PHYSICS 30 MECHANICAL ENERGY B. EFFICIENCY 1. A 1.00 kg...

PHYSICS 30 MECHANICAL ENERGY B. EFFICIENCY 1. A 1.00 kg pendulum bob is released from a height of 2.00 m. Its speed at the bottom of its swing is 1.95 m/s on the first pass. [2 marks] a. How much energy is lost due to friction on the way to the bottom of the swing of the pendulum? b. How efficient is the pendulum in transferring GPE to KE? 2. A 12.0 kg mass is dropped from a height onto a spring that compresses and stops the mass. The ball has dropped from a height of 15.0 m before it hits the spring. The spring recoils and the mass is thrown upward. [3 marks] a. How high would the ball go if 200.0 J of energy were converted to heat during the entire interaction? b. What is the efficiency of this spring? c. When fully compressed, the spring stores 2000.0 Joules of Energy. What is the maximum mass that can be projected to a height of 18.0 m?

Transcript

00:01 Okay, so we've got a question about energy conservation and efficiency.

00:03 So part a, sorry part 1, a one kilogram pendulum is released from a vertical height of two meters and its speed at the bottom is 1 .95 meters per second.

00:21 So its initial speed u is zero meters per second and the height that it drops is two meters.

00:29 So this is how much energy is lost due to friction.

00:32 So the initial energy at the top is all gravitational potential and it's going to be just using our formula mgh.

00:41 So the difference in height is two meters, that's two, h is two, sorry, but m is one, g is 9 .81 and h is two.

00:51 And so that's just going to give us 19 .62 joules.

01:03 Then the energy at the bottom is, since we've lost that two meters in height, we're just thinking about kinetic energy now.

01:14 So that's a half mv squared and that's a half times one times 1 .95 squared, which gives you 1 .90 joules.

01:24 Thus the energy lost is equal to the energy at the bottom minus the energy at the top, 19 .62.

01:35 And that's going to give us minus 17 .72 joules of energy.

01:44 So that was part a.

01:46 Part b, how efficient is the pendulum at trading gravitational energy to kinetic energy? so it's not very efficient at all.

01:53 We've lost loads of energy.

01:56 The efficiency is going to be given by the kinetic energy we have at the bottom divided by the energy we started off with, the gravitational potential energy we start off with, and then times by 100 to get it as a percentage.

02:06 And this is 10 .2.

02:12 Sorry, that's not right.

02:14 That's 9 .7%.

02:16 Sorry, i was thinking about a different answer.

02:19 Okay.

02:19 And then question two, how high, so we've got a 12 kilogram mass dropped from a height onto a spring that compresses it and stops the mass and then launches it back up again.

02:34 It falls a height of 15 meters before it hits the spring and it recalls and then throws it back upwards.

02:40 So part a, how high would the ball go if 200 joules of energy was converted into heat during the entire interaction? so we have that the initial gpe minus the energy lost, so that's 200, equals the final gpe.

03:04 Now, suppose this is the initial setup...

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