A shipping container is hauled up a roller ramp that is effe

 A shipping container is hauled up a roller ramp that is effectively frictionless at a constant speed of 2.10 m/s by a 2250 N force that is parallel to the ramp. If the ramp is at a 24.6° incline, what is the container\'s mass?

Solution

Since our ramp is frictionless the only forces we\'re concerned withwill be the gravitational force, and the force we\'re using to dothe work. Since we know that the net force is zero on the shipping containerthat tells us the vector component of the gravitational forceparallel and opposite our applied force is 2250 N. With thatknowledge all we need to do is break up the acceleration of thegravitational force into its vector components due to the ramp. I wish I could draw the ramp for you and do the triangle. Essentially the magnitude of the gravitational acceleration isassumed to be 9.81 m/s^2, with a direction straight down, ifyou draw the triangles on the ramp making a perpendicular line fromits surface, and one straight down to represent gravity, you\'llnotice you have a triangle with a similar angle 24.6 degrees. The magnitude of the parallel vector component will then become9.81 * Sin(24.6)   which will give youthe acceleration due to gravity on the container(that makes the netforce zero) and allow you to apply 2250 N = M * a where a = 9.81 * Sin(24.6)

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