Two blocks are attached by a thin inextensi-
ble string over a frictionless, massless pulley.
There is a frictional force between the block
on the incline and the incline.
The acceleration of gravity is 9.8 m/s2 .
13 kg
13 kg
μ
T
1.1 m/s
0 m/s2
39◦
Calculate the magnitude of the frictional
force acting on the block on the incline.
Answer in units of N.
To calculate the magnitude of the frictional force acting on the block on the incline, we need to follow these steps:
Step 1: Determine the net force on the block on the incline.
The net force can be calculated using Newton's second law:
Net force = (mass of the block) x (acceleration)
In this case, the acceleration is given as 1.1 m/s^2 and the mass of the block is 13 kg.
Net force = 13 kg x 1.1 m/s^2
Net force = 14.3 N
Step 2: Determine the force due to gravity on the block on the incline.
The force due to gravity can be calculated using the formula:
Force due to gravity = (mass of the block) x (acceleration due to gravity)
The acceleration due to gravity is given as 9.8 m/s^2 and the mass of the block is 13 kg.
Force due to gravity = 13 kg x 9.8 m/s^2
Force due to gravity = 127.4 N
Step 3: Determine the force of tension in the string.
The force of tension in the string is the same on both blocks. We can calculate it by considering only one of the blocks. In this case, let's consider the block on the incline.
Force of tension = Force due to gravity - Net force
Force of tension = 127.4 N - 14.3 N
Force of tension = 113.1 N
Step 4: Determine the frictional force acting on the block on the incline.
The frictional force can be calculated using the formula:
Frictional force = (coefficient of friction) x (normal force)
The coefficient of friction (μ) and the normal force can be obtained from the given information. However, we need the normal force first.
Step 4.1: Calculate the normal force.
The normal force is the perpendicular force exerted by a surface on an object resting on it. In this case, the normal force is equal to the force due to gravity acting on the block perpendicular to the incline.
Normal force = Force due to gravity x cos(angle of incline)
The angle of incline is given as 39 degrees.
Normal force = 127.4 N x cos(39 degrees)
Normal force = 127.4 N x 0.766 = 97.56 N
Step 4.2: Calculate the frictional force.
Since the frictional force is opposing the motion of the block on the incline, it acts in the opposite direction of the force of tension in the string. Therefore, the frictional force is equal to the force of tension.
Frictional force = Force of tension
Frictional force = 113.1 N
Therefore, the magnitude of the frictional force acting on the block on the incline is 113.1 N.