A motor vehicle weighs 7000N traveling along a level road at a constant speed of 20m/s . When it comes to a hill , which rises vertically 100m and 11•0km long. The driver increases the power output of his engine to keep the speed constant at 20m/s. Calculate
(1) How long does it take for the car to climb the hill .
(2) how much work does the car do against gravity.
(3) what power is needed to do the work against gravity
(1) First, let's convert the length of the hill from 11.0 km to meters: 11.0 km * 1000 = 11000 meters.
Since the car is traveling at a constant speed of 20 m/s, we can calculate the time it takes to climb the hill by dividing the distance by the speed:
time = distance / speed
time = 11000 m / 20 m/s
time = 550 seconds
So it takes 550 seconds for the car to climb the hill.
(2) To determine the work done against gravity, we need to find the force component acting vertically along the hill. The vertical height of the hill is given as 100 meters.
We can use the Pythagorean theorem to find the angle between the hill and the horizontal road:
sin(angle) = opposite / hypotenuse
sin(angle) = 100 m / 11000 m
angle = arcsin(100/11000) = 0.516 radians
Now we can calculate the vertical component of the gravitational force (Fy) acting on the vehicle:
Fy = Weight * sin(angle)
Fy = 7000 N * sin(0.516) = 3436.02 N
Next, we can calculate the work done against gravity as the product of the force acting vertically and the vertical distance climbed:
Work = Fy * vertical distance
Work = 3436.02 N * 100 m
Work = 343602 Joules
So the work done against gravity is 343,602 Joules.
(3) To find the power needed to do the work against gravity, we divide the work by the time it takes to climb the hill:
Power = Work / time
Power = 343602 J / 550 s
Power = 624.73 Watts
So the power needed to do the work against gravity is 624.73 Watts.