Question

block 1 of mass 3.0 kg is on a horizontal surface and is pulled at a constant velocity to the right by a string, as shown in the figure. block 2 of mass 1.0 kg is on block 1 and held at rest by another string attached to a vertical wall. the coefficients of kinetic and static friction between all surfaces are 0.20 and 0.40, respectively, and the strings have negligible mass. what is the tension in the string attached to block 1?
a 6 n
b 8 n
c 10 n
d 12 n

Explanation:

Step1: Calculate normal force on lower - upper block interface

The normal force between Block 1 and Block 2, $N_{12}=m_2g$, where $m_2 = 1.0\ kg$ and $g = 10\ m/s^2$. So $N_{12}=1\times10 = 10\ N$.

Step2: Calculate friction force between Block 1 and Block 2

The friction force between Block 1 and Block 2, $f_{12}=\mu_kN_{12}$, with $\mu_k = 0.20$. So $f_{12}=0.2\times10=2\ N$.

Step3: Calculate normal force on lower - surface interface

The normal force between Block 1 and the horizontal surface, $N_{1s}=(m_1 + m_2)g$, where $m_1 = 3.0\ kg$ and $m_2 = 1.0\ kg$, so $N_{1s}=(3 + 1)\times10=40\ N$.

Step4: Calculate friction force between Block 1 and the surface

The friction force between Block 1 and the surface, $f_{1s}=\mu_kN_{1s}$, with $\mu_k = 0.20$. So $f_{1s}=0.2\times40 = 8\ N$.

Step5: Analyze forces on Block 1

Since Block 1 moves at a constant velocity, the net force on it is zero. The tension in the string attached to Block 1, $T=f_{1s}+f_{12}$. Substituting the values of $f_{1s}$ and $f_{12}$, we get $T = 8+2=10\ N$.

Answer:

C. 10 N