What is the Work Done on a Car by Gravity on an Inclined Plane?

In summary: The force acting on the car is gravity, and the angle is 15º. The vector equation for work done is F = W * d.
  • #1
dance_sg
113
0

Homework Statement



A car of mass 1500 kg rolls down a hill for a distance of 150 m as shown.
If the road makes an angle of 15º with the horizontal, how much work is done on the car by the force of gravity?


Homework Equations


ep=mgh, w=fd, f=ma


The Attempt at a Solution


i really have no idea. am i trying to find acceleration(gravity)?
 
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  • #2


You need a better expression for work than the one you have put down. The definition of work is not force times distance. Check your textbook.
 
  • #3


Well, there are two ways to do this problem. The first uses the definition of work: What you need to do is find the component of the force acting along the car's plane of motion and then use W = F * d. The second way uses the definition of gravitational potential energy: The GPE at a point is the amount of work necessary to lift an object against a gravitational field to a specific height (the amount of work done against gravity).
 
  • #4


"What you need to do is find the component of the force acting along the car's plane of motion"

---> how do i do that?
 
  • #5


Perhaps you should try the approach using potential energy . . .

Alright, assuming that the hill is essentially an inclined plane, draw your freebody diagram and orient one of your coordinate axes in the direction of the normal force. Now, since force is a vector component, you now need to resolve the gravitational force into its "vertical" and "horizontal" components using trigonometry (the vertical component is opposite the direction of the normal force and the horizontal component is perpendicular to both).
 
  • #6
dance_sg said:
"What you need to do is find the component of the force acting along the car's plane of motion"

---> how do i do that?

i] what is the force?
ii] what is the angle?
iii] what is the vector formula for work done?
 

FAQ: What is the Work Done on a Car by Gravity on an Inclined Plane?

What is acceleration and how is it measured?

Acceleration is the rate of change of an object's velocity over time. It is measured in meters per second squared (m/s^2). Acceleration can be calculated by dividing the change in velocity by the change in time.

What is the difference between acceleration and velocity?

Velocity is the rate of change of an object's position over time, while acceleration is the rate of change of an object's velocity over time. Velocity is a vector quantity, meaning it has both magnitude and direction, while acceleration is a scalar quantity, meaning it only has magnitude.

How can acceleration be positive, negative, or zero?

Acceleration can be positive when the object's velocity is increasing, negative when the object's velocity is decreasing, and zero when the object's velocity is constant. This depends on the direction of the object's motion and whether it is speeding up, slowing down, or maintaining a constant speed.

What factors can affect an object's acceleration?

An object's acceleration can be affected by its mass, the force acting on it, and the direction of the force. The greater the force acting on an object, the greater its acceleration will be. Additionally, the same force will cause a greater acceleration on an object with a smaller mass compared to one with a larger mass.

How is acceleration used in real-world applications?

Acceleration is used in many real-world applications, such as calculating the speed and distance traveled by a vehicle, predicting the path of a projectile, analyzing the motion of objects in sports, and designing roller coasters and other amusement park rides. It is also essential in understanding the laws of motion and the behavior of objects in the universe.

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