A person must move two heavy packages over a surface level so they place a 20kg package over a 30kg package and decide to move them together. The coefficient of kinetic friction between the lower package and the ground is 0.3. The person exerts a force of 400N at an angle of 36.87degrees from the horizontal.
Assuming that the upper package doesn't slide off the lower, determine the rate at which the accelerate.
I've never done/learned how to do a problem with an object on top of the other. Can someone please explain it and every step. Thanks!
To solve this problem, we need to consider the forces acting on the system and apply Newton's second law of motion. Let's break down the steps:
1. Draw a free-body diagram: Draw a diagram representing the two packages and the forces acting on them. In this case, there are three main forces: the gravitational force (weight) acting downwards on each package, the normal force exerted by the ground on the lower package, and the force of friction acting between the lower package and the ground.
2. Resolve forces into components: Since the force exerted by the person is at an angle, we need to resolve it into horizontal and vertical components. The horizontal component will be used to overcome friction, while the vertical component will affect the normal force.
3. Calculate the vertical forces: The weight of the two packages creates a vertical force (downward). The normal force is the force exerted by the ground to counteract the weight. Since the lower package is pressed against the ground, the normal force will be equal to the weight of the lower package plus the weight of the upper package.
4. Determine the frictional force: The coefficient of kinetic friction (given as 0.3) and the normal force will help us calculate the frictional force. The formula for kinetic friction is F_friction = μ * F_normal, where μ is the coefficient of friction and F_normal is the normal force.
5. Calculate the net horizontal force: The net horizontal force is the force exerted by the person minus the frictional force.
6. Use Newton's second law: Newton's second law states that the acceleration of an object is equal to the net force acting on it divided by its mass. In this case, the mass of the system is the combined mass of both packages.
7. Calculate the acceleration: Divide the net horizontal force by the total mass of the two packages to find the acceleration.
8. Solve for the rate of acceleration: Since the question asks for the rate of acceleration, you need to specify if you want the answer in meters per second squared (m/s²) or in another unit.
By following these steps and applying the appropriate formulas, you should be able to determine the rate at which the packages accelerate.