Projectile Motion: Frisbee Sliding up a Sloped Roof

[Th3Proj3ct]

Homework Statement

One side of the roof of a building slopes up at 30.0°. A student throws a Frisbee onto the roof. It strikes with a speed of 15.0 m/s and does not bounce, but slides straight up the incline. The coefficient of kinetic friction between the plastic and the roof is 0.460. The Frisbee slides 10.0 m up the roof to its peak, where it goes into free-fall, following a parabolic trajectory with negligible air resistance.

Homework Equations

Determine the maximum height the Frisbee reaches above the point where it struck the roof.

The Attempt at a Solution

honestly... i haven't been able to do much, I try to find the acceleration using F=ma, and then maybe finding the speed when it's at the top, and continue from there; but the problem doesn't have a mass, so i don't have a clue where to start in any type of formula except for the basic kinematic equations, but I'm not even sure how those can be applied.

I've created a free-body diagram of it, but as I said without any mass, and maybe even with it I don't know where to start ( this problem is unlike any other one we've had this chapter.) I assume that when it reaches 10m, it will have Vxf, and then I can use that as Vx0 for a new diagram for parabolic motion... but I don't know how to find A, since the only formulas for A involving force is Fk=Uk/N, and you can't get the normal force without M, because N = mass*Gravity, or since it's on a slant, n=mass*cos(30)

 

[hotvette]

Welcome to PF!

You are definitely on the right track. It's a 2 part problem where the answer the first part is the initial condition to the 2nd part. Just write the F = ma for the object sliding up the incline. You'll see that it is solveable.

 

[m2003]

I would approach this problem by breaking it down into smaller parts and using fundamental principles to solve each part.

First, I would consider the motion of the Frisbee as it slides up the roof. Since the Frisbee does not bounce, we can assume that the kinetic energy of the Frisbee is converted into potential energy as it slides up the roof. We can use the work-energy theorem to determine the height the Frisbee reaches at its peak. The work done by the friction force is equal to the change in kinetic energy, which is equal to the change in potential energy. So we can write:

Wfriction = ΔKE = ΔPE

The work done by the friction force can be calculated using the equation W = Fd, where F is the friction force and d is the distance the Frisbee slides up the roof. The friction force is equal to the coefficient of kinetic friction multiplied by the normal force, which can be calculated using the weight of the Frisbee and the angle of the roof. So we can write:

μk * N * d = m * g * sin(30°) * d

Substituting this expression for Wfriction into the work-energy theorem equation, we get:

μk * N * d = ½ * m * v^2

Where v is the speed of the Frisbee when it reaches the top of the roof. We can rearrange this equation to solve for v:

v = √(2 * μk * N * d / m)

Now, we can use this value of v to solve for the height the Frisbee reaches at its peak. We can use the kinematic equations for constant acceleration motion to determine the height, h, using the initial speed, v, and the acceleration due to gravity, g:

h = v^2 / (2 * g)

Next, we can consider the motion of the Frisbee as it falls from its peak. Since we are neglecting air resistance, the only force acting on the Frisbee is the force of gravity. So we can use the kinematic equations again to determine the time it takes for the Frisbee to fall back down to the roof. We can use the equation for displacement to solve for the time, t:

h = ½ * g * t^2

Finally, we can use the time, t, to solve for the horizontal distance the Fr