A block is launched up the incline(coefficient of friction is 0.3) with an initial speed of 12m/s. What is the maxximum displacement of the block up the incline?
To find the maximum displacement of the block up the incline, we need to analyze the forces acting on the block and determine at what point it comes to a stop. Here's how you can solve it step by step:
1. Split the forces: Split the weight of the block into two components, one parallel to the incline (mg*sinθ) and one perpendicular to the incline (mg*cosθ), where θ is the angle of the incline.
2. Calculate the force due to friction: The maximum frictional force can be calculated by multiplying the coefficient of friction (μ) with the perpendicular component of the weight. In this case, the frictional force (f friction) is equal to μ * (mg*cosθ).
3. Determine the net force: Calculate the net force acting on the block parallel to the incline by subtracting the frictional force from the applied force. In this case, the applied force (f applied) is equal to the product of the mass (m) and the acceleration due to gravity (g). The net force (f net) is equal to f applied - f friction.
4. Calculate the acceleration: Divide the net force by the mass of the block to find the acceleration (a) along the incline. In this case, a = f net / m.
5. Calculate the displacement: Use the equation of motion to find the displacement (s) of the block. The equation is s = (v^2 - u^2) / (2 * a), where v is the final velocity (which is 0 m/s as it comes to a stop), and u is the initial velocity of the block (12 m/s).
Now, let's plug in the values and calculate the maximum displacement:
Given:
Initial velocity, u = 12 m/s
Coefficient of friction, μ = 0.3
Step 1: No calculations are needed for this step, just make sure you split the forces correctly.
Step 2: Calculating the frictional force:
f friction = μ * (mg*cosθ)
Step 3: Calculating the net force:
f applied = m * g
f net = f applied - f friction
Step 4: Calculating the acceleration:
a = f net / m
Step 5: Calculating the displacement:
s = (v^2 - u^2) / (2 * a)
Plug in the values and solve the equations step by step to find the maximum displacement of the block up the incline.