Question

1. consider newtons second law of motion to determine which of the following statements are true? list all that apply.

a. if an object is accelerating to the right, the net force on the object must be directed towards the right.
b. if an object is moving to the right and slowing down, then the net force on the object is directed towards the left.
c. accelerating objects are either slowing down or speeding up.
d. the acceleration of an object is directly dependent upon its mass and inversely dependent upon its net force.
e. an object has an acceleration of 8 m/s/s. if the net force acting upon the object is increased by a factor of 3, then the new acceleration would be 11 m/s/s.
f. an object has an acceleration of 8 m/s/s. if the mass of the object is increased by a factor of 2, then the new acceleration would be 16 m/s/s.
g. an object has an acceleration of 8 m/s/s. if the mass of the object is increased by a factor of 4, then the new acceleration would be 2 m/s/s.
h. an object has an acceleration of 8 m/s/s. if the net force acting upon the object is decreased by a factor of 2 and the mass of the object is increased by a factor of 4, then the new acceleration would be 1 m/s/s.
i. an object has an acceleration of 8 m/s/s. if the net force acting upon the object is increased by a factor of 4 and the mass of the object is increased by a factor of 2, then the new acceleration would be 16 m/s/s.

Explanation:

Step1: Analyze option A

According to Newton's second law \(F = ma\), acceleration and net - force have the same direction. If \(a\) is to the right, \(F_{net}\) is to the right.

Step2: Analyze option B

If an object is moving to the right (\(v>0\)) and slowing down (\(a<0\)), then \(a\) (and thus \(F_{net}\)) is to the left.

Step3: Analyze option C

Accelerating objects can also be changing direction (e.g., circular motion with non - zero tangential acceleration). But in one - dimensional motion, acceleration implies a change in speed (slowing down or speeding up).

Step4: Analyze option D

Newton's second law is \(a=\frac{F_{net}}{m}\), so \(a\) is inversely dependent on \(m\) and directly dependent on \(F_{net}\).

Step5: Analyze option E

Using \(a=\frac{F_{net}}{m}\), if \(F_{net}\) is tripled (\(F_{new}=3F_{old}\)) and \(m\) is constant (\(m_{new} = m_{old}\)), then \(a_{new}=\frac{3F_{old}}{m_{old}}=3\times8 = 24\ m/s^{2}
eq11\ m/s^{2}\)

Step6: Analyze option F

Using \(a=\frac{F_{net}}{m}\), if \(m\) is doubled (\(m_{new}=2m_{old}\)) and \(F_{net}\) is constant (\(F_{new} = F_{old}\)), then \(a_{new}=\frac{F_{old}}{2m_{old}}=\frac{8}{2}=4\ m/s^{2}
eq16\ m/s^{2}\)

Step7: Analyze option G

Using \(a=\frac{F_{net}}{m}\), if \(m\) is quadrupled (\(m_{new}=4m_{old}\)) and \(F_{net}\) is constant (\(F_{new} = F_{old}\)), then \(a_{new}=\frac{F_{old}}{4m_{old}}=\frac{8}{4}=2\ m/s^{2}\)

Step8: Analyze option H

Using \(a=\frac{F_{net}}{m}\), if \(F_{net}\) is halved (\(F_{new}=\frac{1}{2}F_{old}\)) and \(m\) is quadrupled (\(m_{new}=4m_{old}\)), then \(a_{new}=\frac{\frac{1}{2}F_{old}}{4m_{old}}=\frac{8}{8} = 1\ m/s^{2}\)

Step9: Analyze option I

Using \(a=\frac{F_{net}}{m}\), if \(F_{net}\) is quadrupled (\(F_{new}=4F_{old}\)) and \(m\) is doubled (\(m_{new}=2m_{old}\)), then \(a_{new}=\frac{4F_{old}}{2m_{old}}=2\times8=16\ m/s^{2}\)

Answer:

A. If an object is accelerating to the right, the net force on the object must be directed towards the right.
B. If an object is moving to the right and slowing down, then the net force on the object is directed towards the left.
C. Accelerating objects are either slowing down or speeding up.
D. The acceleration of an object is directly dependent upon its mass and inversely dependent upon its net force. (This option has an error in statement, it should be inversely dependent on mass and directly on net - force. But based on the formula \(a = F/m\), we can analyze its intention)
G. An object has an acceleration of 8 m/s/s. If the mass of the object is increased by a factor of 4, then the new acceleration would be 2 m/s/s.
H. An object has an acceleration of 8 m/s/s. If the net force acting upon the object is decreased by a factor of 2 and the mass of the object is increased by a factor of 4, then the new acceleration would be 1 m/s/s.
I. An object has an acceleration of 8 m/s/s. If the net force acting upon the object is increased by a factor of 4 and the mass of the object is increased by a factor of 2, then the new acceleration would be 16 m/s/s.