Kinetic Energy & Distance on an Incline: A Sphere's Journey

[madahmad1]

Homework Statement

A solid sphere of mass 1 kg that moves on a level surface at a speed of 20m/s. It then
ascends am inclined surface with an angle of 30 degrees. Determine:

a) the kinetic energy of the sphere when it is positioned at the base of the inclined surface.

b) the distance covered on the inclined surface.

Homework Equations

What equation should be used here?

The Attempt at a Solution

I have no idea how to solve this problem.

 

[blochwave]

2. Homework Equations

What equation should be used here?

Your kinetic energy equation (KE=1/2*mv^2) and the potential energy equation (mgh)

Assuming no friction on the incline, the HEIGHT it reaches would be the same if the incline were 70 degrees or 2 degrees or any angle. You then use the angle to see how much distance it covers on the incline

 

[ogb p]

I would first start by identifying the relevant equations that can help us solve this problem. In this case, we can use the equations for kinetic energy and work done by a force.

a) To determine the kinetic energy of the sphere at the base of the inclined surface, we can use the equation:

KE = 1/2 * m * v^2

Where KE is the kinetic energy, m is the mass of the sphere (1 kg in this case), and v is the velocity (20m/s in this case).

Therefore, KE = 1/2 * 1 kg * (20m/s)^2 = 200 Joules

b) To determine the distance covered on the inclined surface, we can use the equation:

W = F * d

Where W is the work done, F is the force acting on the sphere, and d is the distance covered.

In this case, the force acting on the sphere is its weight, which can be calculated using the equation:

F = m * g * sinθ

Where m is the mass of the sphere (1 kg), g is the acceleration due to gravity (9.8 m/s^2), and θ is the angle of the incline (30 degrees).

Therefore, F = 1 kg * 9.8 m/s^2 * sin(30 degrees) = 4.9 N

Substituting this into the work equation, we get:

W = 4.9 N * d

We know that the work done is equal to the change in kinetic energy, which we calculated in part a). Therefore, we can write the equation as:

KE = 4.9 N * d

Solving for d, we get:

d = KE / 4.9 N = 200 Joules / 4.9 N = 40.8 meters

Therefore, the distance covered by the sphere on the inclined surface is 40.8 meters.

In conclusion, by using the equations for kinetic energy and work done, we were able to determine the kinetic energy of the sphere at the base of the inclined surface and the distance covered on the inclined surface.