Answer to Question #272771 in Classical Mechanics for joseph

Question

1. A water tank is being towed by a truck on a level road, and the angle the free surface makes with the horizontal is measured to be 8 degrees. Determine the acceleration of the truck.

2. Consider two water tanks filled with water. The first tank is 8 m high and is stationary, while the second tank is 2 m high and is moving upward with an acceleration of 5 m/s². Which tank will have a higher pressure at the bottom?

3. A water tank is being towed on an uphill road that makes 14° with the horizontal with a constant acceleration of 3.5 m/s² in the direction of motion. Determine the angle the free surface of the water makes with the horizontal. What would your answer be if the direction of motion were downward on the same road with the same acceleration?

Answer 1

1.

$a=g\tan \theta=1.4~\frac{m}{s^2}.$

2.

$p_1=\rho gh_1=80~kPa,$

$p_2=\rho(g+a)h_2=30~kPa,$

$p_1>p_2.$

3.

$\theta_1=\arctan\frac{a_x}{g+a_y}=\arctan\frac{a\cos\alpha}{g+a\sin\alpha}=17.7°,$

$\theta_2=\arctan\frac{a_x'}{g+a_y'}=\arctan\frac{-a\cos\alpha}{g-a\sin\alpha}=-20.8°.$