Two masses are connected by a string which passes over a pulley with negligible mass and friction. One mass hangs vertically and one mass slides on a frictionless 30.0 degree incline. The vertically hanging mass is 6.00 kg and the mass on the incline is 4.00 kg. The magnitude of the acceleration of the 4.00 kg mass is A) 2.98 m/s². B) 3.92 m/s². C) 5.88 m/s². D) 6.86 m/s². E) 7.84 m/s².

Question

Quizplus · Accepted Answer

First, we need to draw a free-body diagram for each mass:
For the 6 kg mass:
- Force of gravity (weight) pulling down
- Tension force pulling up

For the 4 kg mass:
- Force of gravity pulling down (broken into components)
- Normal force perpendicular to the incline
- Force of gravity pulling parallel to the incline (broken into components)
- Tension force pulling up

Next, we can use Newton's second law to write equations for each mass:
For the 6 kg mass:
T - m1g = m1a

For the 4 kg mass:
m2g sin(30) - T = m2a
N - m2g cos(30) = 0

We can solve for tension in the first equation:
T = m1g + m1a

Then substitute into the second equation:
m2g sin(30) - m1g - m1a = m2a
Solving for acceleration:
a = (m2g sin(30) - m1g) / (m1 + m2)

Plugging in the given values:
a = (4 kg)(9.81 m/s^2)(sin(30)) - (6 kg)(9.81 m/s^2) / (4 kg + 6 kg)
a = 3.92 m/s^2

Therefore, the answer is B.

Two Masses Are Connected by a String Which Passes Over