A car m = 1850 kg is traveling at a constant speed of v = 30 m/s. The car experiences a force of drag (air resistance) of Fd = 300 N.

Write an expression for the power the car must produce Pi to maintain its speed.

Part (b) What is the power in HP?
No Attempt No Attempt Part

(c) The car encounters an incline which makes an angle of θ = 12 degrees with respect to the horizontal. The cruise control kicks in and increases the cars power to maintain its speed. What is the new power (in HP) required to maintain a constant speed?

Part (a)

To find the power the car must produce to maintain its speed, we can use the equation:
Pi = Fd * v

where Pi is the power, Fd is the force of drag, and v is the velocity.

Substituting the given values, we have:
Pi = 300 N * 30 m/s
Pi = 9000 N*m/s

Part (b)

To convert the power from N*m/s to horsepower (HP), we use the conversion factor: 1 HP = 745.7 N*m/s.

Using this conversion factor, we can calculate:
Pi_HP = Pi / 745.7
Pi_HP = 9000 N*m/s / 745.7
Pi_HP ≈ 12.06 HP

Therefore, the power in HP is approximately 12.06 HP.

Part (c)

When the car encounters an incline, the force required to maintain a constant speed increases. In this case, the force on the car can be divided into two components: the force of drag acting against the motion and the force of gravity acting downhill.

To find the new power required to maintain a constant speed, we need to take into account the component of the force of gravity opposing the motion uphill. The force of gravity acting downhill does not require any additional power as it pulls the car in the same direction as the motion.

Assuming there is no friction and neglecting other forces, the force of gravity acting uphill can be calculated using the equation:
Fg = m * g * sin(θ)

where Fg is the force of gravity, m is the mass of the car, g is the acceleration due to gravity (approximately 9.8 m/s^2), and θ is the angle of the incline (12 degrees).

Substituting the given values, we have:
Fg = 1850 kg * 9.8 m/s^2 * sin(12 degrees)

The new total force acting against the motion can be found by adding the force of drag and the force of gravity:
F_total = Fd + Fg

The new power required to maintain a constant speed is given by:
Pi_new = F_total * v

Substituting the calculated values, we have:
Pi_new = (300 N + Fg) * 30 m/s

To convert the power from N*m/s to horsepower (HP), we can use the same conversion factor as before: 1 HP = 745.7 N*m/s.

Therefore, the new power required to maintain a constant speed can be calculated as:
Pi_new_HP = Pi_new / 745.7 HP

I'm sorry, but I'm not going to provide a humorous response for this question.

To find the expression for the power the car must produce, we can use the formula:

Power (P) = Force (F) x Velocity (v)

In this case, the force that opposes the car's motion is the force of drag (Fd), so we have:

Power (Pi) = Force of drag (Fd) x Velocity (v)

Substituting the given values of Fd = 300 N and v = 30 m/s, we get:

Pi = 300 N x 30 m/s
= 9000 N⋅m/s

Now, to find the power in horsepower (HP), we can use the conversion:

1 horsepower (HP) = 735.5 watts (W)

So, to convert the power from watts to horsepower, we divide the power in watts by 735.5:

Power (in HP) = Pi / 735.5

Substituting the value of Pi = 9000 N⋅m/s, we get:

Power (in HP) = 9000 N⋅m/s / 735.5
≈ 12.23 HP

Now, let's consider the case where the car encounters an incline of θ = 12 degrees. The force opposing the car's motion now consists of the drag force (Fd) and the component of the car's weight (mg) that acts parallel to the incline.

The formula to calculate the parallel component of the weight is:

Force (Fpar) = mg sin(θ)

where m is the mass of the car, g is the acceleration due to gravity (approximately 9.8 m/s²), and θ is the angle of the incline.

The total force opposing the car's motion is then:

Total force (FTotal) = Fd + Fpar

To maintain a constant speed, the power required is given by:

Power (P) = FTotal x v

Substituting the given values of Fd = 300 N, v = 30 m/s, m = 1850 kg, and θ = 12 degrees, we can calculate the new power required:

P = (Fd + Fpar) x v

First, calculating the parallel component of the weight:

Fpar = mg sin(θ)
= 1850 kg x 9.8 m/s² x sin(12 degrees)
≈ 355.4 N

Then, calculating the total force:

FTotal = Fd + Fpar
= 300 N + 355.4 N
≈ 655.4 N

Finally, calculating the new power required:

P = FTotal x v
= 655.4 N x 30 m/s
= 19,662 N⋅m/s

To convert this power to horsepower (HP), we divide by 735.5:

Power (in HP) = 19,662 N⋅m/s / 735.5
≈ 26.77 HP

So, the new power required to maintain a constant speed on the incline is approximately 26.77 HP.

To find the expression for the power the car must produce to maintain its speed, we need to calculate the drag force on the car first.

The drag force (Fd) acting on the car is given as 300 N.

Power (P) is defined as the rate at which work is done or energy is transferred, and it can be calculated using the formula:

P = F*v

where F is the force applied, and v is the velocity or speed of the object.

In this case, the force applied is the drag force (Fd). Therefore, the expression for the power the car must produce (Pi) to maintain its speed can be written as:

Pi = Fd*v

Substituting the given values:

Pi = 300 N * 30 m/s
Pi = 9000 N*m/s

Now, let's move on to part (b) to calculate the power in horsepower (HP).

To convert the power (Pi) from N*m/s to horsepower (HP), we need to use the conversion factor:

1 horsepower (HP) = 735.5 N*m/s

Dividing the power (Pi) by the conversion factor, we get:

Pi (in HP) = (9000 N*m/s) / 735.5 N*m/s
Pi (in HP) ≈ 12.24 HP

Therefore, the power required to maintain the car's speed is approximately 12.24 horsepower.

For part (c), we need to find the new power required to maintain a constant speed when the car encounters an incline.

When a car climbs an incline, it experiences an additional force called the gravitational force due to the inclination. The gravitational force can be calculated using the formula:

Fg = m * g * sin(θ)

where m is the mass of the car, g is the acceleration due to gravity (9.8 m/s^2), and θ is the angle of the incline.

The additional force requires more power to maintain a constant speed. Therefore, the total power required can be calculated as:

P_new = Fd*v + Fg*v

Substituting the given values:

P_new = (300 N + (1850 kg * 9.8 m/s^2 * sin(12 degrees))) * 30 m/s

Calculating the value within the parentheses gives:

P_new ≈ (300 N + 3338.59 N) * 30 m/s
P_new ≈ 3668.59 N * 30 m/s
P_new ≈ 110056.7 N*m/s

Now, let's convert the power (P_new) from N*m/s to horsepower (HP), using the same conversion factor as before:

P_new (in HP) = (110056.7 N*m/s) / 735.5 N*m/s
P_new (in HP) ≈ 149.63 HP

Therefore, the new power required to maintain a constant speed when encountering an incline is approximately 149.63 horsepower.

P(i)=F(d) •v =300 •30=9000 W=12.07 hp

P=[P(d)+mgsinα] •v=
=(300+1850•9.8•sin12) •30 =
=18231.3 W=24.45 hp