Some motion + electricity questions

[TrueTears]

1. A boy of mass 64kg bounces on a mini trampoline supported by 20 identical springs. While bouncing the difference between his highest point and his lowest point is 0.8m. At the lowest point each spring has stretched 4.2cm. Calculate the spring constant of each spring.

2. Jim works on the 18th floor of a city building. For some time he has noticed that each night as he starts to go down in the lift he feels lighter than his normal weight. To investigate this he borrows an accelerometer and some bathroom scales. While standing on the scales in the lift he measures his downward acceleration as 4ms^-2 and notes the reading on the scales is 48kg. What is Jim's mass?

I had a go... but was wrong lol.

Fg = 48 x 10 = 480N

F=ma. 480 = m x 4    m = 120kg.

3. A cannon (mass 1800kg) fires a cannonball (mass 7.1kg) horizontally from the side of a ship. The cannonball leaves the muzzle with a speed of 320ms^-1 4.8m above the waterline. (assume air resistance is negligible). What is the magnitude of the acceleration of the cannonball just before hitting the water?

Had a go here but was also wrong.

The range(distance traveled by cannonball) = u

so u=320 h = 4.8 g = 10 so the range = 313.53 (this part is correct)

also we know t = so t= = 0.98s

Overall we have u = 320 x = 313.53 and t = 0.98. By using the equation x=ut+0.5at^2 313.53 = 320 x 0.98 + 0.5 x a x 0.98^2. a = -0.15ms^-2

Answer is not -0.15ms^-2 can anyone show how to get the correct answer?

4. The batteries, resistors and lamps in the four circuits below are identical. Assume the batteries have zero internal resistance.

a) In which circuit will the battery last the longest?
b) In which circuit will the lamp glow the brightest?



First circuit is circuit A, next is B, next is C and the last one on the far right is D.
(Sorry for my bad paint job lol)

I had A for part a) and B for part b) however the answer says B is for part a) and A is for part b). Can someone explain why?

Any help is much appreciated

[Flaming_Arrow]

is the answer to the first question 72kg?

[TrueTears]

u mean spring constant or Jim's mass? the answer to Jim's mass is 80kg. The spring constant, i don't know the exact answer but its big number, in the 20000's or sometihng.

[Mao]

the first question might be a bit difficult, from the looks of it I don't see an 'easy' way of doing it. The force is variable throughout, and we don't know the average position of the spring....

[bigtick]

20 x 1/2 k 0.042^2 = 64 x 9.8 x 0.8, k = 2.8 x 10^4 N/m

[TrueTears]

20 x 1/2 k 0.042^2 = 64 x 9.8 x 0.8, k = 2.8 x 10^4 N/m

haha big tick thanks! As soon as u posted i was just about to post the exact same answer as u Our answers match

hehe only 3 left to go...

[bigtick]

mg -48g = 4m, m = 81 kg

[bigtick]

q3   9.8 m/s2 down

[bigtick]

q4a second
q4b first

[TrueTears]

yeah i get q1 and q2. Q 3 and 4 some more explanation and working out would help

[mark_alec]

Q3

It asks for the acceleration of the cannon ball as it hits the water. Since air resistance is negligible, the only force is due to gravity, so its acceleration must be g (9.8 or 10, whatever value is assumed.)

Q4

a) The battery will last longest when the resistance is maximised, since that reduces the current. Resistance is maximised in a serial circuit, which is circuit B.

b) The bulb will glow brightest when the maximum voltage and current passes through it. This will be in a parallel circuit, since the voltage drop across the bulb will be the voltage of the battery, and since the resistance of the circuit is minimised, the current is maximised. This is far from obvious, and I don't believe it can be determined unless the resistance of the circuit elements is known (otherwise D could be the answer.)

[TrueTears]

Q3

It asks for the acceleration of the cannon ball as it hits the water. Since air resistance is negligible, the only force is due to gravity, so its acceleration must be g (9.8 or 10, whatever value is assumed.)

Q4

a) The battery will last longest when the resistance is maximised, since that reduces the current. Resistance is maximised in a serial circuit, which is circuit B.

b) The bulb will glow brightest when the maximum voltage and current passes through it. This will be in a parallel circuit, since the voltage drop across the bulb will be the voltage of the battery, and since the resistance of the circuit is minimised, the current is maximised. This is far from obvious, and I don't believe it can be determined unless the resistance of the circuit elements is known (otherwise D could be the answer.)

Yeah thanks for your help, that really makes much more sense Just for part a) Q4. The lasting of a battery depends on the amount of current in a circuit and not the amount of voltage drop across the circuit?

[mark_alec]

Just for part a) Q4. The lasting of a battery depends on the amount of current in a circuit and not the amount of voltage drop across the circuit?

The voltage drop across the circuit will always be the battery's voltage. The current in the circuit determines the longevity of the battery.

[TrueTears]

ahhh thanks very much mark_alec