Physics force of friction question
a shuffle board disk is accelerated to a speed of 5.8m/s and released. if the coefficient of the kinetic friction between the disk and the concrete court is 0.3,
how far does the disk go before it comes to a stop?The courts are 15.8meters long
isn't vf 5.8
F=m*a So u*m*g=m*a
m cancels out cause its on both sides of the equation.
so u*g=a (mu*gravity=acceleration)
solve for acceleration then plug a into the formula vf^2=Vi^2+2*a*d to solve for d.
force friction= .3*mg
Vf^2=Vi^2+2ad but a= -forcefricion/m
Vf=0, Vi is known, solve for d.
To find out how far the disk goes before coming to a stop, we need to consider the force of friction.
The force of friction can be calculated by multiplying the coefficient of kinetic friction (μk) by the normal force (N) between the disk and the court.
First, we need to find the normal force. The normal force is the force exerted by a surface to support the weight of an object resting on it. In this case, the normal force is equal to the weight of the disk.
The weight of an object can be calculated by multiplying its mass (m) by the acceleration due to gravity (g ≈ 9.8 m/s^2).
Now, let's assume the mass of the shuffleboard disk is m = 1 kg.
Weight (W) = mass (m) x acceleration due to gravity (g)
W = 1 kg x 9.8 m/s^2
W = 9.8 N
Since the disk is moving horizontally, the normal force is equal to the weight, N = 9.8 N.
Next, we can calculate the force of friction, which is given by:
Force of friction (Ff) = coefficient of kinetic friction (μk) x normal force (N)
Ff = 0.3 x 9.8 N
Ff ≈ 2.94 N
Now, we know that the force of friction acts in the opposite direction to the motion of the disk.
The net force on the disk is equal to the force of friction, so we can use Newton's second law:
Net force (Fnet) = mass (m) x acceleration (a)
Since the disk comes to a stop, the net force is equal to zero.
0 = 1 kg x a
From this, we can conclude that the acceleration (a) is zero.
With no acceleration, the disk will continue to move at a constant velocity until the force of friction slows it down to a stop.
To determine the distance covered, we can use the equation of motion:
Distance (d) = initial velocity (v0) x time (t)
Since the final velocity is zero, the distance covered is proportional to the initial velocity.
Therefore, the disk will travel a distance equal to its initial velocity.
d = 5.8 m/s (the given initial velocity)
So, the disk will go approximately 5.8 meters before it comes to a stop, which is less than the length of the court (15.8 meters).