Question 1

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

First, we need to find the tension in the string using the weight of the mass:
T = mg = (0.35 kg)(9.81 m/s^2) = 3.43 N

Next, we can use the forces in the vertical and horizontal directions to find the angle the string makes with the vertical. In the vertical direction, we have the weight of the mass and the tension in the string:
T cos θ = mg

In the horizontal direction, we have the deceleration of the coach:
T sin θ = ma

Since we know the values of T, m, and a, we can solve for θ:

sin θ/cos θ = a/g
tan θ = a/g
θ = tan^-1(a/g)

Plugging in the numbers, we get:
θ = tan^-1(3.0 m/s^2 / 9.81 m/s^2) = 17º

Since the acceleration is to the left, the string will be at an angle toward the front of the coach (as seen from inside the coach). Therefore, the answer is B: 17º toward the front of the coach.

Question 2

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 concept of a field provides us with a way to understand how a body's presence is known over great distances, is a useful alternative to action at a distance for explaining gravitational forces, is that of space distorted by the presence of an object, and is useful in describing electromagnetic interactions as well as gravitational interactions.

Question 3

Which of the following free-body diagrams represents the car going uphill at a constant speed? 
A) 1
B) 2
C) 3
D) 4
E) 5

Accepted Answer

The answer of  Which of the following free-body diagrams...

Question 4

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

According to Hooke's Law, the force required to extend or compress a spring is directly proportional to the displacement of the spring from its rest position (assuming the spring is not stretched beyond its elastic limit). Therefore, if a force F is required to extend a spring by 20 cm, then to extend it by 30 cm, we need a force that is 1.5 times greater than F (since 30/20=1.5). Therefore, the force required to extend the spring by 30 cm is (3/2)F.

Question 5

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 6

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 an object is the force exerted by the object due to gravity, which is proportional to the mass of the object and the acceleration due to gravity. On Mars, the acceleration due to gravity is much weaker than on Earth (about 38% of Earth's gravity). Therefore, even though the elevator may be accelerating upwards on both Earth and Mars, the net force acting on the person inside the elevator (which determines their weight) will be less on Mars than on Earth. Hence, their weight on Mars will be less than their weight on Earth.

Question 7

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 8

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, because it arises from the repulsion between the electrons in the table and the book. The other fundamental forces (gravitational, weak nuclear, and strong nuclear) do not play a significant role in the normal force.

Question 9

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.

Question 10

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 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

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 direction of the net force, which is east.

Question 13

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 14

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 15

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 16

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 answer of We all know it makes sense to...

Question 17

Which of the following free-body diagrams represents the block sliding down a frictionless inclined plane? 
A) 1
B) 2
C) 3
D) 4
E) 5

Accepted Answer

The answer of  Which of the following free-body diagrams...

Question 18

Which of the following free-body diagrams represents the car going downhill without acceleration? 
A) 1
B) 2
C) 3
D) 4
E) 5

Accepted Answer

Free-body diagram 3 shows the forces acting on the car going downhill without acceleration, where the weight force is counteracted by the normal force from the road and the force of friction. The other diagrams either show a car with acceleration (A) or do not properly balance the forces (B, D, E).

Question 19

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

The answer of Of the following values, which is most...

Question 20

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.

Quiz 4: Newtons Laws

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

The concept of a field

Which of the following free-body diagrams represents the car going uphill at a constant speed?

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

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.

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.

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 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

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

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?

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 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 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

Which of the following is not a unit of mass?

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

Which of the following free-body diagrams represents the block sliding down a frictionless inclined plane?

Which of the following free-body diagrams represents the car going downhill without acceleration?

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

Which of the following is a unit of force?