A 4.10 kg block is pushed along the ceiling with an constant applied force of F = 81.5 N that acts at an angle è = 52° with the horizontal, as in the figure below. The block accelerates to the right at 5.10 m/s2. Determine the coefficient of kinetic friction between the block and the ceiling.
A football punter accelerates a 0.61 kg foot- ball from rest to a speed of 9 m/s in 0.24 s.
What constant force does the punter exert on the ball?
Answer in units of N.
To determine the coefficient of kinetic friction between the block and the ceiling, we can follow these steps:
Step 1: Identify the forces acting on the block:
- Applied force (F)
- Force of gravity (mg)
- Normal force (N)
- Kinetic friction force (fk)
Step 2: Analyze the horizontal forces:
Since the block is accelerating horizontally, we can focus on the horizontal forces.
The horizontal component of the applied force is F_x = F * cos(θ), where θ is the angle with the horizontal.
The horizontal component of the force of gravity is mg_x = mg * sin(θ), where θ is the angle with the horizontal.
Step 3: Calculate the net horizontal force:
The net horizontal force is given by:
F_net = F_x + fk
Step 4: Calculate the mass of the block:
The mass of the block is given as 4.10 kg (given in the question).
Step 5: Calculate the acceleration due to the net force:
Newton's second law states that F_net = ma, where F_net is the net force and a is the acceleration. In this case, the acceleration is given as 5.10 m/s^2.
Step 6: Determine the kinetic friction force:
Since the block is accelerating to the right, the kinetic friction force opposes the applied force. So, we have:
fk = m * a - F_x
Step 7: Calculate the normal force:
The normal force, N, is equal in magnitude but opposite in direction to the vertical component of the force of gravity. So, we have:
N = mg_y = mg * cos(θ), where θ is the angle with the horizontal.
Step 8: Calculate the coefficient of kinetic friction:
The coefficient of kinetic friction can be calculated using the formula:
μk = fk / N
By following these steps and substituting the given values into the respective equations, you can find the coefficient of kinetic friction between the block and the ceiling.