Physics question pls help

Question

1) A temporary structure loses 60 kWh of energy each day. If modifications to the structure are made so that the energy flux decreases by a factor of 2, what will the new energy loss per day be?

a) 60 kWh

b) 120 kWh

c) 30 kWh

d) 15 kWh

2) a 1500 kg cars speed changes from 30 m/s to 15 m/s after the brakes are applied. Calculate the work done onto the car from the brakes.

a) -506,250 J

b) 506,250 J

c) 168,750 J

d) -168,750 J

Answer 1

1)

Let

P = 60 kWh/day be the power loss,

S be the surface area through which the energy flows.

There are two definitions of the term "energy flux".

1) One defines it as being the same as P.

If that is your definition then the problem statement tells you the new energy loss per day.

2) The other defines it as the power loss per unit surface.

This definition commonly refers to it as "specific energy flux" to

differentiate it from the first definition.

If this is your notion of "energy flux", then the question cannot be answered

without knowing what happens to the total area S.

If we assume that S remains the same, then energy loss per day decrease by

the same factor as energy flux.

2)

Let

m = 1500 kg be the mass of the car.

v₀ = 30 m/s be the initial speed of the car,

v₁ = 15 m/s be the final speed of the car.

I will assume that

1) all friction and resistance, other than in the breaks, is 0.

2) there is no force acting on the car other than forces perpendicular to the direction of travel.

Without assumption 1) the loss of speed might be due to wind, or other factors.

Under assumption 1) all the work of the breaks gets converted to loss of

mechanical energy.

That is, none of the loss of speed is due to friction of the road, or air resistance,

or other factors normally slowing a car.

Without assumption 2) the reduction in speed might be due the car coasting uphill.

Also without assumption 2) the breaks might be working against somebody pulling the car.

Under assumption 2) none of the change of mechanical energy is due to change

in potential energy; it is all due to change in kinetic energy.

Any force acting on the car is perpendicular to the direction of motion, which makes its work

amount to 0.

Under those two assumptions the work performed by the breaks

equals the change in kinetic energy.

That is,

mv₁²/2 - mv₀²/2 = m/2(v₁²- v₀²) = 1500/2 × (15² - 30²) = -506250 J

The moral of the story is the cutting speed in half reduces kinetic energy by a factor of 4, not factor of 2.