Assuming the woman starts at rest, she descends the slide with acceleration <em>a</em> such that
(20.3 m/s)² = 2 <em>a</em> (42.6 m) → <em>a</em> ≈ 4.84 m/s²
which points parallel to the slide.
The only forces acting on her, parallel to the slide, are
• the parallel component of her weight, <em>w</em> (//)
• friction, <em>f</em>, opposing her descent and pointing up the slide
Take the downward sliding direction to be positive. By Newton's second law, the net force in the parallel direction acting on the woman is
∑ <em>F</em> (//) = <em>w </em>(//) - <em>f</em> = <em>ma</em>
where <em>m</em> = 77.0 kg is the woman's mass.
Solve for <em>f</em> :
<em>mg</em> sin(42.3°) - <em>f</em> = <em>ma</em>
<em>f</em> = <em>m</em> (<em>g</em> sin(42.3°) - <em>a</em>)
<em>f</em> = (77.0 kg) ((9.80 m/s²) sin(42.3°) - 4.84 m/s²) ≈ 135 N
Compute the work <em>W</em> done by friction: multiply the magnitude of the friction by the length of the slide.
<em>W</em> = (135 N) (42.6 m) ≈ 5770 N•m = 5770 J
It would be the electromagnet because that is how it spins
As per kinematics equation we are given that

now we are given that
a = 2.55 m/s^2


now we need to find x
from above equation we have



so it will cover a distance of 93.2 m
Answer: 288.8 m
Explanation:
We have the following data:
is the time it takes to the child to reach the bottom of the slope
is the initial velocity (the child started from rest)
is the angle of the slope
is the length of the slope
Now, the Force exerted on the sled along the ramp is:
(1)
Where
is the mass of the sled and
its acceleration
In addition, if we draw a free body diagram of this sled, the force along the ramp will be:
(2)
Where
is the acceleration due gravity
Then:
(3)
Finding
:
(4)
(5)
(6)
Now, we will use the following kinematic equations to find
:
(7)
(8)
Where
is the final velocity
Finding
from (7):
(9)
(10)
Substituting (10) in (8):
(11)
Finding
:

Answer:
11.) g = 3.695 m/s^2
12.) g = 8.879 m/s^2
13.) E = 8127 N/C
Explanation:
11.) Given that the
Mercury mass M = 3.3 × 10^23kg
Radius r = 2.44 ×10^6 m
Gravitational constant G = 6.67408 × 10^-11 m3kg-1 s^-2
Gravitational field strength g can be calculated by using the formula below
g = GM/r^2
Substitutes all the parameters into the formula
g = (6.67408 × 10^-11 × 3.3 × 10^23)/(2.44×10^6)^2
g = 2.2×10^13/5.954×10^12
g = 3.695 m/s^2
12.) Given that the
Venus mass M = 4.87×10^24kg
Radius r = 6.05 × 10^6 m
Using the same formula for gravitational field strength g
g = GM/R2
Substitute all the parameters into the formula
g = (6.67408 × 10^-11 × 4.87×10^24)/(6.05×10^6)^2
g = 3.25×10^14/3.66×10^13
g = 8.879 m/s^2
13.) Given that the
Charge = 2.26 nC = 2.26×10^-9
Distance d = 0.05m
Electric field strength E can be calculated by using the formula below
E = Kq/d^2
Where
K = electrostatic constant 8.99 × 10^9 Nm2/C2
Substitutes all the parameters into the formula
E = (8.99 × 10^9 × 2.26×10^-9)/0.05^2
E = 20.3174/2.5×10^-3
E = 8126.96 N/C