If the coefficient of kinetic friction is 0.15 find the tension in the string.

[mickeychief]

Can anyone tell me how to solve the below question?

A 9.0kg hanging weight is connected to a string over a pulley to a 5.0 kg block that is sliding on a flat table. If the coefficient of kinetic friction is 0.15 find the tension in the string.

 

[cepheid]

Start by drawing free body diagrams for block, hanging mass, and pulley (ideal pulley just changes direction of the tension force in the rope though). Account for all forces...use Newton's third law to help you out. That way you'll be able to identify the specific force you are asked to solve for and how it relates to the others.

 

[wais]

To solve this question, we can use the equation for Newton's Second Law, which states that the net force acting on an object is equal to its mass multiplied by its acceleration. In this case, the net force is the tension in the string.

First, we need to find the acceleration of the 5.0 kg block. We can use the equation for the force of friction, which states that the force of friction is equal to the coefficient of friction multiplied by the normal force. In this case, the normal force is equal to the weight of the block, which is 5.0 kg multiplied by the acceleration due to gravity (9.8 m/s^2). So, the force of friction is 0.15 x 5.0 kg x 9.8 m/s^2 = 7.35 N.

Next, we can set up an equation for the net force on the 5.0 kg block. The net force is equal to the tension in the string minus the force of friction. So, we have:

Net force = Tension - Force of friction

We know that the net force is equal to mass multiplied by acceleration, so we can substitute in the values we know:

5.0 kg x a = Tension - 7.35 N

We also know that the acceleration of the block is the same as the hanging weight, since they are connected by the string. So, we can substitute in the mass of the hanging weight (9.0 kg) for the acceleration:

5.0 kg x 9.8 m/s^2 = Tension - 7.35 N

Solving for tension, we get:

Tension = 49 N + 7.35 N = 56.35 N

Therefore, the tension in the string is 56.35 N.