A 9.10-kg hanging object is connected by a light, inextensible cord over a light, frictionless pulley to a 5.00-kg block that is sliding on a flat table. Taking the coefficient of kinetic friction as 0.203, find the tension in the string.
To find the tension in the string, we need to consider the forces acting on the hanging object and the sliding block separately.
First, let's analyze the forces on the hanging object. The only force acting on it is its weight, given by the formula:
Weight = mass * acceleration due to gravity
where mass is the mass of the object and acceleration due to gravity is approximately 9.8 m/s^2.
Therefore, the weight of the hanging object is:
Weight = 9.10 kg * 9.8 m/s^2 = 89.18 N
Since the object is hanging and in equilibrium, the tension in the string is equal to its weight:
Tension (in string) = Weight = 89.18 N
Now, let's consider the forces acting on the sliding block. The forces acting on it are the tension in the string, the friction force, and its weight. The friction force can be calculated using the formula:
Friction force = coefficient of kinetic friction * normal force
where the normal force is equal to the weight of the block:
Normal force = mass * acceleration due to gravity
Therefore, the normal force is:
Normal force = 5.00 kg * 9.8 m/s^2 = 49 N
Now, we can calculate the friction force:
Friction force = 0.203 * 49 N = 9.947 N
Since the block is sliding on a flat table and the tension in the string is in the opposite direction of the friction force, we can write the following equation for the forces:
Tension (in string) - Friction force - Weight (of the block) = mass (of the block) * acceleration
Rearranging the equation, we can solve for the tension:
Tension (in string) = Weight (of the block) + Friction force + mass (of the block) * acceleration
Since the block is sliding, its acceleration is non-zero. We can use Newton's second law to find the acceleration:
mass (of the block) * acceleration = net force on the block
The net force on the block can be calculated as the difference between the tension in the string and the friction force:
net force on the block = Tension (in string) - Friction force
Rearranging the equation, we have:
mass (of the block) * acceleration = Tension (in string) - Friction force
Substituting the known values, we can solve for the acceleration:
5.00 kg * acceleration = Tension (in string) - 9.947 N
To find the value of the acceleration, we need more information or an additional equation relating the acceleration to the system. If you can provide more information, I can help you further.