Your teacher placed a 4.5 kg block at the position marked with a “ +” (horizontally, 0.5 m from the origin) on a large incline outlined on the graph below and let it slide, starting from rest.
Find the horizontal distance from the bottom (right-hand) edge of the incline to the point of contact with the floor; i.e., when y = 0 . The coefficient of kinetic friction for the block on the incline is 0.55 and the acceleration due to gravity is 9.8 m/s^2.
This is the graph:
0.178
To find the horizontal distance from the bottom edge of the incline to the point of contact with the floor, we need to analyze the motion of the block as it slides down the incline.
First, let's break down the forces acting on the block. Since the block is on an incline, there are two main forces at play: the force of gravity and the friction force. The force of gravity can be separated into two components: one parallel to the incline (mg*sinθ) and one perpendicular to the incline (mg*cosθ), where θ is the incline angle.
The friction force opposes the motion of the block and can be calculated using the equation F_friction = μ*F_normal, where μ is the coefficient of kinetic friction and F_normal is the normal force perpendicular to the incline. In this case, the normal force is equal to mg*cosθ.
Since the block is starting from rest, the net force acting on it will be the sum of the force of gravity parallel to the incline and the friction force. The net force can be calculated using the equation F_net = m*a, where m is the mass of the block and a is its acceleration.
The acceleration of the block can be determined using the equation a = F_net / m.
To find the horizontal distance from the bottom edge of the incline to the point of contact with the floor, we need to consider the time it takes for the block to reach the bottom.
Using the kinematic equation s = u*t + (1/2)*a*t^2, where s is the distance, u is the initial velocity (which is zero in this case since the block starts from rest), t is the time, and a is the acceleration, we can solve for t.
Once we have the time it takes for the block to reach the bottom, we can calculate the horizontal distance using the equation s = v*t, where v is the horizontal velocity of the block.
To find the horizontal velocity, we can use the equation v = u + a*t, where u is the initial velocity and a is the acceleration.
By plugging in the known values for the mass of the block (4.5 kg), the coefficient of kinetic friction (0.55), the angle of the incline, and the acceleration due to gravity (9.8 m/s^2), we can solve for the desired horizontal distance.