Four
Sometimes I think the creators of problems out to drawn and quartered. 60 g does not mean 60 grams. It means 60 * the acceleration due to gravity.
So the question really reads. The acceleration delivered by the air bag is 60 times that of a normal gravitational. This acceleration is delivered to the person where his mass is putting up a whole lot of resistance because he and his 75 kg are moving forward with the impact of the car. The 36 msec. has nothing to do with the problem.
The Force of the Air Bag is mass * a
F_airbag = mass * acceleration = 75 kg * 60 * 9.81 mass * acceleration = 44145 newtons
The answer is 4.41 * 10^4
Answer C
Five
This problem is governed by one formula that you sort of have to get out of your hat -- a piece of magic if you will.
Fg - Bf = m * a
Fg = the Force of gravity
Bf = the braking force
The mass of the rocket is derived from its weight
The acceleration is derived from one of your big 4 equations.
m of the rocket = 75600 / 9.81 = 7706 kg
The acceleration =
vi = 1 km/s = 1000 m/s
vf = 0
t = 2 minute * 60 sec/ min = 120 seconds
a = (vf - vi)/t = (0 - 1000 m/s) / 120 sec
a = - 8.333 m/s^2 The minus sign makes perfect sense. Remember the rocket is slowing down
The net downward force = mass * acceleration = - 7706 kg * - 8.333 m/s^2
The net force = - 64217 N
So going back to the problem's equation we have
Gravitational force - Braking Force = Net Force
Gravitational Force = 75600
Net Force = - 64217
Bracking force = ?
75600 - Bracking force = - 64217 Subtract 75600 from both sides
- Bracking force = - 64217 - 75600
- Braking force = - 139817
Braking force = 139817 N = 1.398 * 10^5 N
Braking Force = 1.4 * 10^5
Answer: Last One.
Six
The first thing you should do is derive a general formula for this problem.
The force pulling both masses down is M*g where g is the acceleration due to gravity.
The formula for this problem is
Mg = (m + M) * a
Now you need to solve for a
a = [M/(M + m) ] * g
Look what is happening. is a smaller or larger than g? This is a question you should really pay attention to. If it was larger, everyone would have this system in their basement because you'd get more energy output than you put in. Something for nothing is always appealing.
So what's the answer? (I get to ask it. No one posing the question ever should).
A
A is incorrect. M never goes away. The acceleration may get very tiny, but there always is some acceleration.
B must be true. It is just what I finished saying about A
C Who said anything about velocity? It's a red herring. If the velocity became 0 the acceleration would have to turn minus. This answer sounds good, but sounds good doesn't make it right. C is wrong.
D The acceleration does not remain constant no matter what. The answer to A still applies. So D is wrong.
