A 5 kg block is placed on top of a 10 kg block as shown above. A horizontal force of 45 N is applied to the 10 kg block, while the 5 kg block is tied to the wall. The coefficient of kinetic friction between the moving surfaces is 0.20. Determine (a) the tension in the string and (b) the acceleration of the 10 kg block.
9.7N
To determine the tension in the string and the acceleration of the 10 kg block, we need to apply Newton's laws of motion.
(a) To find the tension in the string, we need to analyze the forces acting on the 5 kg block. The only force acting on it is the tension in the string, and this force causes the block to move horizontally.
To find the tension, we can use the equation:
Tension = mass * acceleration
Since the 5 kg block is tied to the wall and does not accelerate vertically, the vertical component of its weight is balanced by the normal force from the floor. Therefore, we only need to consider the horizontal motion.
(b) To find the acceleration of the 10 kg block, we need to analyze the forces acting on it. The forces acting on the 10 kg block are the force applied horizontally and the force of friction opposing its motion.
The equation for the net force on the 10 kg block is:
Net force = applied force - force of friction
We can calculate the force of friction using the equation:
Force of friction = coefficient of friction * normal force
Since the 5 kg block lies on top of the 10 kg block, the normal force exerted by the 5 kg block is equal to its weight. Therefore, we can rewrite the equation as:
Force of friction = coefficient of friction * weight of 5 kg block
The normal force on the 5 kg block can be calculated as:
Normal force = mass * acceleration due to gravity
Now that we have the force of friction, we can calculate the net force and the resulting acceleration of the 10 kg block using Newton's second law:
Net force = mass * acceleration
Now let's substitute the given values and calculate the required quantities:
Mass of 5 kg block (m1) = 5 kg
Mass of 10 kg block (m2) = 10 kg
Applied force = 45 N
Coefficient of kinetic friction (μ) = 0.20
Acceleration due to gravity (g) = 9.8 m/s²
(a) Tension in the string:
Since the 5 kg block is tied to the wall and does not accelerate vertically, its vertical component is balanced by the normal force. Therefore, the tension in the string is equal to the mass of the 5 kg block multiplied by its acceleration:
Tension = m1 * acceleration of 5 kg block
To find the acceleration of the 5 kg block, we need to calculate the net force acting on it. The net force is given by:
Net force = applied force - force of friction
To find the force of friction, we need to calculate the normal force acting on the 5 kg block:
Normal force = m1 * g
Substitute the given values into the equation to calculate the normal force.
Once we have the normal force, we can calculate the frictional force using the equation:
Force of friction = μ * normal force
Substitute the given values into the equation to calculate the force of friction.
Now, substitute the values of the applied force and the force of friction into the equation for the net force.
Finally, substitute the mass and the net force into the equation for tension to calculate the tension in the string.
(b) Acceleration of the 10 kg block:
To find the acceleration of the 10 kg block, we need to calculate the net force acting on it, which is equal to the applied force minus the force of friction.
To calculate the force of friction, use the equation:
Force of friction = μ * normal force
Substitute the given values into the equation to calculate the force of friction.
Once you have the force of friction, you can calculate the net force using the equation:
Net force = applied force - force of friction
Finally, divide the net force by the mass of the 10 kg block to find the acceleration.