The two blocks in the sketch are connected by a
light cord over a frictionless pulley and are initially held in
place. The block m1 has a mass of 2,00 kg and m2 has
a mass of 3,00 kg. The inclined
plane is frictionless and the
coefficient of kinetic friction
between block m1 and the
horizontal surface is 0,25. The
inclined plane makes an angle
of 30,0° with the horizontal.
Calculate the acceleration of
I
the blocks and the tension in the cord when the two
(7) blocks are released.
Answer it
To calculate the acceleration of the blocks and the tension in the cord when they are released, we can use Newton's second law of motion.
1. Calculate the gravitational forces acting on each block:
The gravitational force (weight) can be calculated using the mass of each block (m1 = 2.00 kg, m2 = 3.00 kg) and the acceleration due to gravity (g = 9.8 m/s^2):
F_gravity1 = m1 * g
F_gravity2 = m2 * g
2. Calculate the normal force on block m1:
Since the inclined plane is frictionless, the normal force acting on m1 is equal to the component of the weight perpendicular to the inclined plane:
N1 = F_gravity1 * cos(30°)
3. Calculate the force of friction on block m1:
The coefficient of kinetic friction between m1 and the horizontal surface is given as 0.25. Therefore, the force of friction can be calculated as:
F_friction = N1 * μ_kinetic
= N1 * 0.25
4. Calculate the net force on block m1:
The net force on m1 can be calculated by considering the forces in the x-direction (parallel to the inclined plane):
F_net1 = F_gravity1 * sin(30°) - F_friction
5. Calculate the acceleration of the blocks:
We can now use Newton's second law of motion to find the acceleration:
F_net1 = m1 * a
a = F_net1 / m1
6. Calculate the tension in the cord:
The tension in the cord can be determined by considering the forces in the y-direction (perpendicular to the inclined plane):
Tension = F_gravity2 - N1
Now you can plug in the values you have for m1, m2, g, and μ_kinetic (0.25) to calculate the acceleration of the blocks and the tension in the cord.