Answer: 3,383.5 kg
Explanation:
from the question we were given the following
tension (T) = 4.5 x 10^4 N
maximum acceleration (a) = 3.5 m/s^2
acceleration due to gravity (g) = 9.8 m/s^2 ( it's a constant value )
mass of the car and its contents (m) = ?
we can get the mass of the car and it's contents from the formula for tension which is T = ma + mg
T = m (a + g)
therefore m = T / (a+g)
m = (4.5 x 10^4 / ( 3.5 + 9.8 )
m = 3,383.5 kg
Answer:
x = 4.32 [m]
Explanation:
We must divide this problem into three parts, in the first part we must use Newton's second law which tells us that the force is equal to the product of mass by acceleration.
∑F = m*a
where:
F = force = 700 [N]
m = mass = 2030 [kg]
a = acceleration [m/s²]
Now replacing:
![F=m*a\\700=2030*a\\a = 0.344[m/s^{2}]](https://tex.z-dn.net/?f=F%3Dm%2Aa%5C%5C700%3D2030%2Aa%5C%5Ca%20%3D%200.344%5Bm%2Fs%5E%7B2%7D%5D)
Then we can determine the final speed using the principle of conservation of momentum and amount of movement.

where:
m₁ = mass of the car = 2030 [kg]
v₁ = velocity at the initial moment = 0 (the car starts from rest)
Imp₁₋₂ = The impulse or momentum (force by the time)
v₂ = final velocity after the impulse [m/s]
![(2030*0) + (700*5)=(2030*v_{2})\\3500 = 2030*v_{2}\\v_{2}=1.72[m/s]](https://tex.z-dn.net/?f=%282030%2A0%29%20%2B%20%28700%2A5%29%3D%282030%2Av_%7B2%7D%29%5C%5C3500%20%3D%202030%2Av_%7B2%7D%5C%5Cv_%7B2%7D%3D1.72%5Bm%2Fs%5D)
Now using the following equation of kinematics, we can determine the distance traveled.

where:
v₂ = final velocity = 1.72 [m/s]
v₁ = initial velocity = 0
a = acceleration = 0.344 [m/s²]
x = distance [m]
![1.72^{2}=0^{2} +(2*0.344*x) \\2.97 = 0.688*x\\x = 4.32 [m]](https://tex.z-dn.net/?f=1.72%5E%7B2%7D%3D0%5E%7B2%7D%20%2B%282%2A0.344%2Ax%29%20%5C%5C2.97%20%3D%200.688%2Ax%5C%5Cx%20%3D%204.32%20%5Bm%5D)
Answer:
(a) The magnitude of the applied force is (0.0001524k) Newton
(b) Corresponding stress in the steel core = (0.0001524k/area) Newton per meter square
Explanation:
(a) From Hookes law of elasticity,
Force applied = force constant (k) × compression
compression = 0.006 in = 0.006 × 0.0254 = 0.0001524 meter
Force applied = k × 0.0001524 = (0.0001524k) Newton
(b) Stress = Force applied (Newton)/area of steel core (meter square) = (0.0001524k/area) Newton per meter square
Answer:

Explanation:
Kinetic energy is given by the following equation:
, where
is mass in
and
is velocity in
.
Since the cell phone's mass is given in grams, we need to convert this into kilograms:
.
Therefore, the kinetic energy of the cell phone is:
.
(a) The efficiency of an engine is defined as the ratio between the work done by the engine and the heat it takes in:

The engine in this problem does a work of

and it takes in

of heat, therefore its efficiency is

(b) The heat taken by the machine is 4000 J; of this amount of heat, only 1100 J are converted into useful work. This means that the rest of the heat is wasted. Therefore, the wasted heat is the difference between the heat in input and the work done by the engine: