force in the x-direction with magnitude Fx=18N-(0.530N/m)x is applied to a 5.50 box that is sitting on the horizontal, frictionless surface of a frozen lake. is the only horizontal force on the box.
what is the speed after 12m. starting from rest and x=0
F=18-0.53•x
a=F/m=(18-0.53•x)/5.5
v=sqrt(2•a•x)=sqrt[(18-0.53•x)x/5.5]=
= sqrt[(18 - 0.53•12) •12/5.5=5.04 m/s
the first answer is wrong
Integral of F(x) = .5mv^2
18x-.5(.53)x^2=.5mv^2
find v.
8.04m/s
To find the speed of the box after it has traveled a distance of 12m, we need to determine the work done on the box and use that to calculate the change in kinetic energy. We can then use the equation for kinetic energy to find the speed.
1. Determine the work done:
The work done on an object is equal to the force applied multiplied by the distance traveled in the direction of the force. In this case, the distance traveled is 12m, and the force is given by Fx = 18N - (0.530N/m)x. We need to integrate the force function over the range of x = 0 to x = 12m to find the work done:
Work = ∫[0,12] Fx dx
Integrating the force function, we get:
Work = ∫[0,12] (18N - (0.530N/m)x) dx
= [18x - (0.530N/m)(x^2)/2] evaluated from x = 0 to x = 12
= [18(12) - (0.530N/m)(12^2)/2] - [18(0) - (0.530N/m)(0^2)/2]
= [216N - (0.530N/m)(72)/2] - [0 - (0N/m)(0)/2]
= [216N - (0.530N/m)(36)] - [0]
= 216N - 18.36N
= 197.64 N
2. Calculate the change in kinetic energy:
The work done on an object is equal to the change in kinetic energy. So, the change in kinetic energy of the box is equal to 197.64 N.
3. Use the equation for kinetic energy:
The kinetic energy of an object is given by the equation: KE = (1/2)mv^2
Where m is the mass of the object (which is not given) and v is the speed. Since mass is not given, we can assume it to be 1 kg to simplify the calculation. Now we can write the equation as:
(1/2)(1 kg)v^2 = 197.64 N
Simplifying further:
v^2 = (2 * 197.64 N) / (1 kg)
v^2 = 395.28 N/kg
v = sqrt(395.28 N/kg)
v ≈ 19.88 m/s
Therefore, the speed of the box after traveling a distance of 12m starting from rest at x = 0 is approximately 19.88 m/s.