A 100-N mass on a horizontal table is connected to a 50.0-N hanging mass over a
frictionless pulley. The two masses are moving at constant speed. What is the value of
the coefficient of kinetic friction between the table and the horizontal mass?
0=N-m₁g => N = m₁g
0=T-F(fr) => T=F(fr)=μN= μ•m₁g
0=T-m₂g => T= m₂g
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μ•m₁g = m₂g
μ = m₂g/m₁g= 50/100 =0.5
Well, if the two masses are moving at constant speed, that means the net force acting on the system is zero.
The force due to gravity on the hanging mass is 50.0 N, and the force due to gravity on the horizontal mass is 100 N.
Since the net force is zero, that means the force of friction between the table and the horizontal mass must be equal and opposite to the force due to gravity on the horizontal mass.
So, the force of friction is also 100 N.
Now, we can use the equation for the force of friction, which is equal to the coefficient of friction times the normal force.
Since the normal force is equal to the force due to gravity on the horizontal mass, the coefficient of friction is simply 100 N divided by the normal force.
And since the force due to gravity on the horizontal mass is 100 N, the coefficient of friction is equal to... um... I'm getting some funny looks here, seems like I've misplaced my calculator. Anyone seen it?
Guess we'll never know the value of the coefficient of kinetic friction between the table and the horizontal mass. But hey, who needs numbers anyway? They're so overrated!
To find the value of the coefficient of kinetic friction between the table and the horizontal mass, we need to consider the forces acting on the system.
1. The weight of the hanging mass (the force due to gravity) is given by:
Force_hanging = m_hanging * g
Force_hanging = 50.0 N
2. The tension in the string (which is also the force applied on the horizontal mass) is given by:
Force_tension = Force_hanging = 50.0 N
3. The force of kinetic friction between the table and the horizontal mass is given by:
Force_friction = coefficient_of_friction * Normal_force
4. Since the system is moving at a constant speed, the net force in the horizontal direction is zero:
Net_force_horizontal = Force_tension - Force_friction = 0
Now, let's calculate the normal force acting on the horizontal mass:
5. The normal force is equal in magnitude and opposite in direction to the weight of the horizontal mass:
Normal_force = Weight_horizontal
6. The weight of the horizontal mass is given by:
Weight_horizontal = m_horizontal * g
Weight_horizontal = 100 N
7. Substituting the values into the equation for net force, we have:
Force_tension - coefficient_of_friction * Normal_force = 0
50.0 N - coefficient_of_friction * 100 N = 0
8. Solving for the coefficient_of_friction:
coefficient_of_friction = Force_tension / Normal_force
coefficient_of_friction = 50.0 N / 100 N
coefficient_of_friction = 0.5
Therefore, the value of the coefficient of kinetic friction between the table and the horizontal mass is 0.5.
To find the value of the coefficient of kinetic friction between the table and the horizontal mass, we can use the following steps:
Step 1: Calculate the net force acting on the system.
The net force on the system can be determined by considering the forces acting on each mass. The 100 N mass experiences a force due to friction, which opposes its motion, while the 50.0 N mass experiences a gravitational force pulling it downwards. Since the masses are moving at a constant speed, the net force acting on the system is zero.
Step 2: Determine the frictional force.
Since the system is in equilibrium, the force due to friction must be equal in magnitude and opposite in direction to the sum of the gravitational force on the hanging mass and the tension in the string.
The gravitational force on the hanging mass can be calculated using the formula:
Force_gravity = mass * acceleration due to gravity
Given that the mass of the hanging mass is 50.0 N and the acceleration due to gravity is approximately 9.81 m/s^2, we can calculate the gravitational force as follows:
Force_gravity = 50.0 N * 9.81 m/s^2 = 490.5 N
The tension in the string is equal to the gravitational force on the horizontal mass, as they are connected by a string passing over a pulley. Hence, the tension is also 490.5 N.
The frictional force, which counteracts the motion of the 100 N mass, is equal to the gravitational force on the hanging mass plus the tension in the string.
Frictional force = Force_gravity + Tension
Frictional force = (490.5 N + 490.5 N) = 981 N
Step 3: Calculate the normal force.
The normal force is the force exerted by the table perpendicular to the surface. Since the table is horizontal, the normal force is equal in magnitude and opposite in direction to the gravitational force on the horizontal mass.
Normal force = gravitational force = 100 N
Step 4: Calculate the coefficient of kinetic friction.
The coefficient of kinetic friction can be found using the equation:
Coefficient of kinetic friction = Frictional force / Normal force
Given that the frictional force is 981 N and the normal force is 100 N, we can calculate the coefficient of kinetic friction as follows:
Coefficient of kinetic friction = 981 N / 100 N = 9.81
Therefore, the value of the coefficient of kinetic friction between the table and the horizontal mass is 9.81.