One
The engine must exert force enough to move all 4 cars. The vertical component is not present and is not accounted for by friction. So
the mass = 38000*4
The acceleration = 1.1
The force exerted by the engine on the first car is
F = m * a
F = 38000*4 * 1.1
F = 1.67 * 10^5
A
Two
The is a very interesting problem. The force on the ball consists of two forces: one going straight down which is it's gravitational weight, and another force created by the horizontal acceleration. I really suggest you draw a diagram of this situation. You don't need to know the mass of the pith ball that is hanging there. Nor do you need to know anything about the string holding the ball up, although both would be important in "real life."
The angle is derived from Tan(theta) = opposite force (which is the horizontal one) divided by the adjacent force whish is the weight of the orange ball. Notice that the masses cancel out.
Tan(theta) = m*a_horizontal / m*9.81
Tan(theta) = a_horizontal / 9.81
but the horizontal acceleration is given as 3
Tan(theta) = 3/9.81 = 0.3058
Theta = tan-1(0.3058)
Theta = 17.00
Answer: D
Three
The answer is 2.08 m/s^2
Make a drawing of the right angle triangle. Put the 12 degrees on top and the right angle on your lower right. The math on this is not difficult but the physics can be a bit of a nightmare. The down part of the right triangle is 3 N. That would be the adjacent side. The opposite side of the 12 degree angle is the horizontal force created by the acceleration.
So the horizontal force is found from
tan(12) = opposite/Adjacent.
The adjacent = 3N The opposite is unknown.
Tan(12) opposite / adjacent = horizontal_force / 3N
The horizontal force = adjacent * Tan(12);
Horizontal_force = 3N*0.2126 ;
Horizontal_Force = 0.6377
But that is the horizontal force. It is not the horizontal acceleration. To get the acceleration, you need to calculate the mass from 3N. This is vertical, so you use 9.81 for the "acceleration."
F = m *a ; Substitute for a and F from the comments above
3N = m * 9.81 ;
m = 3 / 9.81;
m = 0.3058 kg
Finally you can find the horizontal acceleration.
a = F_horizontal / m
a= 0.6377 / 0.3058
a = 2.08 m/s^2
Answer B
Note
It is not the math that is difficult here. It is knowing why you are applying the math as you have. The explanations are as important as the math and the answer is not as important as either one of the explanation or the math. Be sure and read everything carefully. This is the time where if you have questions, ask them.
