)A block with mass m = 11.3 kg slides down an inclined plane of slope angle 43.4 ° with a constant velocity. It is then projected up the same plane with an initial speed 1.45 m/s. How far up the incline will the block move before coming to rest?
To find out how far up the incline the block will move before coming to rest, we need to analyze the forces acting on the block in both cases - sliding down the incline with constant velocity and moving up the incline until it comes to rest.
Firstly, when the block slides down the incline with a constant velocity, the force of gravity acting downwards and the frictional force acting up the incline oppose each other. Since the block is moving at a constant velocity, the force of friction is equal in magnitude and opposite in direction to the force of gravity. Therefore, the force of friction can be calculated using the formula:
force of friction = force of gravity * coefficient of kinetic friction
Next, when the block is projected up the incline with an initial speed of 1.45 m/s, the force of gravity acting downwards and the force of friction acting up the incline again oppose each other. Additionally, there is an applied force acting up the incline to propel the block. When the block comes to rest, the applied force will be equal in magnitude and opposite in direction to the sum of the force of gravity and the force of friction. Therefore, we can express this as an equation:
applied force - force of gravity - force of friction = 0
Now let's break down these forces and calculate the distance the block will move up the incline before coming to rest.
1. Calculate the force of gravity:
force of gravity = mass * acceleration due to gravity
2. Calculate the force of friction when the block is sliding down the incline with constant velocity:
force of friction = force of gravity * coefficient of kinetic friction
3. Calculate the applied force when the block is projected up the incline:
applied force = force of gravity + force of friction
4. Calculate the distance the block will move up the incline before coming to rest:
distance = (initial velocity^2) / (2 * acceleration)
By plugging in the values and solving the equations step by step, you can find the distance the block will move up the incline before coming to rest.