An object weighing 60N rest on a slope forming an angle of 17.5 degrees with the horizontal. A force of 44N parallel to the sloping surface just moves the object upwards. Calculate the frictional force.
break the 44 N force into components up the slope, and normal to the slope.
F=44cos17.5 u + 44sin17.5 n
now break the weight in to normal, and up the slope components.
60N down= 60cos17.5 n - 60 sin17.5 u
frictional force opposes upward, so it is a negative force up the slope.
Now consider just the n forces.
friction=mu(60cos17.5+44sin17.5)
well, at this point, you are stuck without mu. So,
compute that
then up the slope...
fu=friction
44cos17.5 u-60 sin17.5=friction
now you can compute friction, and go back with the normal equation, and compute mu.
m*g = 60 N. = Wt. of object.
Fp = 60*sin17.5 = 18.04 N. = Force
parallel to the incline.
Fn = 60*cos17.5 = 57.22 N. = Normal =
force perpendicular to the incline.
Fap-Fp-Fs = m*a
44-18.04-Fs = m*0 = 0
Fs = 44-18.04 = 26 N. = Force of static
friction.
To calculate the frictional force, we first need to calculate the gravitational force acting on the object.
The gravitational force is equal to the weight of the object, which is given as 60N.
Next, we need to decompose this gravitational force into its components. The component of the gravitational force acting parallel to the slope is given by:
F_parallel = F_gravity * sin(theta)
where theta is the angle of the slope. Given that theta is 17.5 degrees, we can calculate F_parallel as follows:
F_parallel = 60N * sin(17.5 degrees) = 17.796 N
Now we can compare this force with the applied force parallel to the sloping surface. If the applied force is greater than the parallel component of the gravitational force, the object will move upwards.
In this case, the applied force is given as 44N, which is greater than 17.796N. Therefore, the object will move upwards.
Since the object is just starting to move, the frictional force must be equal to the parallel component of the gravitational force.
So, the frictional force is equal to 17.796 N.
To summarize:
- The parallel component of the gravitational force is 17.796 N.
- The applied force is 44 N.
- The frictional force is also 17.796 N.