How Fast Will the Car Hit the Garage Door at the Bottom of the Incline?

In summary, the problem involves a 2000 kg car at the top of a 20 degree inclined 20 meter long driveway with a parking brake that slips. The objective is to determine the speed at which the car will hit the garage door at the bottom of the incline, assuming no retarding forces. The suggested approach is to use energy and trigonometry to break down the force of gravity into components, use Newton's second law to find acceleration, and then use the given distance to calculate the final velocity. However, it is important for the OP to attempt solving the problem on their own before providing further help.
  • #1
Renee8
1
0
1. A 2000 kg car in neutral at the top of a 20 degree inclined 20 meter long driveway slips its parking break and rolls downward. at what speed will it hit the garage door at the bottom of the incline? Neglect all retarding forces



Homework Equations





The Attempt at a Solution

 
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  • #2


Work shown?

I would use energy by the way, since you're dealing with speed/velocity and a change in height.
 
  • #3


Use trig to break the car's force of gravity down into components. Find acceleration using F=ma and use the given distance to find final velocity.
 
  • #4


Important! Read this before posting!

Moderator's note: please do not provide further help until the OP shows some attempt towards solving the problem.
 
  • #5


To solve this problem, we can use the equation for the potential energy of an object on an incline:

PE = mgh

Where m is the mass of the car, g is the acceleration due to gravity (9.8 m/s^2), and h is the height of the incline (20 meters).

We can then use the equation for the kinetic energy of an object:

KE = 1/2 mv^2

Where m is the mass of the car and v is the velocity at which it will hit the garage door.

Since we are neglecting all retarding forces, we can assume that the total energy of the car (PE + KE) remains constant throughout its motion.

Therefore, we can set the initial potential energy at the top of the incline equal to the final kinetic energy at the bottom of the incline:

mgh = 1/2 mv^2

Solving for v, we get:

v = √(2gh)

Plugging in the given values, we get:

v = √(2*2000*9.8*20*cos(20))

v = 44.3 m/s

Therefore, the car will hit the garage door at the bottom of the incline at a speed of 44.3 m/s.
 

Related to How Fast Will the Car Hit the Garage Door at the Bottom of the Incline?

1. What is the force that causes a car to roll on an incline?

The force that causes a car to roll on an incline is gravity. Gravity pulls the car towards the center of the Earth, and on an incline, this force acts perpendicular to the surface of the incline, causing the car to roll downwards.

2. Does the weight of the car affect its rolling motion on an incline?

Yes, the weight of the car does affect its rolling motion on an incline. A heavier car will have a greater force of gravity pulling it down the incline, resulting in a faster rolling motion compared to a lighter car.

3. How does the angle of the incline affect the rolling motion of a car?

The angle of the incline affects the rolling motion of a car by changing the magnitude and direction of the force of gravity. A steeper incline will have a greater force of gravity pulling the car down, resulting in a faster rolling motion, while a gentler incline will have a smaller force of gravity and a slower rolling motion.

4. What other factors can affect the rolling motion of a car on an incline?

Besides the weight of the car and the angle of the incline, other factors that can affect the rolling motion of a car on an incline include the coefficient of friction between the car's wheels and the incline surface, the shape and size of the car's wheels, and any external forces or obstacles that may impact the car's motion.

5. How does the rolling motion of a car on an incline change if the incline is not flat?

If the incline is not flat, the rolling motion of the car will be affected by the change in angle along the incline. The car will experience a change in speed and direction as it moves up or down the incline, depending on the shape and steepness of the incline. The car may also experience changes in acceleration and friction forces as it encounters different parts of the incline.

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