Physics problems

[JimC]

Just for fun, this is a worksheet I made on an area of physics for my students, who are in their second last year of secondary school:

11 Physics Extra problems on energy and momentum
• Working must be shown. Round off to 2 decimal places where needed
• Be aware of units; some may need converting, and answers need to show correct units
• Formulae such as the motion equations from previous chapters may be required
1. A bullet with a mass of 20 grams is fired, with a velocity of 450 m/s. It strikes a sandbag (with a mass of 50 kg) sitting on a frictionless trolley, and penetrates it to a depth of 8 cm before coming to a halt inside it. (Note - the 50 kg is the combined mass of the trolley + sandbag)
a) Calculate the velocity of the sandbag after the impact
b) Calculate the rate of deceleration of the bullet in the sandbag
c) Calculate the time the bullet would take to come to a halt over the 8 cm
d) Calculate the average force exerted on the bullet by the sand
e) A further firing is done, with a 25 gram bullet. It causes the sandbag on the trolley to move with a velocity of 0.22 m/s. Calculate the velocity of the bullet in this case.
2. A stationary ball with a mass of 270 grams is hit by a bat, and develops a velocity of 67 m/s. Time lapse photography shows that the impact lasted for 15 ms
a) Calculate the momentum gained by the ball
b) What would the momentum lost by the swinging bat be?
c) What impulse was given to the ball?
d) Calculate the magnitude of the average force exerted by the bat on the ball.
e) What would the average force exerted by the ball on the bat be, and what effect would this have on the swinging bat?
f) Calculate the kinetic energy of the ball after it was struck
3. A 50 ton tank fires a projectile with a mass of 15 kg at a velocity of 1200 m/s at an opposing tank.
a) Calculate both the kinetic energy and the momentum of the projectile
b) The tank designers are now going to alter the main gun, so it now fires a projectile with a mass of 10 kg, and a velocity of 1800 m/s. Calculate the momentum and the kinetic energy of the new projectile. Discuss whether this would change the recoil effects on the tank, and the damage done to the target in comparison to the original projectile. Further compare this to a 30 kg projectile fired at 600 m/s
4. An electric motor has a power rating of 10 kW. It is used to lift an object with a mass of 600 kg for a distance of 140 m. The lift takes 1 minute and 30 seconds
a) Calculate the total electrical energy consumed during the lift
b) Calculate the gravitational potential energy gained by the object
c) Calculate the wasted heat energy during the lift.
d) In this context, what represents the “useful energy”?
e) Calculate the efficiency of the electrical motor
 
5. An 70 kg object, starting from rest, slides down a long inclined plane with an angle to the horizontal of 50o, against a frictional force of 170 N. It slides for 230 m until the slope changes (smoothly) to horizontal.
a) Using trigonometry, calculate the initial height of the object
b) Calculate the acceleration of the object down the slope
c) Calculate its velocity at the bottom
d) Calculate the kinetic energy of the object at the bottom
e) Calculate the gravitational potential energy lost by the object
f) Calculate the heat energy produced by friction during the descent.

[Hermit]

Are you intending to give that assignment to your students in their next period? If so, what have you planned for them in the second half?

[JimC]

Are you intending to give that assignment to your students in their next period? If so, what have you planned for them in the second half?

No, it's additional homework to top up various questions from their textbook. A good student could do it well inside an hour, sure...

[Hermit]

That makes it an open book type assignment. No challenge then.

[JimC]

Fairly basic, I agree. But students need to master these types of problems before they do more complex ones under test conditions. One leads the horse gently to water, in the hopes that it will drink...

And now, clever clogs, present us with your solutions...

[JimC]

Stung by Hermit's allegations that my homework assignment was a bit lacking, I've added this:

6. A toy plastic dart with a mass of 20 grams is fired vertically by a spring-loaded toy gun, reaching a maximum height of 3.8 m above the gun. When the dart was loaded, the spring was compressed by a length of 6.5 cm. We will assume the spring to be an ideal spring, and we will ignore any energy losses due to friction or air resistance.
a) Calculate the gravitational potential energy gained by the dart from firing to maximum height.
b) Based on that, what was its K.E. just after firing?
c) Calculate the initial velocity of the dart
d) What elastic energy was in the spring before firing?
e) What was the maximum force required during loading?
f) Calculate the spring constant

[JimC]

I've just realised that many of my examples involve guns of some sort. Am I in fact a militaristic bastard?



(I always use an example of cannon firing from an English ship in class, blasting yet another Frenchman out of the water. Sorry, Svarty...)

[Xamonas Chegwé]

1a would be 0.17992802878848 m/s - so 0.18 rounded. Note that I added the weight of the bullet to the sandbag/trolley to get that result - but that doesn't affect the rounded figure - I would have made sure that it did!

1b

v2 = u2 +2as

so 0 = 202500 + 2 x a x 0.08

a = -202500 / 0.16 = -1,265,625 m/s2

1c

v = u + at

so 0 = 450 - 1,265,625t

t = 450 / 1,265,625 = 0.000355555557s - which rounds to 0s by your instructions!

1d

F = ma

so F = .02 x 1,265,625 = 25,312.5N

1e

.025 x v = 50.045 x 0.22 (Note that I have assumed that the first bullet is still in the bag - and that the frictionless trolley has been stopped in between firings!)

v = 440.396 m/s - rounds to 440.40.

Can't be arsed to do the rest.

[Xamonas Chegwé]

PS. Send details of any fuck ups to Messrs. Cabernet & Sauvignon.

[JimC]

I haven't worked out the answers myself, yet...

And yes, I probably should be specifying a certain number of significant figures rather than decimal places...

[Hermit]

Stung by Hermit's allegations that my homework assignment was a bit lacking...

Actually, I was totally joking. Besides, a good thing about open book type assignments is that students who have been too lazy to learn will have to learn this shit now if they want to get the work done. Additional encouragement for them to get their arses into gear already might be to mention that these are the sort of questions they'll face in their final tests, which will be closed book tests!

[mistermack]

This very rarely happens, owing to the serious shortage of frictionless trolleys and zero drag darts.

[Xamonas Chegwé]

This very rarely happens, owing to the serious shortage of frictionless trolleys and zero drag darts.

Yes. Jim missed out the obligatory, "State what assumptions you have made to calculate these results." part of the questions! For example, assuming that a bullet that is fired at 450m/s will still be travelling at 450 m/s when it hits, etc. etc. etc....

[JimC]

In Physics classes, we wave our hands a lot, and assume all sorts of factors have negligible effect on our current problem...

[JimC]

Stung by Hermit's allegations that my homework assignment was a bit lacking...

Actually, I was totally joking. Besides, a good thing about open book type assignments is that students who have been too lazy to learn will have to learn this shit now if they want to get the work done. Additional encouragement for them to get their arses into gear already might be to mention that these are the sort of questions they'll face in their final tests, which will be closed book tests!

Certainly closed book, but all relevant formulae are provided on the test (I do that because that's what they are given in their Year 12 Exams)

But, back in my day, we had to memorise all the formulae! I frequently tell my class they don't know how lucky they are!