There is a weight on a table, connected by a cord to another weight hanging over a pulley, as shown
in the diagram below. The coefficient of kinetic friction for the weight on the table is 0:25. How fast
does the hanging weight accelerate? Top weight is 12 kg and bottom is 5kg.
To determine the acceleration of the hanging weight, we need to consider the forces acting on both weights and apply Newton's second law of motion.
1. Calculate the force of gravity on each weight:
- The force of gravity on the top weight is given by the formula Fg = m * g, where m is the mass of the top weight (12 kg) and g is the acceleration due to gravity (approximately 9.8 m/s^2). Therefore, the force of gravity on the top weight is Fg = 12 kg * 9.8 m/s^2.
- The force of gravity on the bottom weight is Fg = 5 kg * 9.8 m/s^2.
2. Calculate the force of friction on the top weight:
- The force of friction is given by the equation Ff = μ * N, where μ is the coefficient of kinetic friction (0.25) and N is the normal force.
- The normal force is equal to the force of gravity acting on the top weight, which we calculated in step 1.
3. Calculate the net force on the system:
- The net force is the difference between the force of gravity on the top weight and the force of friction: Fnet = Fg - Ff.
4. Determine the acceleration:
- Apply Newton's second law of motion: Fnet = m * a, where Fnet is the net force and m is the mass of the system (combined mass of both weights).
- Rearrange the equation to solve for acceleration: a = Fnet / m.
Substitute the values calculated in the previous steps into the equation to find the acceleration of the hanging weight:
Fg = 12 kg * 9.8 m/s^2 (force of gravity on the top weight)
Ff = 0.25 * Fg (force of friction on the top weight)
Fnet = Fg - Ff (net force on the system)
m = 12 kg + 5 kg (combined mass of both weights)
a = Fnet / m
I'll let you do the calculations to find the final value of the acceleration.