A cube of mass M=0.703 kg is placed on an incline and given a push. It slides down, and its speed down the incline is measured at two positions, [1] and [2] on the diagram below, with V1 = 0.923 m/s and V2 = 1.207 m/s. Note that the incline passes through at least two grid intersections and that one cube corner is at x grid lines.
A. Calculate mk, the coefficient of kinetic friction for the block on the incline.
The height of the Right triangle is .38m and the length is 1m
Help will be provided on problems where you have shown work. This is not one of them.
Ok here is where I have got so far.
Tan (theta) = .38m/1m
theta = 20.807 deg
Sum Fy=mg*sin(theta)-Fn=ma=0
.703kg(9.81)*sin(20.807)-Fn=o
Fn=2.45N
Sum Fx=mgcos(theta)-Ff=ma
.703(9.81)*cos(20.807)-mk(2.45)=.703*a
This is where I am stuck
Thank you for showing your work!
The angle is arctan0.38 = 20.81 degrees, as you calculated.
Unfortunately, I need to know the vertical (H) or horizontal distance between the two measurement stations in order to proceed. I don't know what you mean by "grid intersection" or "cube corner". This would probably make sense if I could see the figure.
The decrease in potential energy between the two measurement stations, M g H, equals the kinetic energy increase,
(M/2)(V2^2 - V1^2)
PLUS
the work done against friction,
M g cos20.8 *mk* H/sin20.8
= M*g*H*mk/tan20.8
M cancels out. Solve for mk
To calculate the coefficient of kinetic friction (mk) for the block on the incline, you can use the following steps:
1. Determine the height (h) and the length (L) of the inclined plane. According to the information provided, the height of the right triangle is 0.38 m and the length is 1 m.
2. Use the given speeds (V1 and V2) to calculate the acceleration (a) of the cube. The acceleration can be found using the equation:
a = (V2^2 - V1^2) / (2 * L)
Substituting the given values, we have:
a = (1.207^2 - 0.923^2) / (2 * 1)
3. Calculate the gravitational force acting on the cube (Fg). The gravitational force can be found using the equation:
Fg = M * g
where M is the mass of the cube and g is the acceleration due to gravity (approximately 9.8 m/s^2).
Substituting the given mass value (M = 0.703 kg) and g, we have:
Fg = 0.703 * 9.8
4. Calculate the net force (Fn) acting on the cube down the incline. The net force can be calculated using the equation:
Fn = M * a
where M is the mass of the cube and a is the acceleration calculated in step 2.
Substituting the given mass value (M = 0.703 kg) and the calculated acceleration from step 2, we have:
Fn = 0.703 * a
5. Calculate the force of kinetic friction (Fk) acting on the cube. The force of kinetic friction can be calculated using the equation:
Fk = mk * Fn
where mk is the coefficient of kinetic friction and Fn is the net force calculated in step 4.
Rearranging the equation, we can solve for mk:
mk = Fk / Fn
Substituting the calculated value of Fn from step 4, we have:
mk = Fk / (0.703 * a)
6. Calculate the force of kinetic friction (Fk). Since the cube is sliding down the incline, the force of kinetic friction is opposing its motion and can be calculated using the equation:
Fk = Fg * sin(theta)
where Fg is the gravitational force calculated in step 3 and theta is the angle of the incline.
In this case, theta can be found using the right triangle formed by the height (0.38 m) and the length (1 m) of the incline:
theta = atan(h / L)
Substituting the given values, we have:
theta = atan(0.38 / 1)
Calculate the value of theta using a calculator.
Once theta is calculated, substitute the values of Fg and theta to calculate Fk:
Fk = Fg * sin(theta)
7. Substitute the calculated value of Fk from step 6 and the calculated value of Fn from step 4 into the equation from step 5:
mk = Fk / Fn
Substitute the values and calculate mk.
By following these steps, you can determine the coefficient of kinetic friction (mk) for the block on the incline.