In my physic book there is a question which is as follows;-

A food shopper pushes a wood crate of cabbage heads of mass $m$ =14kg across a concrete floor with a constant horizontal force $\vec{F}$ of magnitude 40$N$. In a straight- line displacement of magnitude $d$ = 0.50m/s, the speed of the crate decreases from $v_0$ = 0.60$m/s$ to $v$ = 0.20$m/s$. Find the work done by force and on what system it does work?

How can the block's speed decrease when the we apply a horizontal force to it in the same direction of motion?

You might say it is friction, and the solution of the book says it is friction as is mention

"If there were no friction then the block should be accelerating and the velocity shouldn't decrease."

but when the block had initial velocity $v_0$ then also friction(was) should be acting on the block. Also the value of force due to friction $f_k = \mu_k$N where $\mu_k$ is the coefficient due to kinetic friction and N is the normal reaction. As both are fixed in this case so $f_k$ is fixed and when the initial velocity was taken then the $f_k$ force was removed(subtracted) from the earlier force(assumed as force needed to move object) which moved the block at a velocity $v_0$ of 0.60$m/s$.

Then why would the speed of block reduce?

  • $\begingroup$ The question does seem a bit vague. . . $\endgroup$ – Praneet Srivastava Jan 7 '15 at 13:24
  • $\begingroup$ @HadrianEvan Is there anything you didn't understand in the question $\endgroup$ – pcforgeek Jan 7 '15 at 13:25
  • $\begingroup$ No, that's not what i meant. You are correct. If a constant force is applied as given in the question, the object shouldn't show down. Maybe the author meant that the crate was moving at constant velocity when the force was being applied, and started to slow down once the force speed acting. $\endgroup$ – Praneet Srivastava Jan 7 '15 at 13:29
  • $\begingroup$ What you quote is not a question. Have you omitted something? The book migth say there is friction or something like that. $\endgroup$ – jinawee Jan 7 '15 at 13:30
  • $\begingroup$ @jinawee Yes it is a part of the question. The rest part of the question asked to "find the work done by force and on what system it does work?". The question doesn't mention anything about friction, but being a solved example the theory part of the solution say that friction act. If there were no friction then the block should be acclerating and the velocity shouldn't decrease. $\endgroup$ – pcforgeek Jan 7 '15 at 13:42

It seems clear to me that "something happened " before time 0 - something that caused the velocity of the cart to be 0.6 m/s at $t=0$. Presumably that something was a harder push that accelerated the cart (which was at rest at some point in the past) and overcame friction.

We then observe the system and see one measurable force (person pushing) and one observable effect (cart decelerating). We conclude there must be another (invisible) force acting on the cart - and from the information given we can deduce the magnitude and direction of that force.


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