Two blocks are attached together with a piece of string. Block #1 (3 kg) slides along a
rough horizontal surface and block #2 (2 kg) hangs off the end of the surface. If the blocks
accelerate at 2.5 m/s2
in the directions shown, determine the tension in the string and the
coefficient of kinetic friction (µk) between block #1 and the surface.
To solve this problem, you'll need the tension formula which is T=Ma. T is tension, mass M is weight Mg and tension or in other words the mass that is on the surface, & a is acceleration.
M=3kg a=2.5m/s2 T=?
Just plug it into the formula...
T=(3kg)(2.5m/s2)
T=7.5N
To determine the tension in the string and the coefficient of kinetic friction, we need to analyze the forces acting on the system.
Let's first calculate the net force acting on the system. Since the blocks are accelerating, there must be a net force causing this acceleration.
For block #1, the net force can be calculated using Newton's second law:
F_net = m1 * a
where m1 is the mass of block #1 and a is the acceleration.
F_net = (3 kg) * (2.5 m/s^2)
F_net = 7.5 N
Now, let's consider the forces acting on block #1. There are two main forces: the tension (T) in the string and the force of kinetic friction (F_friction) between block #1 and the rough horizontal surface.
The tension in the string pulls block #1 forward, so it opposes the force of friction. Therefore, the tension can be calculated as:
T = F_net + F_friction
T = 7.5 N + F_friction
Next, let's consider the forces acting on block #2. The only force acting on block #2 is its weight (mg). Since it is hanging off the surface, its weight is pulling it downward.
To find the weight of block #2, we can use the formula:
Weight = mass * acceleration due to gravity (g)
Weight = (2 kg) * (9.8 m/s^2)
Weight = 19.6 N
Since block #2 is in equilibrium (not accelerating in its direction), the tension in the string must be equal to its weight:
T = Weight
T = 19.6 N
We can substitute this value of T back into the equation for block #1:
19.6 N = 7.5 N + F_friction
Now, let's solve for F_friction, the force of kinetic friction:
F_friction = 19.6 N - 7.5 N
F_friction = 12.1 N
Finally, to find the coefficient of kinetic friction (μk), we can use the formula:
F_friction = μk * N
where N is the normal force. In this case, the normal force is equal to the weight of block #1:
N = m1 * g
N = (3 kg) * (9.8 m/s^2)
N = 29.4 N
Now, we can substitute the values of F_friction and N into the equation:
12.1 N = μk * 29.4 N
Solving for μk:
μk = 12.1 N / 29.4 N
μk = 0.41