If a laptop of mass 1.4 kg is lifted to a table of height 0.8 m, how much gravitational potential energy is added to the laptop?
2 answers:
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a) Average power: 1425 W
b) Instantaneous power at 3.0 sec: 2850 W
Explanation:
a)
The motion of the object along the ramp is a uniformly accelerated motion (because the force applied is constant), so we can use the suvat equation
where
s = 18 m is the displacement along the ramp
u = 0 is the initial velocity
t = 3.0 s is the time taken
a is the acceleration of the object along the ramp
Solving for a,
Now we can apply Newton's second law to find the net force on the object:
This net force is the resultant of the applied force forward () and the component of the weight acting backward (
), so we can find what is the applied force:
where
m = 24 kg is the mass of the object
is the acceleration of gravity
Now we can finally find what is the work done by the applied force, which is parallel to the ramp, therefore:
where s = 18 m is the displacement.
Therefore the average power needed is:
b)
The instantaneous power at any point of the motion is given by
where
is the force applied
v is the velocity of the object
We already calculated the applied force:
While since this is a uniformly accelerated motion, we can find the velocity at the end of the 3.0 seconds using the suvat equation:
And therefore, the instantaeous power at 3.0 sec is:
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Answer:
As shown in the attachment
Explanation:
The detailed steps and mathematical assumptions and manipulation is as shown in the attachment.
Answer:
v' = -18 m/s
Explanation:
- Assuming no external forces acting during the collision, total momentum must be conserved, as follows:
- The initial momentum can be expressed as follows (taking as positive the initial direction of the ball):
- The final momentum can be expressed as follows (since we know that v'b is opposite to the initial vb):
- If we assume that Mc >> mb, we can assume that the car doesn't change its speed at all as a result of the collision, so we can replace V'c by Vc in (3).
- So, we can write again (3) as follows:
- Replacing (2) and (4) in (1), we get:
- Simplifying, and rearranging, we can solve for v'b, as follows:
, which is reasonable, because everything happens as if the ball had hit a wall, and the ball simply had inverted its speed after the collision.