Q4.6-38PE - College Physics (Urone)

Question

Unreasonable Results 

(a) Repeat Exercise 4.29, but assume an acceleration of 1.20 m/s2 is produced. (b) What is unreasonable about the result? 

(c) Which premise is unreasonable, and why is it unreasonable?

Step-by-Step Solution

Answer

(a) -260 N

(b) The result is unreasonable because the force of friction can never be in the direction of motion.

(c) The unreasonable premise is that the acceleration of 1.20 m/s² can be produced.

Step 1: Given Data

• The net force acting on the system = 1900 N.
• The sum of the boat's mass and the mass of the trailer = 700 kg.
• m_c is the mass of the car = 1100 kg.
• a is the acceleration = 1.20 m/s².

Step 2: (a) Determine the total resistance force

Apply Newton’s second law of motion as:

 

$F_{net}=Ma$

$F-f=\left(m_b+m_t+m_c\right)a$             …………. (i)

 

Here, F_net is the net force acting on the system, m_b is the mass of the boat, m_t is the mass of the trailer, m_c is the mass of the car, a is the acceleration, F is the force exerted by the car, and f is the resistance force.

 

Substitute 700 kg for (m_b+m_t), 1100 kg for m_c, 1900 N for F, and 1.20 m/s² for a in equation (i), and we get,

 

$\begin{array}{c}1900\text{\hspace{0.33em}N}-f=\left(700+1100\right)\text{\hspace{0.33em}kg}\times {\text{1.20\hspace{0.33em}m/s}}^2\\ 1900\text{\hspace{0.33em}N}-f=1800\text{\hspace{0.33em}kg}\times {\text{1.20\hspace{0.33em}m/s}}^2\\ f=\left(1900-2160\right)\text{\hspace{0.33em}N}\\ f=-260\text{\hspace{0.33em}N}\end{array}$

 

Hence, the total resistance force is -260 N.

Step 3: (b) The cause of unreasonability of the result

The result is unreasonable because the force of friction can never be in the direction of motion. It's always in the opposite direction.

Step 4: (c) The cause of unreasonability of the result

The unreasonable premise is that an acceleration of 1.20 m/s² can be produced.