Final answer:
The pressure in a bucket of water pushed across a horizontal surface is higher at the point on the left side due to the increased speed of water on the right side, where the pressure is lower by the equation of continuity and Bernoulli's principle.
Step-by-step explanation:
When considering a bucket of water being pushed with increasing speed across a horizontal surface, it's important to understand how pressure in the water is affected. According to the principles of fluid dynamics, specifically the equation of continuity and Bernoulli's principle, in an incompressible fluid such as water, if the fluid is pushed to move faster on one side compared to the other, there will be a difference in pressure due to the change in kinetic energy.
Therefore, as the bucket of water is accelerated from left to right, the pressure at a point on the left side of the bucket (where water is entering the moving section) becomes higher compared to the pressure at a point on the right side (where water is leaving the moving section). This is because the speed of the water at the right is greater due to the motion of the bucket. Consequently, according to Bernoulli's principle, where the speed is greater, the pressure is lower. Thus, the correct answer is B) It is higher at the point on the left.
This scenario aligns with the concept that when water enters a narrow section, it must speed up, and the pressure in that area drops; conversely, where the flow slows down, the pressure increases. Additionally, Pascal's principle indicates that within the same fluid, at the same level, pressure changes equally, but this applies to static situations. Since the bucket is moving and not static, the fluid dynamics principles that take into account fluid motion and changes in velocity are more applicable.