A block of mass 0.8kg is dragged along a level surface at constant velocity by hahanging block of mass 0.2kg
since there is no acceleration, there must be some friction.
To analyze this situation, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration. In this case, since the velocity is constant, the acceleration is zero, and therefore the net force on the system must also be zero.
Let's denote the force exerted by the person hanging the block as \( F_h \), and the force of friction between the block and the surface as \( F_f \). Additionally, let's denote the masses of the hanging block and the dragged block as \( m_h \) and \( m_d \) respectively, and the acceleration due to gravity as \( g \).
The force equation for the hanging block can be expressed as:
\[ F_h = m_h \cdot g \]
where \( F_h \) is the force exerted by the person, \( m_h \) is the mass of the hanging block, and \( g \) is the acceleration due to gravity.
Since the system is in equilibrium, the net force on the system is zero, which means the force of friction is equal in magnitude but opposite in direction to the force applied by the person:
\[ F_f = -F_h \]
The force of friction can be calculated using the equation:
\[ F_f = \mu \cdot F_N \]
where \( \mu \) is the coefficient of friction and \( F_N \) is the normal force exerted on the block.
On a level surface, the normal force is equal to the weight of the block, which can be calculated as:
\[ F_N = m_d \cdot g \]
where \( m_d \) is the mass of the dragged block, and \( g \) is the acceleration due to gravity.
Substituting the expressions for \( F_N \) and \( F_h \) into the equation for the force of friction, we get:
\[ \mu \cdot m_d \cdot g = -m_h \cdot g \]
Now let's plug in the values from the problem statement:
\( m_h = 0.2 \) kg (mass of the hanging block)
\( m_d = 0.8 \) kg (mass of the dragged block)
\( g \) is the acceleration due to gravity, approximately \( 9.8 \) m/s²
Substituting the values, we have:
\[ \mu \cdot 0.8 \cdot 9.8 = -0.2 \cdot 9.8 \]
To find the coefficient of friction (μ), we can solve the equation for it:
\[ \mu = \frac{-0.2 \cdot 9.8}{0.8 \cdot 9.8} \]
Simplifying the expression, we find:
\[ \mu = -0.2 \]
Since the coefficient of friction cannot be negative, we have made an error somewhere in our calculations. Please check the numbers provided in the problem statement and make sure they are accurate.