8)
9) 958 kg
10)
11)
Explanation:
8)
The total force exerted on an object is equal to the rate of change of momentum of the object; mathematically:
where
F is the force
is the change in momentum
is the time elapsed
The change in momentum can be written as
where
m is the mass
v is the final velocity
u is the initial velocity
For the plane in this problem:
u = 0 (it starts from rest)
v = 68.2 m/s
m = 29545 kg
Therefore, the force exerted on the F-14 is:
9)
As in the previous problem, the force exerted on the car can be written as
where in this problem, we have:
u = 0 is the initial velocity of the car
v = 27 m/s is the final velocity of the car
is the time elapsed during the acceleration of the car
F = 4106 N is the force exerted on the car
Re-arranging the equation for m, we can find the mass of the car:
So, the mass of the car is 958 kg.
10)
The relationship between force exerted on a body and acceleration of the body is given by Newton's second law of motion:
where
F is the force
m is the mass
a is the acceleration
At the beginning, with a certain force , the acceleration of the boy is
So we have
(1)
Later, after the boy has taken the pill, the force is , while the acceleration is now
So we have
(2)
To do a comparison between the two forces, we divide (2) by (1), and we get:
So,
Which means that the force in the 2nd case is 5.6 times larger than the force in the 1st case.
We are also told that the boy's earlier force is
Therefore, the force in the 2nd case is:
12)
For this problem we can use again Newton's second law of motion:
where
F is the force
m is the mass
a is the acceleration
At the beginning, with one engine only running, the acceleration of the plane is
And we can write it as
where F is the force exerted by 1 engine only.
Later, when all 4 engines are running, the new force will be 4 times:
F' = 4F
Therefore, the new acceleration will be:
So, 4 times the previous acceleration; and therefore: