# Finding distance traveled up a ramp given m, angle, and velocity

• emilea
In summary: So, the acceleration of the block would be down the incline, not up. The equation you should use is t=x/(Vocostheta)), which would give x=Vo(t) + 1/2a(t^2).
emilea

## Homework Statement

A block with mass m=18.4 kg slides down a ramp of slope angled 43.5 deg with a constant velocity. It is then projected up the plane with a Vo=1.55 m/s. How far does it go before stipping?

## Homework Equations

Fnet=ma
Fg + Ff=Fnet
Ff=uk(Fn)
Fn=mgcos(theta)
a=(uk)cos(theta) + gsin(theta)

## The Attempt at a Solution

I drew a free body diagram to solve for the coefficient of friction down the ramp, which was uk=0.948. I then used that to find the acceleration down the ramp using the a=(uk)cos(theta) + gsin(theta), which was 7.45. Here is where I got stuck. I think I could use deltax=Vo(t) + (1/2)a(t)^2, but I don't know if the downward acceleration would still be applicable or how to find the time. The equation I was thinking of using is t=x/(Vocostheta)), but I don't know x or t. could I combine that equation with x=Vo(t) + 1/2a(t^2)? Am I even on the right track?

emilea said:
I drew a free body diagram to solve for the coefficient of friction down the ramp, which was uk=0.948. I then used that to find the acceleration down the ramp using the a=(uk)cos(theta) + gsin(theta), which was 7.45.
If the block slides down the incline at constant velocity, the acceleration must be ... ? Drawing a free body diagram is the way to go. If you still cannot finish the problem, please post the details of what you did so that we can correct anything that might be wrong.

I figured out that the downward acceleration is zero becausen it is at a constant velocity, which means the net downward force is also zero. I recalculated uk as 0.83 by setting Fg + Ff=0. My problem now is I have no idea how to connect this to any equations I could use to solve for x. I tried just using an equation for stopping distance: d=(Vo^2)/2ug, but that didn't work.

I think your initial coefficient of kinetic friction (0.948) is the correct one. I questioned your statement that the acceleration down is not zero. Now you need to find the acceleration of the block when is is sliding up the incline. You already have an expression for that, a=(uk)cos(theta) + gsin(theta) in a direction down the incline. To find how far up the incline the block goes before it stops, use the kinematic equation that involves speed and displacement, but not time.

$$\mu_k=0.948$$ is what I get.

If I'm understanding you correctly, emilea, I believe the expression you've posted for the acceleration down the plane [a=(uk)cos(theta) + gsin(theta)] is incorrect. Keep in mind that friction wants to act opposite the direction of motion.

## 1. How do you calculate the distance traveled up a ramp given mass, angle, and velocity?

The formula for calculating the distance traveled up a ramp is distance = (mass x velocity^2 x sin(2 x angle)) / (2 x gravity), where mass is in kilograms, velocity is in meters per second, angle is in degrees, and gravity is 9.8 meters per second squared.

## 2. Can you provide an example of how to use the formula to calculate distance traveled up a ramp?

For example, if an object with a mass of 2 kilograms is pushed up a ramp at a velocity of 5 meters per second at an angle of 30 degrees, the distance traveled would be (2 x 5^2 x sin(2 x 30)) / (2 x 9.8) = 3.19 meters.

## 3. What is the unit of measurement for distance traveled up a ramp?

The unit of measurement for distance traveled up a ramp is meters (m).

## 4. Is there a specific angle that maximizes the distance traveled up a ramp?

Yes, the angle that maximizes the distance traveled up a ramp is 45 degrees. This is because at this angle, the sine function reaches its maximum value of 1, resulting in the longest possible distance traveled.

## 5. What other factors can affect the distance traveled up a ramp?

Other factors that can affect the distance traveled up a ramp include friction, the shape and material of the ramp, and any external forces acting on the object. These factors may alter the velocity and acceleration of the object, ultimately affecting the distance traveled.

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