Chapter 4, Problem 48QAP

To determine

(a)

Acceleration of the object if the force is doubled

Answer to Problem 48QAP

Acceleration of the object when net force is doubled is $20{\text{m/s}}^{\text{2}}$

Explanation of Solution

Given:

Constant net force is applied to an object causes it to accelerate at $10{\text{m/s}}^{\text{2}}$

  $a=\frac{F}{m}=10{\text{m/s}}^{\text{2}}$

Formula used:

Newton's second law of motion,

  $F=ma$

Calculation:

When the net force applied is doubled, the acceleration will also be doubled,

Now, force is 2F,

So, acceleration will be,

  $a=\frac{2F}{m}=2\times 10{\text{m/s}}^2=20{\text{m/s}}^{\text{2}}$

Conclusion:

Acceleration of the object when net force is doubled is $20{\text{m/s}}^{\text{2}}$

To determine

(b)

Acceleration of the object if the mass is halved

Answer to Problem 48QAP

Acceleration of the object when mass is halved is $20{\text{m/s}}^{\text{2}}$

Explanation of Solution

Given:

Constant net force is applied to an object causes it to accelerate at $10{\text{m/s}}^{\text{2}}$

  $a=\frac{F}{m}=10{\text{m/s}}^{\text{2}}$

Calculation:

When the mass is halved i.e. m/2, the acceleration will be

  $a=\frac{F}{(m/2)}=2F/m=20{\text{m/s}}^{\text{2}}$

Conclusion:

Acceleration of the object when mass is halved is $20{\text{m/s}}^{\text{2}}$

To determine

(c)

Acceleration of the object if the force is doubled and mass is doubled.

Answer to Problem 48QAP

Acceleration of the object when the force is doubled and mass is doubled is $10 m/s^2$

Explanation of Solution

Given:

Constant net force is applied to an object causes it to accelerate at $10 m/s^2$

  $a=\frac{F}{m}=10{\text{m/s}}^{\text{2}}$

Calculation:

When the force is doubled i.e. 2F, and mass is doubled i.e. 2m, the acceleration will be

  $a=\frac{2F}{2m}=F/m=10{\text{m/s}}^{\text{2}}$

Conclusion:

Acceleration of the object when the force is doubled, and mass is doubled is $10{\text{m/s}}^{\text{2}}$

To determine

(d)

Acceleration of the object if the force is doubled and mass is halved.

Answer to Problem 48QAP

Acceleration of the object when the force is doubled and mass is halved is $40 m/s^2$

Explanation of Solution

Given:

Constant net force is applied to an object causes it to accelerate at $10 m/s^2$

  $a=\frac{F}{m}=10{\text{m/s}}^{\text{2}}$

Calculation:

When the force is doubled i.e. 2F and mass is halved i.e. m/2, the acceleration will be

  $a=\frac{2F}{(m/2)}=4F/m=40{\text{m/s}}^{\text{2}}$

Conclusion:

Acceleration of the object when the force is doubled, and mass is halved is $40{\text{m/s}}^{\text{2}}$

To determine

(e)

Acceleration of the object if the force is halved.

Answer to Problem 48QAP

Acceleration of the object when the force is halved is $\text{5}{\text{m/s}}^{\text{2}}$

Explanation of Solution

Given:

Constant net force is applied to an object causes it to accelerate at $10{\text{m/s}}^{\text{2}}$

  $a=F/m=10{\text{m/s}}^{\text{2}}$

Calculation:

When the force is halved i.e. F/2, the acceleration will be

  $a=\frac{(F/2)}{m}=F/2m=5{\text{m/s}}^{\text{2}}$

Conclusion:

Acceleration of the object when the force is halved is $5{\text{m/s}}^{\text{2}}$

To determine

(f)

Acceleration of the object if the mass is doubled.

Answer to Problem 48QAP

Acceleration of the object when the mass is doubled is $5{\text{m/s}}^{\text{2}}$

Explanation of Solution

Given:

Constant net force is applied to an object causes it to accelerate at $10{\text{m/s}}^{\text{2}}$

  $a=F/m=10{\text{m/s}}^{\text{2}}$

Calculation:

When the mass is doubled i.e. 2m, the acceleration will be

  $a=\frac{F}{2m}=5{\text{m/s}}^{\text{2}}$

Conclusion:

Acceleration of the object when the mass is doubled is $5{\text{m/s}}^{\text{2}}$

To determine

(g)

Acceleration of the object if the force is halved and mass is halved.

Answer to Problem 48QAP

Acceleration of the object when the force is halved, and mass is halved is $10{\text{m/s}}^{\text{2}}$

Explanation of Solution

Given:

Constant net force is applied to an object causes it to accelerate at $10{\text{m/s}}^{\text{2}}$

  $a=F/m=10{\text{m/s}}^{\text{2}}$

Calculation:

When the force is halved i.e. F/2 and mass is halved i.e. m/2, the acceleration will be

  $a=(F/2)/(m/2)=F/m=10{\text{m/s}}^{\text{2}}$

Conclusion:

Acceleration of the object when the force is halved, and mass is halved is $10{\text{m/s}}^{\text{2}}$

To determine

(h)

Acceleration of the object if the force is halved and mass is doubled.

Answer to Problem 48QAP

Acceleration of the object when the force is halved, and mass is doubled is $2.5{\text{m/s}}^{\text{2}}$

Explanation of Solution

Given:

Constant net force is applied to an object causes it to accelerate at $10{\text{m/s}}^{\text{2}}$

  $a=F/m=10{\text{m/s}}^{\text{2}}$

Calculation:

When the force is halved i.e. $\frac{F}{2}$ and mass is doubled i.e. $2m$, the acceleration will be

  $a=(F/2)/2m=F/4m=2.5{\text{m/s}}^{\text{2}}$

Conclusion:

Acceleration of the object when the force is halved, and mass is doubled is $2.5{\text{m/s}}^{\text{2}}$