7 indiana jones who is 750 kg starts from rest and slides...

7. Indiana Jones, who is 75.0 kg, starts from rest and slides down a stiff rope that exerts a constant friction force of 300 N. A spring-loaded 20.0 kg platform is 4.00 m below him. The spring itself is massless and has a spring constant of 4,000 hI/m. (a) What is Indiana's speed right before colliding with the platform? (b) What is the maximum distance the spring is compressed if the friction force acts during the entire slide?

Transcript

00:01 So our individual has a mass of 75 kilograms.

00:08 They have a frictional force acting against them the whole way of 300 newtons.

00:16 They are four meters above the spring loaded board.

00:22 The spring loaded board has a mass of 20 kilograms and a k value of 4 ,000 meters per meter.

00:30 We're starting at rest at zero meters per second.

00:34 We want to know how faster they're traveling right as they land on the board there.

00:42 They have some potential energy due to gravity, and they are doing work against friction.

00:51 So those combined, when they get to the bottom, the gravitational potential energy is converted to kinetic energy, but we lose some of it due to friction.

01:01 It's all going to become our final kinetic energy.

01:04 So we have mgy minus force of friction times y equals 1 half mv squared.

01:15 We can plug everything in.

01:17 We have 75 kilograms for the mass.

01:20 We have 9 .8 meters per second squared for g.

01:23 We are 4 meters above our target.

01:28 And we have 300 newtons for friction, traveling 4 meters.

01:34 And our mass is still 75.

01:36 And we're solving for v squared.

01:40 Rearrange everything and solve for v.

01:42 You should get a final speed, 6 .8 meters per second.

01:51 Now, taking this information, when we land on that board, how far are we going to depress the spring from where it's standing at? again, we have some shifting of energy to consider.

02:06 First of all, we have this kinetic energy which is solved for.

02:10 Now we have some potential energy due to gravity again because it's the height above wherever we expect the spring to land at.

02:19 And on our way down there, we still have friction acting on the rope, from the rope on us.

02:26 So we're going to lose some to that.

02:28 And this is all going to be converted into potential energy from the spring.

02:32 So again, we have, this is the v we just solved for.

02:38 We have our new mass.

02:41 So i'm going to put a m prime times gravity, times.

02:47 This new height that we're thinking of.

02:49 I'll explain why that m is different...