Question 1

A force accelerates a body of mass M. A second body requires half as much force to produce twice the acceleration. What is the mass of the second body?
A) M
B) 2M
C) M/2
D) 4M
E) M/4

Accepted Answer

D

Question 2

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 in this case is toward the east. Therefore, the answer is option B.

Question 3

A force F produces an acceleration a on an object of mass m. A force 3F is exerted on a second object, and an acceleration 8a results. What is the mass of the second object?
A) 3m
B) 9m
C) 24m
D) 3/8)m
E) 8/3)m

Accepted Answer

D

Question 4

A force accelerates a body of mass M. A second body requires twice as much force to produce the same acceleration. What is the mass of the second body?
A) M
B) 2M
C) M/2
D) 4M
E) M/4

Accepted Answer

The force required to produce the same acceleration on the second body is twice that of the force required on the first body. This means the second body has twice the inertial mass as the first. Therefore, the mass of the second body is 2M.

Question 5

A net force of 64 N acts on a mass of 16 kg. The resulting acceleration is A) 16 m/s². B) 0.51 m/s². C) 64 m/s². D) 9.0 m/s². E) 4.0 m/s².

Accepted Answer

The acceleration can be calculated using Newton's second law: a = F/m = 64 N / 16 kg = 4.0 m/s².

Question 6

A 10-N force is applied to mass M. The same force is applied to mass 4M. The ratio of the acceleration of the smaller mass to the acceleration of the larger mass is
A) 4 to 1.
B) 20 to 1.
C) 1 to 1.
D) 1 to 2.
E) 1 to 4.

Accepted Answer

According to Newton's second law of motion, the force applied on an object is proportional to its acceleration, with the constant of proportionality being the mass of the object. Mathematically, F=ma.
Here, the force applied is the same for both masses, and the acceleration of each mass is directly proportional to its mass. Thus, the acceleration of mass M is a and the acceleration of mass 4M is 1/4 of a.
Therefore, the ratio of acceleration of smaller mass to larger mass is a/(1/4a), which simplifies to 4:1. Hence, the correct answer is A) 4 to 1.

Question 7

A mass m is traveling at an initial speed of 25.0 m/s. It is brought to rest in a distance of 62.5 m by a net force of 15.0 N. The mass is
A) 37.5 kg.
B) 3.00 kg.
C) 1.50 kg.
D) 6.00 kg.
E) 3.75 kg.

Accepted Answer

Using the work-energy principle, the work done by the force is equal to the change in kinetic energy. The work done is force times distance (15 N * 62.5 m = 937.5 J). The initial kinetic energy is (1/2)mv^2 = (1/2)m(25)^2. Setting these equal gives m = 3.00 kg.

Question 8

If you apply the same net force to objects with masses M and 4M, the acceleration of the mass M is
A) the same as for the mass 4M.
B) four times the acceleration of the mass 4M.
C) one-fourth the acceleration of the mass 4M.
D) twice the acceleration of the mass 4M.
E) one-half the acceleration of the mass 4M.

Accepted Answer

According to Newton's second law, acceleration is inversely proportional to mass when the force is constant. Therefore, the acceleration of mass M is four times that of mass 4M.

Question 9

A net force is exerted on an object toward the north. The object 
A) is moving toward the north.
B) is moving toward the east.
C) is moving toward the west.
D) is moving toward the south.
E) may be moving in any direction.

Accepted Answer

The net force determines the acceleration, not the direction of motion. The object could be moving in any direction while accelerating toward the north.

Question 10

A 3.00 kg mass is traveling at an initial speed of 25.0 m/s. What is the magnitude of the force required to bring the mass to rest in a distance of 62.5 m?
A) 7.50 N
B) 3.00 N
C) 15.0 N
D) 62.5 N
E) 37.5 N

Accepted Answer

The answer of A 3.00 kg mass is traveling at...

Question 11

A force accelerates a body of mass M. The same force applied to a second body produces three times the acceleration. What is the mass of the second body?
A) M
B) 3M
C) M/3
D) 9M
E) M/9

Accepted Answer

Let F be the force applied and a1 and a2 be the accelerations produced on the first and second bodies respectively. Then we have the equations:
F = Ma1
F = (1/3)(Mx)a2  (where x is the mass of the second body)
From these equations, we get:
a2/a1 = 3
(Mx)(a2) = F = Ma1
(Mx)(a2) = (M)(a1/3)
(Mx)(3a2) = Ma1
3x = 1
x = M/3
Therefore, the mass of the second body is M/3, so the answer is (C).

Question 12

A mass of 25 kg is acted on by two forces, one of which is 10 N due east while the second one is 15 N due north. The acceleration of the mass is A) 0.72 m/ s², 56.3^o north of east. B) 0.20 m/ s², due east. C) 0.72 m/ s², 33.7^o north of east. D) 1.0 m/ s², 33.7^o north of east. E) 0.20 m/ s², 56.3^o north of east.

Accepted Answer

The resultant force is calculated using the Pythagorean theorem: √(10² + 15²) = √325 = 18.03 N. The acceleration is then F/m = 18.03 N / 25 kg = 0.72 m/s². The angle is calculated using tan⁻¹(15/10) = 56.3° north of east.

Question 13

If you want the same acceleration with masses M and 4M, the force applied on the mass M is
A) the same as for the mass 4M.
B) four times the force applied on the mass 4M.
C) one-fourth the force applied on the mass 4M.
D) twice the force applied on the mass 4M.
E) one-half the force applied on the mass 4M.

Accepted Answer

The force applied is proportional to the mass, so if the acceleration is the same for masses M and 4M, the force applied on M must be one-fourth of the force applied on 4M.

Question 14

A ball of mass 2.0 kg is acted on by two forces, and . The magnitude of the acceleration is A) 2.5 m/s². B) 3.9 m/s². C) 4.6 m/s². D) 5.1 m/s². E) 5.8 m/s².

Accepted Answer

The answer of A ball of mass 2.0 kg is...

Question 15

A particle with a mass of 200 g is acted on by a net force of 4.5 N. The acceleration of the particle is A) 90 cm/s². B) 2.3 cm/s². C) 0.90 km/s². D) 23 m/s². E) 9.0 m/s².

Accepted Answer

The answer of A particle with a mass of 200...

Question 16

A mass of 25 kg is acted on by two forces, one of which is 15 N due east while the second one is 10 N due north. The acceleration of the mass is A) 0.72 m/ s², 56.3^o north of east. B) 0.20 m/ s², due east. C) 0.72 m/ s², 33.7^o north of east. D) 1.0 m/ s², 33.7^o north of east. E) 0.20 m/ s², 56.3^o north of east.

Accepted Answer

First, we need to find the resultant force acting on the mass:
- Using Pythagorean theorem, the magnitude of the resultant force (F_r) is: 
F_r = sqrt((15 N)^2 + (10 N)^2) = 18.03 N
- Using trigonometry, the direction of the resultant force (theta) is:
theta = tan^-1 (10 N / 15 N) = 33.7 degrees north of east

Next, we can use Newton's second law to find the acceleration of the mass:
F_r = m*a
a = F_r / m
a = 18.03 N / 25 kg
a = 0.72 m/s^2

Finally, we need to find the direction of acceleration, which is the same as the direction of the resultant force:
The direction of acceleration is 33.7 degrees north of east.

Question 17

A ball of mass 2.0 kg is acted on by two forces , and . The acceleration vector, , of the mass is in m/s²) A) . B) . C) . D) . E) .

Accepted Answer

The answer of A ball of mass 2.0 kg is...

Question 18

A third force is applied on the object so that the net force on the object is zero. Which force vector best represents the third force?
A) 1)
B) 2)
C) 3)
D) 4)
E) none of the vectors

Accepted Answer

In order for the net force on an object to be zero, the vector sum of all the forces acting on the object must be zero. Therefore, the third force vector must be in the opposite direction and equal in magnitude to the vector sum of the other two forces. Since vector 4) is equal in magnitude but opposite in direction to the vector sum of vectors 1) and 2), it would create a net force of zero and is the best choice.

Question 19

A ball of mass 2.0 kg is acted on by two forces,  , and  . The direction of the acceleration vector  ) w.r.t to the +x-axis is
A)  .
B)  .
C)  .
D)  .
E)  .

Accepted Answer

The answer of A ball of mass 2.0 kg is...

Question 20

An object is moving to the right at a constant speed. Which one of the following statements must be correct?
A) No forces are acting on the object.
B) A larger number of forces are acting on the object to the right than to the left.
C) The net force acting on the object is to the right.
D) No net force is acting on the object.
E) Just one force is acting on the object, and it is acting downward.

Accepted Answer

If an object is moving at a constant speed, then its velocity is constant. According to Newton's first law, an object will maintain its velocity unless acted upon by an external force. Therefore, since the object is moving at a constant speed, there must be no net force acting on it.

Quiz 4: Forces and Motion I: Newtons Laws

A force accelerates a body of mass M. A second body requires half as much force to produce twice the acceleration. What is the mass of the second body?

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 force F produces an acceleration a on an object of mass m. A force 3F is exerted on a second object, and an acceleration 8a results. What is the mass of the second object?

A force accelerates a body of mass M. A second body requires twice as much force to produce the same acceleration. What is the mass of the second body?

A net force of 64 N acts on a mass of 16 kg. The resulting acceleration is

A 10-N force is applied to mass M. The same force is applied to mass 4M. The ratio of the acceleration of the smaller mass to the acceleration of the larger mass is

A mass m is traveling at an initial speed of 25.0 m/s. It is brought to rest in a distance of 62.5 m by a net force of 15.0 N. The mass is

If you apply the same net force to objects with masses M and 4M, the acceleration of the mass M is

A net force is exerted on an object toward the north. The object

A 3.00 kg mass is traveling at an initial speed of 25.0 m/s. What is the magnitude of the force required to bring the mass to rest in a distance of 62.5 m?

A force accelerates a body of mass M. The same force applied to a second body produces three times the acceleration. What is the mass of the second body?

A mass of 25 kg is acted on by two forces, one of which is 10 N due east while the second one is 15 N due north. The acceleration of the mass is

If you want the same acceleration with masses M and 4M, the force applied on the mass M is

A ball of mass 2.0 kg is acted on by two forces, and . The magnitude of the acceleration is

A particle with a mass of 200 g is acted on by a net force of 4.5 N. The acceleration of the particle is

A mass of 25 kg is acted on by two forces, one of which is 15 N due east while the second one is 10 N due north. The acceleration of the mass is

A ball of mass 2.0 kg is acted on by two forces , and . The acceleration vector, , of the mass is in m/s2)

A third force is applied on the object so that the net force on the object is zero. Which force vector best represents the third force?

A ball of mass 2.0 kg is acted on by two forces, , and . The direction of the acceleration vector ) w.r.t to the +x-axis is

An object is moving to the right at a constant speed. Which one of the following statements must be correct?

A ball of mass 2.0 kg is acted on by two forces , and . The acceleration vector, , of the mass is in m/s²)