Question

question 6 (5 points)
(02.07 mc)
a horizontal force of 50 n is required to push a wagon across a sidewalk at a constant speed.
a. what is the net (unbalanced) force acting on the wagon?
b. what is the value of the force of friction acting on the wagon?
c. if the mass on the wagon increased, use newtons second law to explain what must change to get the object moving at constant speed.

Explanation:

Step1: Recall Newton's first - law for constant speed

When an object moves at a constant speed, the net force acting on it is zero according to Newton's first law. So for part a, since the wagon is moving at a constant speed, the net force $F_{net}=0\ N$.

Step2: Analyze the forces in the horizontal direction

The horizontal force applied $F = 50\ N$ and the frictional force $F_f$ act on the wagon. Since $F_{net}=0$ and $F_{net}=F - F_f$, then $F_f=F$. So the frictional force $F_f = 50\ N$.

Step3: Apply Newton's second - law

Newton's second law is $F = ma$. When the mass $m$ of the wagon increases and we want to keep $a = 0$ (constant speed), and the frictional force $F_f=\mu N=\mu mg$ (where $\mu$ is the coefficient of friction and $N$ is the normal force, and $N = mg$ on a horizontal surface). As $m$ increases, the frictional force $F_f$ increases. To maintain $a = 0$ (constant speed), the applied force $F$ must be increased to balance the increased frictional force.

Answer:

a. $0\ N$
b. $50\ N$
c. The applied force must be increased. As the mass of the wagon increases, the frictional force (which is proportional to the mass) increases. To keep the object moving at a constant speed (acceleration $a = 0$), the applied force must be increased to balance the increased frictional force according to Newton's second law $F=ma$.