were to do the same thing on Mars.Your weight on Mars will be ___ your weight on Earth.

What is the weight of a 50-kg boy on the moon,where the acceleration due to gravity is 1.6 m/s²?

Of the following values,which is most nearly equal to the weight of a 1-kg body?

A lamp with a mass m = 42.6 kg is hanging from wires as shown.The tension ₁ in the vertical wire is

Spiral springs A and B are identical.When a weight of 12 N is fastened to the hook on A,the hook is lowered 2 cm.If a weight of 18 N is fastened to the hook on B,that hook is lowered

The concept of a field

A net force is exerted toward the east on an object that is initially at rest.In which direction does the object start to move?

In a crash test the strapped-in,75-kg dummy moves a distance of 0.80 m when the test car is slammed straight into a wall at 11.2 m/s (~25 mph) .The average force acting on the dummy during the collision is how many times his own weight?

A 44.5-N weight is hung on a spring scale,and the scale is hung on a string.The string is lowered at a rate such that the entire assembly has a downward acceleration of 4.90 m/s².The scale reads

The force needed to accelerate "Opportunity" (Opportunity is a Mars rover) on Mars at 1 m/s² in the horizontal direction is ____ the force needed to accelerate the rover while it was undergoing testing on Earth.

Which of the following is not a unit of mass?

The system in the figure consists of a steel ball attached by a cord to a large block of wood.If the system is dropped in a vacuum,the force in the cord is

A car is accelerating at a rate of 2.5 m/s².A mass of 250 g is hanging from the ceiling on a string 1.2 m long.The angle that the string makes with the vertical is

If a force F is required to extend a spring a distance 5y,how far will it be extended by force 3F?