A firetruck drive 3 miles to the east and 1.2 miles to the west what is the displacement of the firetruck
1 answer:
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Answer:
Sam is providing the biggest power i.e. 50 W
Explanation:
Sam is moving house and is carrying a 300N box of books up a flight of steps 5m high, it takes her 30 seconds.
Sam's power :
Gary follows her carrying a bag of clothes doing 1000 J of work; it only takes him 25 seconds.
Gary's power :
So, it is clear that Sam is providing the biggest power.
Answer:
Neglecting any frictional losses, the average power delivered by the car's engine is 10565 W
Explanation:
The energy conservation law indicates that the energy must be the same at the bottom of the hill and at the top of the hill.
The energy at the bottom is only the Kinect energy (K_1) of the car in motion, but in the top, the energy is the sum of its Kinect energy (K_2), potential energy (P) and the work (W) done by the engine.
then, the work done by the engine is:
The formulas for the Kinetic and potential energy are:
where, m is the mass of the car, V the velocity, g the gravity and h is the elevation of the hill.
Using the formulas:
Replacing the values:
The negative of this value indicates the direction of the work done, but for the problem, you only care about the magnitude, so the power is W=1690400 J. Now, the power is equal to work/time so you need to find the time the car took to get to the top of the hill.
The average speed of the car is (27+14)/2=20m/s, and t=d/v so the time is:
the power delivered by the car's engine was:
Answer:
a) The car will reach a height of 45.9 m.
b) The amount of thermal energy generated is 173382 J.
c) The magnitude of the force of friction is 417.8 N.
Explanation:
Hi there!
a) In this problem, we have to use the conservation of energy. The energy conservation theorem states that the energy of a system remains constant. Energy can´t be created nor destroyed, only transformed. In the case of the car, the initial kinetic energy is transformed into potential energy as the car´s height increases while coasting up the hill.
Then, all the initial kinetic energy (KE) will be transformed into potential energy (PE) (only if there is no friction).
The equation of KE is the following:
KE = 1/2 · m · v²
Where:
m = mass of the car.
v = speed of the car.
The equation of PE is the following:
PE = m · g · h
Where:
m = mass of the car.
g = acceleration due to gravity.
h = height at which the car is located.
Since work done by friction is negligible, we can assume that all the initial kinetic energy will be transformed into potential energy. Then:
KE at the bottom of the hill = PE at the top of the hill
1/2 · m · v² = m · g · h
Solving for h:
1/2 · v² / g = h
Let´s convert the speed unit into m/s:
108 km/h · 1000 m/ 1 km · 1 h / 3600 s = 30 m/s
Now, let´s calculate h:
h = 1/2 · (30 m/s)² / 9.8 m/s²
h = 45.9 m
The car will reach a height of 45.9 m.
b) In this case, all the kinetic energy is not transformed into potential energy because some energy is transformed into thermal energy due to friction. The thermal energy generated is equal to the work done by friction. Then:
KE at the bottom of the hill = PE + work done by friction
KE = PE + Wfr (where Wfr is the work done by friction).
1/2 · m · v² = m · g · h + Wfr
1/2 · m · v² - m · g · h = Wfr
1/2 · 710 kg · (30 m/s)² - 710 kg · 9.8 m/s² · 21 m = Wfr
Wfr = 173382 J
The amount of thermal energy generated is 173382 J.
c) The work done by friction is calculated as follows:
Wfr = Ffr · Δx
Where:
Ffr = friction force.
Δx = traveled distance
Please, see the attached figure to notice that the traveled distance can be calculated by trigonometry using this trigonometric rule of right triangles:
sin angle = opposite side / hypotenuse
In our case:
sin 2.9° = h / Δx
Δx = h / sin 2.9°
Δx = 21 m / sin 2.9° = 415 m
Then, solving for the friction force using the equation of the work done by friction:
Wfr = Ffr · Δx
Wfr / Δx = Ffr
173382 J / 415 m = Ffr
Ffr = 417.8 N
The magnitude of the force of friction is 417.8 N
