A car of mass 800kg is climbing an incline at 10 degrees to the horizontal. Determine the increase in potential energy of the car mass s it moves a distance of 50m up the incline
324279.36
The increase in potential energy of the car is approximately 324279.36 Joules.
Well, let's do some calculations and take a humorous approach to it!
To determine the increase in potential energy of the car, we need to calculate the work done. And since work is equal to force times distance, we'll need to calculate the force, keeping in mind that the car is climbing an incline.
Now, to make things more interesting, let's imagine the car as a real-life superhero called "Superweight." Superweight is determined to conquer the incline, like it's some sort of evil villain.
First, we need to find the force acting against Superweight as it climbs the incline. Using a little bit of trigonometry, with the angle given, we can determine that the component of the weight force acting in the direction of the incline is:
Force = mass * acceleration due to gravity * sin(angle)
= 800 kg * 9.8 m/s^2 * sin(10 degrees)
Now let's imagine that Superweight is singing a motivational song while climbing the hill, just to make the math more entertaining. We'll call it "I Will Climb (And Win!)."
So, the force Superweight is fighting against is approximately 1,358 N (Newton). Keep climbing, Superweight!
Next, we need to calculate the work done by multiplying the force by the distance:
Work = force * distance
= 1,358 N * 50 m
Now, let's say that Superweight is unleashing some powerful moves while climbing, like a superhero does. With a little bit of math, we find that the work done is approximately 67,900 Joules.
Finally, the increase in potential energy is equal to the work done against gravity. So, the increase in potential energy of Superweight as it moves a distance of 50 m up the incline is approximately 67,900 Joules.
Congratulations, Superweight! You've conquered the incline and gained some serious potential energy along the way. Keep soaring, you magnificent superhero car!
To determine the increase in potential energy of the car as it moves up the incline, we need to calculate the change in height (Δh) that the car has gained.
We can use the formula: Δh = d * sin(θ)
Where:
- Δh is the change in height
- d is the distance traveled along the incline
- θ is the angle of the incline
Given:
- d = 50m (distance moved)
- θ = 10 degrees (angle of the incline)
Let's calculate the change in height:
Δh = 50m * sin(10°)
Δh ≈ 8.68m (rounded to two decimal places)
The increase in potential energy (ΔPE) of the car is given by the formula: ΔPE = m * g * Δh
Where:
- ΔPE is the increase in potential energy
- m is the mass of the car
- g is the acceleration due to gravity (9.8m/s^2)
Given:
- m = 800kg (mass of the car)
- g = 9.8m/s^2
Let's calculate the increase in potential energy:
ΔPE = (800kg) * (9.8m/s^2) * (8.68m)
ΔPE ≈ 67,955.04 Joules (rounded to two decimal places)
Therefore, the increase in potential energy of the car as it moves a distance of 50m up the incline is approximately 67,955.04 Joules.
h = distance up = 50 sin 10
m g h = 800 * 9.81 * 50 sin 10 Joules