a) See free-body diagram in attachment
b) The acceleration down along the ramp is
c) The new acceleration is
d) The power dissipated by friction is 294.2 W
Explanation:
a)
The free body diagram is shown in attachment (first picture). The x-positive direction is taken as down along the ramp, while the positive y-direction is taken up perpendicular to the ramp.
There are only two forces acting on Prof. Holt:
- Her weight, labelled as (mg) (where m is the mass and g the acceleration of gravity), acting vertically downward
- The normal reaction exerted by the slope on the Prof, labelled with N, acting perpendicularly to the plane in the y-direction
We can further resolve the weight of the Prof along the x- and y- direction, obtaining:
Where is the angle at the base of the ramp.
b)
The equation of the forces along the two directions are:
- x direction:
where a is the acceleration,
- y direction:
We can rewrite the two equations as
And from the first equation, we get:
Substituting and , we find the acceleration:
c)
The new free-body diagram is attached in the second picture. In this case, we also have the frictional force , which acts up along the ramp, and whose magnitude is
where
is the coefficient of kinetic friction.
In this situation, therefore, the two equations of motions are:
From the first equation we find the normal reaction:
And substituting into the second equation, we can find the acceleration:
d)
First of all, we have to calculate the magnitude of the force of friction, which is given by:
and substituting m = 45 kg and the other data, we find
Now we can calculate the work done by the force of friction, which is
where d is the displacement along the ramp, which is given by
where h = 10 m is the height of the ramp. Substituting and evaluating,
The work done by the friction is negative since friction acts opposite to the direction of motion.
Now, we can finally calculate the power dissipated:
where
is the magnitude of the work done by friction
t = 3 s is the time interval
Substituting,
Learn more about slopes, force of friction and power:
brainly.com/question/5884009
brainly.com/question/7956557
#LearnwithBrainly