A car is moving by gravity force

In summary: I have to use the formula v=wr, where w is angular velocity and r is the radius of the wheel. Therefore, the correct expression for velocity in function of time is: v = (5.6M + (8m + md^2)/4 + (2m1 + md2^2)/2) * (1/r) * (dv/dt). In summary, we are given a car on an inclined plane with rear wheels weighing 500 lb each and having a diameter of 8 feet, front wheels weighing 800 lb and having a radius of 2 feet, and a vehicle body weighing 9000 lb. We need to find an expression for the velocity of the car in function of time, taking
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Homework Statement



In t=0 a car is free from it's chain and can fall freely through a inclined plane (10 degrees)
rear wheels weight 500 lb each one and have an diameter of eight feet. Front wheel weights 800 lb and have a radius of 2 feet. The body of vehicle weights 9000 lb. Assume that wheels can drift. Obtain a expression for velocity in function of time.

Homework Equations



Summation of forces = ma
We have inerce forces and gravity force. gravity force exerted on vehicle equals to Mgsin10


The Attempt at a Solution


inertia force formula is Ia, then I should add the forces.


M*g*sin(10)+Ialpha=Ma
5.591471 ft/s^2+Ialpha/M=a
alpha is angular acceleration.
A condition for simultaneous rotation and translation movement is v=wr
w=v/r
dw/dt= 1/r(dv/dt)
5.591471M+I(1/r) dv/dt=Mdv/dt
and Inertia applies for each rotating element
5.6M+(I1/r1+I2/r2) dv/dt=Mdv/dt
5.6M+(I1/4+I2/2)dv/dt=Mdv/dt

Moment of inertia for a wheel=mr^2/2.
M is the total mass in the system.
5.6M+(mr^2/2+md^2)/4+ (m1r1^2/2+md2^2)/2))dv/dt=Mdv/dt
5.6M+( (8m+md^2)/4+(2m1+md2^2)/2)dv/dt=Mdv/dt
5.6M+( (8000+1000d^2)/4+(1600+800d2^2)/2)dv/dt=Mdv/dt

D are distances from the axis, they are unknown.
I only should put the expression from dv/dt and integrate for get a expression for v in function of t.

I don't know if my solution is right/
In which step I am wrong?
 
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  • #2
Well, after a few hours I have noticed my mistake.
 

Related to A car is moving by gravity force

1. How does gravity affect a moving car?

Gravity is a force that pulls objects towards each other. In the case of a car, gravity pulls it towards the center of the earth. When a car is moving, gravity affects its speed and acceleration by pulling it downward.

2. Can gravity cause a car to accelerate?

Yes, gravity can cause a car to accelerate. As the car moves downhill, gravity acts as an external force and pulls the car in the same direction, increasing its speed and causing it to accelerate.

3. Why does a car move slower when going uphill?

When a car moves uphill, gravity works against it by pulling it down. This creates a resistance force that slows down the car's speed. In order to maintain its speed, the car's engine must work harder to overcome the force of gravity.

4. How does gravity affect the fuel efficiency of a moving car?

Gravity has a direct impact on a car's fuel efficiency. When a car is moving downhill, gravity helps to pull it along, reducing the amount of energy needed from the engine. However, when going uphill, gravity creates resistance, causing the engine to work harder and use more fuel.

5. Can a car move without gravity?

No, a car cannot move without gravity. Gravity is an essential force for motion, as it provides the necessary downward force for the wheels to grip the road and for the engine to move the car forward. Without gravity, a car would simply float off the ground and be unable to move at all.

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