Answer:
v_{f} = 74 m/s, F = 230 N
Explanation:
We can work on this exercise using the relationship between momentum and moment
I = ∫ F dt = Δp
bold indicates vectors
we can write this equations in its components
X axis
Fₓ t = m ( -v_{xo})
Y axis
t = m (v_{yf} - v_{yo})
in this case with the ball it travels horizontally v_{yo} = 0
Let's use trigonometry to write the final velocities and the force
sin 30 = v_{yf} / vf
cos 30 = v_{xf} / vf
v_{yf} = vf sin 30
v_{xf} = vf cos 30
sin40 = F_{y} / F
F_{y} = F sin 40
cos 40 = Fₓ / F
Fₓ = F cos 40
let's substitute
F cos 40 t = m ( cos 30 - vₓ₀)
F sin 40 t = m (v_{f} sin 30-0)
we have two equations and two unknowns, so the system can be solved
F cos 40 0.1 = 0.4 (v_{f} cos 30 - 20)
F sin 40 0.1 = 0.4 v_{f} sin 30
we clear fen the second equation and subtitles in the first
F = 4 sin30 /sin40 v_{f}
F = 3.111 v_{f}
(3,111 v_{f}) cos 40 = 4 v_{f} cos 30 - 80
v_{f} (3,111 cos 40 -4 cos30) = - 80
v_{f} (- 1.0812) = - 80
v_{f} = 73.99
v_{f} = 74 m/s
now we can calculate the force
F = 3.111 73.99
F = 230 N
Answer:
(a) 1560 W
(b) 576 W
(c) 1.01
Explanation:
Voltage, V = 120 V
Current in dryer, I = 13 A
current in vacuum cleaner, i' = 4.8 A
(a) Power consumed by dryer,
P = V I = 120 x 13 = 1560 W
(b) Power consumed by vacuum cleaner
P' = V I' = 120 x 4.8 = 576 W
(c) Energy consumed by dryer
E = P x t = 1560 x 15 x 60 = 1404000 J
Energy consumed by the vacuum cleaner
E' = P' x t' = 576 x 40 x 60 = 1382400 J
the ratio of energies is
E : E' = 1404000 : 1382400 = 1.01
Answer:
New research reveals that glycans -- branched sugar molecules found in mucus -- can prevent bacteria from communicating with each other and forming infectious biofilms, effectively rendering the microbes harmless.
Explanation:
In physics, weight is a measure of the force exerted by gravity on a mass.
You probably know that you weigh less on the Moon than on Earth. For instance, if you weigh 100. pounds on Earth, you will weigh 16.6 pounds on the Moon. But, if your mass on Earth is 100 kg, your mass on the Moon is... also 100 kg. Because the amount of matter you have does not change from the Earth to the Moon, but the gravitational force on the Earth is stronger than on the Moon, so you weigh more on Earth.
You can think of gravity pulling a mass toward the center of an object like the Earth. It pulls a lot harder for more massive objects like the Earth than for the Moon. That's why there's a difference in weight.
As a caveat, adding energy or mass to an object will affect its mass. Additionally, general relativity informs us that when something as traveling very near the speed of light, the whole idea of mass equivalency is not exactly true...
