The cement bag shown in the figure has a mass of 50 kg and the small pulley has a mass of 2 kg. If the cement bag is pulled upwa
rds with an acceleration of 2 m/s^2, find the force F pulling the rope.
1 answer:
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Answer:
Explanation:
For this problem to be easier to calculate, we can represent the triangle as a right triangle whose right angle is located at the origin of a coordinate system. (See picture attached).
With this disposition of the triangle, we can start finding our integral. The hydrostatic force can be set as an integral with the following shape:
γhxdy
we know that γ=62.5 lb/
from the drawing, we can determine the height (or depth under the water) of each differential area is given by:
h=8-y
x can be found by getting the equation of the line, which we'll get by finding the slope of the line and using one of the points to complete the equation:
when substituting the x and y-values given on the graph, we get that the slope is:
once we got this slope, we can substitute it in the point-slope form of the equation:
which yields:
which simplifies to:
we can now solve this equation for x, so we get that:
with this last equation, we can substitute everything into our integral, so it will now look like this:
Now that it's all written in terms of y we can now simplify it, so we get:
we can now proceed and evaluate it.
When using the power rule on each of the terms, we get the integral to be:
By using the fundamental theorem of calculus we get:
When solving we get:
Answer:
Right Hand Rule
Explanation:
When a charged particle travels in a magnetic field, it experiences a force whose magnitude is given by:
where
q is the charge of the particle
v is the velocity
B is the magnetic field strength
is the angle between the directions of v and B
The direction of the force can be determined by using the Right Hand Rule, as follows:
- index finger: this should be put in the direction of the velocity
- middle finger: this should be put in the direction of the magnetic field
- thumb: this will give the direction of the force -> however, for a negative charge (as the electron) the direction must be reversed, so it will be opposite.