Find Distance 'd' on a Curved Ramp with No Friction | Ramp Problem Solved

[Format]

I have a really difficult question i need help on.

A 1.9-kg block slides down a frictionless ramp. Ths top of the ramp is 1.5-m above the ground; the bottom of the ramp is 0.25-m above the ground. The block leaves the ramp moving horizontally, and lands a horizontal distance 'd' away. Find the distance 'd'.

Oh and the ramp is curved so the block slides horizontally when it leaves the ramp.

Help please!

 

[Doc Al]

First find the speed of the block as it leaves the slide. Use conservation of energy.

Then apply the usual kinematic equations for projectile motion: the y-direction has an acceleration due to gravity; the x-direction is constant speed motion. Note that the initial velocity as it leaves the slide is purely horizontal.

 

[M98Ranger]

To find the distance 'd' on a curved ramp with no friction, we can use the conservation of energy principle. This principle states that the total energy of a system remains constant, so we can equate the initial potential energy of the block at the top of the ramp to its final kinetic energy at the bottom of the ramp.

First, we need to find the initial potential energy of the block at the top of the ramp. We can use the formula PE=mgh, where m is the mass of the block (1.9 kg), g is the acceleration due to gravity (9.8 m/s^2), and h is the height of the ramp (1.5 m). This gives us a potential energy of 28.35 J.

Next, we can find the final kinetic energy of the block at the bottom of the ramp. Since the block leaves the ramp horizontally, its initial vertical velocity is zero. Therefore, we can use the formula KE=1/2mv^2, where m is the mass of the block (1.9 kg) and v is the horizontal velocity of the block. We know that the block lands a horizontal distance 'd' away, so we can use the formula d=v*t, where t is the time it takes for the block to reach the ground. Since the block is only affected by gravity, we can use the formula y=1/2gt^2 to find the time it takes for the block to reach the ground. Setting the initial height to 1.5 m and final height to 0.25 m, we get t=0.49 seconds. Substituting this into the formula d=v*t, we get d=v*0.49. Therefore, the final kinetic energy of the block is KE=1/2*1.9*v^2=0.49v^2.

Now, equating the initial potential energy to the final kinetic energy, we get 28.35=0.49v^2. Solving for v, we get v=9.95 m/s. Finally, we can use the formula d=v*t to find the distance 'd' traveled by the block. Substituting the value of v and t, we get d=9.95*0.49=4.87 m.

Therefore, the distance 'd' on the curved ramp with no friction is 4.87 meters. I hope this helps!