Two masses are being pulled up a 30.0 degree incline by a force F parallel to the incline. The acceleration down the incline is 1.00 m/s² and the velocity is up the incline. The force is applied to a 200 kg mass and a string connects the 200 kg mass to a 150 kg mass. There is no friction. The tension in the string is A) 585 N. B) 1470 N. C) 980 N. D) 771 N. E) 1365 N.

Question

Quizplus · Accepted Answer

Using free body diagrams, we can write the equations of motion for each mass:

For the 200 kg mass:
F - T - m1*g*sin(30) = m1*a
where m1 = 200 kg, g = 9.8 m/s^2, and a = 1.00 m/s^2 (same for both masses)

For the 150 kg mass:
T - m2*g*sin(30) = m2*a
where m2 = 150 kg

We want to solve for T, so we need to eliminate a from the equations. We can do this by setting the equations equal to each other:

F - T - m1*g*sin(30) = T - m2*g*sin(30)
Simplifying and solving for T:
T = (F + (m1 + m2)*g*sin(30))/2
Plugging in the given values:
T = (F + 3500)/2

We also know that F = m1*a + m1*g*sin(30) from the first equation. Plugging this in:
T = (m1*a + m1*g*sin(30) + 3500)/2
T = (200*1.00 + 200*9.8*sin(30) + 3500)/2
T = 585 N

Two Masses Are Being Pulled Up a 30