Two blocks with masses of 5.0kg and 10.0 kg hang on a string through a frictionless pulley with the 5.0-kg mass on a frictionless surface. Find (a) the acceleration of the blocks and(b) the tension along the string.
To find the acceleration of the blocks, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and acceleration. In this case, we have two blocks connected by a string, and the 10.0-kg block is hanging vertically.
(a) To find the acceleration, we need to calculate the net force acting on the system. The net force is determined by the difference between the gravitational force acting on the 10.0-kg block and the tension in the string.
Step 1: Calculate the gravitational force on each block.
The gravitational force can be calculated using the equation F = m * g, where F represents the force, m represents the mass, and g represents the acceleration due to gravity (9.8 m/s^2).
For the 5.0-kg block:
F1 = (5.0 kg) * (9.8 m/s^2)
For the 10.0-kg block:
F2 = (10.0 kg) * (9.8 m/s^2)
Step 2: Determine the net force.
The net force is given by the difference in gravitational force between the two blocks:
Net force = F2 - F1
Step 3: Calculate the acceleration.
Use Newton's second law of motion to find the acceleration:
Net force = (5.0 kg + 10.0 kg) * acceleration
Now, divide both sides of the equation by the combined mass of the system (5.0 kg + 10.0 kg) to solve for acceleration.
(a) acceleration = Net force / (5.0 kg + 10.0 kg)
(b) To find the tension along the string, we need to consider the forces acting on each block.
For the 10.0-kg block, the tension force acts upwards.
Tension = F2 - F_gravity_2
For the 5.0-kg block, the tension force acts downwards.
Tension = F1 + F_gravity_1
Note that the tensions on both sides of the string are equal, as the string is assumed to be massless and to not stretch or compress.
Therefore, the tension along the string is equal to Tension.
(b) tension = Tension