A 1 lb block and a 100 lb block are placed side by side at...

A 1-lb block and a 100-lb block are placed side by side at the top of a frictionless hill. Each is given a very light tap to begin their race to the bottom of the hill. In the absence of air resistance, what can you conclude about the outcome of the race? The 1-lb block wins the race. The 100-lb block wins the race. The two blocks end in a tie. There's not enough information to determine which block wins the race.

Transcript

00:01 So before we look at the two blocks in this problem, let's look at just one block going down a frictionless hill, and let's see what this can tell us about our situation here.

00:13 It says some angle theta.

00:14 Now what are the forces on this block going to be? well, if there's no friction, the only thing we have are the normal force with the contact from the ramp, and then the weight of the block pushing it downwards, which is equal to its mass times acceleration due to gravity.

00:35 And so we can make a free body diagram of that.

00:40 Mass times gravity downwards, the normal force.

00:49 Now which direction is the acceleration of this block going to be, or it's going to be down the ramp? and so let's make our axis direction that way to make our solving a bit easier.

01:00 So we can do x and y.

01:03 And we finally need the angle, and this is angle theta corresponding to that angle there.

01:16 And if we do that, we have angle theta and our right hand angle here.

01:24 This is theta.

01:27 I guess we need to do both of these.

01:34 And this is angle theta.

01:36 This is 90 minus theta, which would leave this as theta.

01:42 A whole bunch of geometrical rules there, but we can get that being our angle.

01:48 But we see it doesn't really matter for what we're doing.

01:50 We're just going to show how mass cancels out.

01:54 So we can look at sum of forces in this problem.

01:58 Do it in second law.