Solving Mechanics Problems: Truck Movement on Hills & Ramps

In summary, the conversation discusses two separate questions about a truck's movement on different surfaces. The first question involves a truck rolling down a 7.8 degree hill and the second question involves the truck going up a 15-degree ramp with a kinetic coefficient of friction of 0.8. The conversation also addresses some uncertainties and corrections made by the speaker.
  • #1
anathema
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0
These are two separate questions, each of them together, in a way.

1. A truck rolls down a 7.8 degree hill with a constant speed of 30.0 m/s. At the bottom of the hill it continues on a horizontal surface. How far will the truck go before it stops?

For this I made a diagram with a right-angle triangle where the hypotenuse of the triangle was gravity, and the shortest side was the hill the truck was moving on. I discovered its deceleration due to friction by multiplying gravity by the sin of 7.8, mass being irrelevant. From this I used the formula vf^2 = vi^2 + 2 * ad,
giving me 0 = 30^2 + 2*-1.33136*d. The d I got was 338 m.

2. The truck instead goes up a 15-degree ramp with a kinetic coefficient of friction of 0.8. How far would it go? What is its deceleration?

I made the slope hill the X axis in a diagram, and determined that two forces were responsible for deceleration, friction and the x component of gravity, each pointing opposite to the movement of the truck. 9.81*sin(15) + 9.81*0.8 = deceleration, which, when used with the same formula as above gave me 43.3 as the distance.

I have an awkward feeling that I didn't do these problems right, and I know my explanations sound confusing when the diagrams aren't there. Any help?
 
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  • #2
Hi anathema,
1. looks OK IMO.
2. looks wrong. I think you should take into account that only the normal component of gravity contributes to friction.
 
  • #3
Thanks! Yeah that's what I discovered too, that I had to take the normal component of gravity to use for friction. In either case I changed them in time and both questions were marked correctly.
 

1. How do I calculate the acceleration of a truck on a hill?

The acceleration of a truck on a hill can be calculated using the formula a = F/m, where a is acceleration, F is the net force acting on the truck, and m is the mass of the truck. The net force can be calculated by subtracting the force of gravity acting on the truck from the force applied by the truck's engine. This will give you the truck's acceleration in meters per second squared (m/s2).

2. What factors affect the movement of a truck on a ramp?

The movement of a truck on a ramp is affected by several factors, including the angle of the ramp, the weight of the truck, the force applied by the truck's engine, and the presence of any friction on the ramp. These factors can impact the acceleration, speed, and overall movement of the truck on the ramp.

3. How do I account for friction when calculating the movement of a truck on a hill?

To account for friction when calculating the movement of a truck on a hill, you can use the formula Ff = μN, where Ff is the force of friction, μ is the coefficient of friction, and N is the normal force. The normal force is equal to the weight of the truck on the hill, and the coefficient of friction can be found in a table based on the type of surface the truck is moving on.

4. What is the difference between a hill and a ramp in terms of mechanics?

A hill and a ramp are essentially the same in terms of mechanics, as they both involve an inclined surface that can affect the movement of an object. However, a hill is typically a natural incline, while a ramp is a man-made structure with a more uniform and controlled incline. This can impact the calculations and considerations when solving mechanics problems involving truck movement.

5. How can I use vector components to solve mechanics problems involving truck movement on hills and ramps?

Vector components can be used to break down the forces acting on a truck on a hill or ramp into their horizontal and vertical components. This can make it easier to calculate the net force and acceleration of the truck in a specific direction. It can also help to visualize the forces acting on the truck and understand how they contribute to its movement on the hill or ramp.

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