The general formula to calculate the work is:
where F is the force, d is the displacement of the couch, and 
is the angle between the direction of the force and the displacement. Let's apply this formula to the different parts of the problem.
(a) Work done by you: in this case, the force applied is parallel to the displacement of the couch, so 
and 
, therefore the work is just equal to the product between the horizontal force you apply to push the couch and the distance the couch has been moved:
(b) work done by the frictional force: the frictional force has opposite direction to the displacement, therefore 
and 
. Therefore, we must include a negative sign when we calculate the work done by the frictional force:
(c) The work done by gravity is zero. In fact, gravity (which points downwards) is perpendicular to the displacement of the couch (which is horizontal), therefore 
and 
: this means
.
(d) Work done by the net force:
The net force is the difference between the horizontal force applied by you and the frictional force:
And the net force is in the same direction of the displacement, so and and the work done is
The initial velocity of the ball is 1.01 m/s
Explanation:
The motion of the ball rolling off the desk is a projectile motion, which consists of two independent motions:
- A uniform horizontal motion with constant horizontal velocity
- A vertical accelerated motion with constant acceleration (
, acceleration due to gravity)
We start by analyzing the vertical motion: we can find the time of flight of the ball by using the following suvat equation
where
s = 1.20 m is the vertical displacement (the height of the desk)
u = 0 is the initial vertical velocity
t is the time of flight
Solving for t,
Now we analyze the horizontal motion. We know that the ball covers a horizontal distance of
d = 0.50 m
in a time
t = 0.495 s
Therefore, since the horizontal velocity is constant, we can calculate it as
So, the ball rolls off the table at 1.01 m/s.
Learn more about projectile motion:
brainly.com/question/8751410
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Given Information:
KEa = 9520 eV
KEb = 7060 eV
Electric potential = Va = -55 V
Electric potential = Vb = +27 V
Required Information:
Charge of the particle = q = ?
Answer:
Charge of the particle = +4.8x10⁻¹⁸ C
Explanation:
From the law of conservation of energy, we have
ΔKE = -qΔV
KEb - KEa = -q(Vb - Va)
-q = KEb - KEa/Vb - Va
-q = 7060 - 9520/27 - (-55)
-q = 7060 - 9520/27 + 55
-q = -2460/82
minus sign cancels out
q = 2460/82
Convert eV into Joules by multiplying it with 1.60x10⁻¹⁹
q = 2460(1.60x10⁻¹⁹)/82
q = +4.8x10⁻¹⁸ C
By law of refraction we know that image position and object positions are related to each other by following relation
here we know that
now by above formula
so apparent depth of the bottom is seen by the observer as h = 3.39 cm
