Name: Drag Force and Terminal Velocity
Uploaded: 2019-07-19
Duration: 6 min 59 s
Description: Ever seen a skydiver sailing through the sky? How do they control the speed of their flight? Watch this video to understand the concept of drag force and ter...

Question

When the three blocks in are released from rest, they accelerate with a magnitude of $0.500 m / s^{2}$ . Block $1$ has mass $M$ , block $2$ has $2 M$ , and block $3$ has $2 M$ . What is the coefficient of kinetic friction between block $2$ and the table?

Accepted Answer

Given,
Mass of block-1, block-2 and block-3 are $M, 2 M$ and $3 M$ respectively.
Acceleration of the system, $M$ .

Let
$T_{1}$ and $T_{2}$ are tension forces on two different string as shown in the above figure.
$N$ and $f_{k}$ are normal force and kinetic friction acting on block 2 as shown in the above figure.
Acceleration due to gravity, $g = 10 {ms}^{- 2}$

Concept and Formula:
1.Newton's second law of motion:
$\sum_{} F = m a$

2. Kinetic friction:
$f_{k} = μ_{k} N$ , Where $μ_{k}$ is the co-efficient of kinetic friction.

As the block-(2) is not moving along vertical direction.
so, $N = 2 M g$ .

Putting the value of $N$ in kinetic friction $f_{k}$
$\Rightarrow f_{k} = μ_{k} \times 2 M g$

Using Newton's second law of motion on block 2 along horizontal direction.
$T_{1} - T_{2} - f_{k} = 2 M a \dots \dots \dots (1)$

Using Newton's second law of motion on block 3 along downward direction.
$3 M g - T_{1} = 3 M a \dots \dots \dots (2)$

Using Newton's second law of motion on block 1 along upward direction.
$T_{2} - M g = M a \dots \dots \dots (3)$

Add equation-1, equation-2 and equation-3.
$3 M g - f_{k} - M g = 2 M a + 3 M a + M a \Rightarrow 2 M g - μ_{k} 2 M g = 6 M a \Rightarrow μ_{k} 2 M g = 2 M g - 6 M a \Rightarrow μ_{k} g = g - 3 a$

Put the value of $a$ and $g$ in the above equation.
$μ_{k} 10 = 10 - 3 \times 0.5 = 8.5 \Rightarrow μ_{k} = \frac{8.5}{10} = 0.085$

So the value of kinetic friction between the block 2 and table is $0.085$

When the three blocks in are released from rest, they accelerate with a magnitude of $0.500 m / s^{2}$ . Block $1$ has mass $M$ , block $2$ has $2 M$ , and block $3$ has $2 M$ . What is the coefficient of kinetic friction between block $2$ and the table?

Important Questions on Force and Motion-II

Learn and Prepare for any exam you want !

When the three blocks in are released from rest, they accelerate with a magnitude of0.500 m/s2. Block 1 has massM, block 2 has 2M, and block 3 has2M. What is the coefficient of kinetic friction between block 2 and the table?

Important Questions on Force and Motion-II

Learn and Prepare for any exam you want !

When the three blocks in are released from rest, they accelerate with a magnitude of $0.500 m / s^{2}$ . Block $1$ has mass $M$ , block $2$ has $2 M$ , and block $3$ has $2 M$ . What is the coefficient of kinetic friction between block $2$ and the table?