Two boxes connected by a light horizontal rope are on a...

Two boxes connected by a light horizontal rope are on a horizontal surface (Fig. E5.37). The coefficient of kinetic friction between each box and the surface is $\mu_k$ = 0.30. Box $B$ has mass 5.00 kg, and box $A$ has mass $m$. A force $F$ with magnitude 40.0 N and direction 53.1$^\circ$ above the horizontal is applied to the 5.00-kg box, and both boxes move to the right with $a =$ 1.50 m/s$^2$. (a) What is the tension $T$ in the rope that connects the boxes? (b) What is $m$?

Transcript

00:01 Part a is asking for the tension connecting blocks a and b.

00:05 And like most of these problems, we're going to start off by drawing a force diagram.

00:09 First, i'm going to draw the force diagram for block a.

00:13 It has a tension force pulling left.

00:16 It has a normal force, which i'm going to call na pushing up.

00:20 It has mass pulling down, which i'm going to call mg, since the mass of block a is unknown.

00:27 We just call it m.

00:29 And then it's got a friction force, which i'm going to call friction force on a point to the right.

00:36 Now some of the forces in the y direction equals zero, zero because there's no acceleration in the y direction and i should set my coordinate system.

00:45 It'll be that where this is positive x and this is positive y.

00:48 So the block's not going to jump up in the y direction so it can say equal to zero, which implies that the normal force on a is equal to mg.

00:59 Now the sum of the forces in the x direction is not equal to zero.

01:02 It's equal to the mass times the acceleration in the x direction.

01:07 This implies that tension minus force of friction on block a is equal to 1 .5 times out.

01:16 And i'm going to denote this equation by star.

01:19 It'll be useful as we do part b.

01:23 Now i'm going to draw the force diagram for block b.

01:28 This one will have a vertical component in b.

01:32 It has a force over here of 40 nons.

01:36 And it's at an angle of 53 .1 degrees.

01:41 We have gravity pulling it down...