Let’s make it simple: If you want to determine work in a physical sense, you have to multiply force times the displacement (distance an object moves) times the cosine of theta, which is the angle between force and the direction an object moves (or between force and the displacement vector). Say you want to push a wagon up a hill. The direction you want to push and the force are parallel. Theta is zero. ‘Nuff said.
So, a component of work is that angle, but at zero value it plays no role in the formula for determining the amount of work. In other words, you can ignore theta when you push that wagon up a hill. What’s left in the formula for work? Well, you have the force times the displacement. And those are significant parameters for determining the amount of work. Now, let’s say the hill is long, but not very steep and that you want to go up 100 feet above the starting elevation. You’ll do so much work to get the wagon up that incline. What if the hill were steeper? To get up that steeper rise to that 100-foot elevation, you’ll do the same amount of work. Stay with me.
You’ll do the same amount of work regardless of the steepness of the incline. That seems counterintuitive, right? Going up a steep hill in everyday experience seems harder than going up a gentler incline. But the numbers don’t lie. The amount of work is the same in both instances. And that’s because of the formulaic definition.
Work is the same on both inclines, but force isn’t the same. Going up a steep incline requires more force than going up a gentler one. You won’t go as far on the steeper climb as on the gentler one, so to make the amount of work equal you need more “push” in the formula. Why should I tell you what you learned in high school physics?
Think of persuasion. You will probably have to expend as much mental effort to ease someone into thinking the way you do or accepting a point you are trying to make as you will expend in trying to shout the person into agreement. One is going to require more force because it is a steeper path. The gentler incline is probably the wiser move. Yes, the work is the same, but the force is different. And, if you easily nudge someone, that is, if you apply the gentle force in the direction you want the person to go, even though distance is longer (and, obviously, in persuasion, you spend more time in the process), you’ll nullify the effect of theta while decreasing the force necessary to get the job done.
When you want to persuade someone, take the gentle incline that requires less force. The distance to the goal will be longer, but you won’t overexert yourself.
So, a component of work is that angle, but at zero value it plays no role in the formula for determining the amount of work. In other words, you can ignore theta when you push that wagon up a hill. What’s left in the formula for work? Well, you have the force times the displacement. And those are significant parameters for determining the amount of work. Now, let’s say the hill is long, but not very steep and that you want to go up 100 feet above the starting elevation. You’ll do so much work to get the wagon up that incline. What if the hill were steeper? To get up that steeper rise to that 100-foot elevation, you’ll do the same amount of work. Stay with me.
You’ll do the same amount of work regardless of the steepness of the incline. That seems counterintuitive, right? Going up a steep hill in everyday experience seems harder than going up a gentler incline. But the numbers don’t lie. The amount of work is the same in both instances. And that’s because of the formulaic definition.
Work is the same on both inclines, but force isn’t the same. Going up a steep incline requires more force than going up a gentler one. You won’t go as far on the steeper climb as on the gentler one, so to make the amount of work equal you need more “push” in the formula. Why should I tell you what you learned in high school physics?
Think of persuasion. You will probably have to expend as much mental effort to ease someone into thinking the way you do or accepting a point you are trying to make as you will expend in trying to shout the person into agreement. One is going to require more force because it is a steeper path. The gentler incline is probably the wiser move. Yes, the work is the same, but the force is different. And, if you easily nudge someone, that is, if you apply the gentle force in the direction you want the person to go, even though distance is longer (and, obviously, in persuasion, you spend more time in the process), you’ll nullify the effect of theta while decreasing the force necessary to get the job done.
When you want to persuade someone, take the gentle incline that requires less force. The distance to the goal will be longer, but you won’t overexert yourself.
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