Question

Block 1 has a mass of 5 kg, and block 2 has a mass of 1 kg. If the angle of the ramp is 40 degrees. What is the acceleration of the moving blocks? Assume no friction between the block and the ramp.

a) 9.8 m/s^2
b) 6.4 m/s^2
c) 4.6 m/s^2
d) 2.5 m/s^2

Answer 1

The acceleration of the connected blocks on the frictionless ramp can be calculated using the components of gravitational force and Newton's second law, resulting in an acceleration of approximately 6.4 m/s².

Step-by-step explanation:

To find the acceleration of the moving blocks, we will use Newton's second law of motion, which is F = ma (force equals mass times acceleration). However, since there is no friction, the net force on the system is just the component of the gravitational force acting down the ramp.

For an object on an inclined plane, the gravitational force acting down the inclined plane (parallel to it) is F = m * g * sin(θ), where g is the acceleration due to gravity (9.8 m/s²), and θ is the angle of inclination.

In this case, both blocks are connected, and they will have the same acceleration because they are treated as a single system. Therefore, the total mass m is the sum of the masses of both blocks, m = m1 + m2 = 5 kg + 1 kg = 6 kg. The force down the ramp is F = 6 kg * 9.8 m/s² * sin(40°).

Now, we apply Newton's second law to solve for the acceleration:
F = ma
6 kg * 9.8 m/s² * sin(40°) = 6 kg * a
a = 9.8 m/s² * sin(40°)
a ≈ 6.3 m/s²

Since the calculated acceleration is not one of the given options, we round it to the closest one, which is 6.4 m/s².