Work Problem

[Mushrooomboy]

#341

The answer is D, but I picked A. I thought work was Fd, and force is gravitational energy so mass is involved? Why does the angle change work done on the mass?

#342

I don't have an answer for this one, any help would be very much appreciated

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[Czarcasm]

#341

The answer is D, but I picked A. I thought work was Fd, and force is gravitational energy so mass is involved? Why does the angle change work done on the mass?

#342

I don't have an answer for this one, any help would be very much appreciated

I always try to dumb it down into simple concepts. Gravitational PE is mgh (even for the incline). You can prove i t: mgsin(theta) x distance = work by gravity. But distance (the hypotenuse) is related to height by trig function: sin(theta)=height/distance, where distance = height/sin(theta). Substituting this in: mgsin(theta) x height/sin(theta) = mgh. Conceptually, to increase the distance would require you to increase the height. Altering the steepness (theta) of the slope would also impact height. And because work in this scenario is dependent on mass (the force due to gravity (mg) parallel to distance x distance), mass plays a role as well.

For #342: F=GMm/r^2. If gravity is the only net force on an object, then F=GMm/r^2 = Fnet = ma. Mass is proportional to gravitational force, but inversely proportional to acceleration. These two effects cancel each other out, which is why acceleration, velocity, and time are all independent of mass. Two objects of different mass dropped from the same height in a vacuum (where only force is gravity) would fall at the exact same acceleration and have the same final velocity. This obviously wouldn't be true if other forces where taken into consideration because in these instances, the net force (ma) is not due to force of gravity alone, but other forces as well (the effect of mass does not cancel out). In real life for example, air resistance plays a significant role (yielding the more intuitive result we would expect).

 

[NextStepTutor_1]

Thoughts on your approach to #341:

1. Just a refresher - F in the W = Fd is not always just the gravitational force, it refers to the net force. However, that's not important here because the gravitational force is the only force present.

2. Ok, so why is an angle going to affect this equation? Simply, because the object is on an inclined (i.e. angled) plane. Here's the science: if the force of gravity as we normally know it (mg) was dictating the direction of the object's motion, it would move down through the incline plane, but that's obviously not what we see. We see the object "slide" down and to the side (left in this example) meaning gravity is acting in some capacity to pull the object down but not straight down in the way we'd see a falling object fall. So the portion of the gravitational force that's forcing this object to move is equal to mgsin(theta) = the effective x-direction vector of gravity.
So now our equation looks like this W = mgsin(theta)*d

#342:
@Czarcasm explains this very well. The answer is A. You can also look at the Work equation we concluded in #341 and realize that mass is present in the equation. So when mass changes, work must too - not the case for velocity, time, and acceleration. Another way to quickly remember this is that all of the translational/kinematics equations you are to memorize for MCAT physics do not take into account mass, but they do take into account time, velocity, distance, and acceleration. The former variable, mass, is independent of these latter variables within the concept of kinematics.