A 700 kg car is pulled up a hill at a 10 degree hill with a 1500N force acting parallel with the hill, friction can be neglected.
What is the work done by the pulling force?
What is the work done by gravity?
If the initial speed of the car is 4 m/s, what is the speed after it has been pulled 40m?
To find the work done by a force, we can use the equation:
Work (W) = Force (F) * Distance (d) * cos(theta)
Where:
- Force (F) is the magnitude of the force exerted
- Distance (d) is the distance the force is applied over
- Theta (θ) is the angle between the force and the direction of motion
1. Work done by the pulling force:
In this case, the force acting parallel to the hill is 1500N and the distance traveled is not given. However, we can calculate the distance traveled using the angle of the hill and the inclined plane equation:
Distance (d) = hypotenuse * sin(theta)
The hypotenuse can be calculated using the Pythagorean theorem:
hypotenuse = mass (m) * acceleration due to gravity (g) / sin(theta)
Given:
- Mass (m) = 700 kg
- Angle (θ) = 10 degrees
- Acceleration due to gravity (g) = 9.8 m/s^2
First, calculate the hypotenuse:
hypotenuse = 700 kg * 9.8 m/s^2 / sin(10 degrees)
Now, calculate the distance traveled:
Distance (d) = hypotenuse * sin(10 degrees)
Once we have the distance, we can calculate the work done:
Work (W) = 1500N * Distance (d) * cos(0 degrees)
2. Work done by gravity:
Since the car is being pulled up the hill, gravity is acting in the opposite direction. The work done by gravity is given by:
Work (W) = Force (mg) * Distance (d) * cos(theta)
Where:
- Force (F) = mass (m) * acceleration due to gravity (g)
- Distance (d) is the same distance calculated above
- Theta (θ) = 180 degrees, as gravity is acting in the opposite direction
Work (W) = (mass (m) * acceleration due to gravity (g)) * Distance (d) * cos(180 degrees)
3. Speed after being pulled 40m:
To find the final speed of the car after being pulled 40m, we can use the work-energy theorem. The work done on the car is equal to the change in its kinetic energy:
Work (W) = Change in Kinetic Energy (ΔKE)
Given:
- Initial speed (Vi) = 4 m/s
- The car starts from rest, so its initial kinetic energy is 0.
To find the final speed (Vf), rearrange the equation as:
ΔKE = 0.5 * mass (m) * (Vf^2 - Vi^2)
Substituting the work done by the pulling force into the equation:
0.5 * mass (m) * (Vf^2 - Vi^2) = Work (W) by the pulling force
Now, rearrange and solve for Vf:
Vf^2 = (2 * Work (W) by the pulling force) / mass (m) + Vi^2
Vf = √[(2 * Work (W) by the pulling force) / mass (m) + Vi^2]
Now you can plug in the values to calculate Vf.