Question

If given the mass, initial velocity, and coefficient of kinetic friction of an object moving down a slope of known degrees and length, how would you find final velocity?

Answer 1

To find the final velocity of an object moving down a slope with known parameters, including mass, initial velocity, coefficient of kinetic friction, slope angle, and length, you can follow these steps:

1. Determine the gravitational force component: Calculate the force component acting on the object due to gravity along the direction of the slope. This force can be determined using the formula:

   Force due to gravity along the slope = mass * gravitational acceleration * sin(slope angle)

2. Calculate the frictional force: Determine the frictional force acting on the object as it moves down the slope. This force is given by:

   Frictional force = coefficient of kinetic friction * normal force

   The normal force can be calculated as the product of the object's mass and the gravitational acceleration, and the normal force is perpendicular to the slope.

   Normal force = mass * gravitational acceleration * cos(slope angle)

3. Calculate the net force: Determine the net force acting on the object by subtracting the frictional force from the gravitational force component:

   Net force = Force due to gravity along the slope - Frictional force

4. Apply Newton's second law: Use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration. In this case, the acceleration is the object's rate of change of velocity. So, we have:

   Net force = mass * acceleration

   Rearrange the equation to solve for acceleration:

   acceleration = Net force / mass

5. Determine the acceleration: Plug in the values of the net force and mass calculated in steps 3 and 1, respectively, into the equation from step 4 to find the acceleration.

6. Apply the kinematic equation: With the acceleration known, you can use the appropriate kinematic equation to find the final velocity. One suitable equation is:

   final velocity^2 = initial velocity^2 + 2 * acceleration * displacement

   Here, the displacement is the length of the slope.

   Rearrange the equation to solve for the final velocity:

   final velocity = √(initial velocity^2 + 2 * acceleration * displacement)

By following these steps, you can calculate the final velocity of the object moving down the slope given the provided parameters.