A factory robot drops a 10kg computer onto a conveyer belt running at 3.1m.s. the material are such as us=0.5 and uk=0.30 between the belt and the computer.how far is the computer dragged before it is ridding smoothly os the belt
First, we need to calculate the force of friction acting on the computer as it is dropped on the conveyor belt. We can do this using the equation:
Ffriction = uk * Fnormal
where Fnormal is the normal force acting on the computer (equal to its weight, mg) and uk is the coefficient of kinetic friction.
Fnormal = mg = 10 kg * 9.81 m/s^2 = 98.1 N
Ffriction = 0.30 * 98.1 N = 29.4 N
Next, we can use the equation for constant acceleration to determine how far the computer is dragged before it reaches a constant speed on the conveyor belt:
d = (v^2 - u^2) / (2a)
where d is the distance traveled, v is the final velocity (equal to the speed of the conveyor belt, 3.1 m/s), u is the initial velocity (0 m/s), and a is the acceleration.
We can calculate the acceleration using the equation:
Fnet = ma
where Fnet is the net force acting on the computer (equal to the force of friction), and m is the mass.
Fnet = Ffriction = ma
a = Fnet / m = 29.4 N / 10 kg = 2.94 m/s^2
Now we can plug in the values:
d = (3.1^2 - 0^2) / (2 * 2.94) = 1.69 m
Therefore, the computer is dragged 1.69 meters before it reaches a constant speed on the conveyor belt.
To determine how far the computer is dragged before it is riding smoothly on the belt, we can use the concept of friction.
First, let's calculate the force of friction acting on the computer. The force of friction can be calculated using the equation:
\(F_{friction} = \mu_k \times m \times g\)
where:
\(F_{friction}\) is the force of friction,
\(\mu_k\) is the coefficient of kinetic friction (given as 0.30),
\(m\) is the mass of the computer (given as 10 kg), and
\(g\) is the acceleration due to gravity (approximately 9.8 m/s^2).
\(F_{friction} = 0.30 \times 10 \times 9.8\)
\(F_{friction} = 29.4 \, \mathrm{N}\)
Next, let's calculate the net force acting on the computer. The net force can be calculated using the equation:
\(F_{net} = m \times a\)
where:
\(F_{net}\) is the net force,
\(m\) is the mass of the computer (given as 10 kg), and
\(a\) is the acceleration of the computer.
Since the computer is riding smoothly on the belt, the net force is equal to zero. Therefore,
\(0 = 10 \times a\)
\(a = 0 \, \mathrm{m/s^2}\)
Since the acceleration is \(0 \, \mathrm{m/s^2}\), the computer is not moving horizontally. Therefore, the computer is not dragged any distance before it is riding smoothly on the belt.
In conclusion, the computer is not dragged any distance before it is riding smoothly on the belt.