Chapter 6, Problem 97A

(a)

To determine

The force exerted by R in pushing the cart.

Answer to Problem 97A

The force exerted by R on the cart is $5.88\text{N}$ .

Explanation of Solution

Given:

The mass of C is $m_{\text{C}}=17.0\text{kg}$ .

The mass of the cart is $m_{\text{Cart}}=12.4\text{kg}$ .

The acceleration of the cart is $a=0.20{\text{m/s}}^2$ .

Formula used:

Newton’s Second Law:

The object’s acceleration is equivalent to the sum of the forces acting on the object divided by the object’s mass. That is,

  $\begin{array}{l}a=\frac{F_{\text{net}}}{m}\\ F_{\text{net}}=ma\end{array}$

Here, $m$ is the mass and $a$ is the acceleration of the object.

Calculation:

Consider C is hanging in the cart.

Consider the R is pushing the cart.

R has to exert a force equivalent to the sum of the weight of the cart and the weight of C.

To find the force exerted by C on the cart, apply Newton’s Second Law of Motion,

  $\begin{array}{c}F=\left(m_{\text{C}}+m_{\text{Cart}}\right)a\\ =\left(17.0+12.4\right)\times 0.20\\ =5.88\text{kg}\cdot {\text{m/s}}^2\times \left(\frac{1\text{N}}{1\text{kg}\cdot {\text{m/s}}^2}\right)\\ =5.88\text{N}\end{array}$

Conclusion:

Therefore, the force exerted by R on the cart is $5.88\text{N}$ .

(b)

To determine

The force exerted by the cart onC.

Answer to Problem 97A

The force exerted by the cart on C is $167\text{N}$ .

Explanation of Solution

Given:

The mass of C is $m_{\text{C}}=17.0\text{kg}$ .

The mass of the cart is $m_{\text{Cart}}=12.4\text{kg}$ .

The acceleration of the cart is $a=0.20{\text{m/s}}^2$ .

Formula used:

Newton’s Second Law:

The object’s acceleration is equivalent to the sum of the forces acting on the object divided by the object’s mass. That is,

  $\begin{array}{l}a=\frac{F_{\text{net}}}{m}\\ F_{\text{net}}=ma\end{array}$

Here, $m$ is the mass and $a$ is the acceleration of the object.

Calculation:

Consider C is hanging in the cart and R is pushing the cart.

The cart will also exert a force (equivalent to the weight of the cart) on R.

Consider the acceleration due to gravity of the Earth as $g=9.80{\text{m/s}}^2$ .

The weight $\left(F_{\text{g}}\right)$ of the cart is,

  $\begin{array}{c}{F}_{\text{g}}=m_{\text{Cart}}g\\ =\left(17\text{kg}\right)\times \left(9.80{\text{m/s}}^2\right)\\ =167\text{kg}\cdot {\text{m/s}}^2\times \left(\frac{1\text{N}}{1\text{kg}\cdot {\text{m/s}}^2}\right)\\ =167\text{N}\end{array}$

Conclusion:

Therefore, the force exerted by the cart on C is $167\text{N}$ .