Answer:
100 ÷ 9.58 = 10.44 (approximate answer)
This is another one of those muddy misleading questions, followed by
a muddy group of choices from which an answer must be selected.
a). is absurd. There's no such thing as a "balanced force", only
a balanced group of forces.
b). is probably the choice the question is aiming for.
c). is not so. The engines of an airplane do plenty of work lifting the plane
off the ground, although the force of the engines is never directed upward.
d). is really awkward. The object's motion is almost never the cause of the force.
The force is almost always the cause of the object's motion.
Now for the big 800-lb gorilla in the room: No moving object needs to be involved
in order for energy to be flowing or work to be getting done.
-- A radio wave radiates through space. Straighten out a wire coat-hanger and
stick it up in the air where the radio wave can pass by it. Electrical current flows
through the wire, and you can drain the electrical energy out the bottom of it.
-- A light bulb is shining. Some distance away, something it's shining on
gets warm, because of the heat energy that has shot across to it from the
light bulb and soaked into it.
-- A lightning bolt jumps from the ground to a passing cloud. Or, if you feel
more comfortable with it, a lightning bolt jumps from a cloud to the ground.
It doesn't matter. Either way, there's enough energy splashing around to
ignite houses, zap TVs and computers, melt concrete, vaporize water, and
light up a city. Although nothing is moving.
A catalytic converter is an exhaust emission control device that reduces toxic gases and pollutants in exhaust gas from an internal combustion engine into less-toxic pollutants by catalyzing a redox reaction (an oxidation and a reduction reaction).
Answer:
1. α = 67.28 rad/s²
2. a = -3.04 m/s²
3. t = 0.76 s
4. x = 5.28 m
5. vf = 5.78 m/s
Explanation:
1. Let's use the torque definition: τ = Iα.
The inertial moment of a sphere is I = (2/5)*m*R²
And we know that the torque is the cross product between force and distance, so we would have τ = FxR=|F|*|R|*sin(90)=|F|*|R|=μ*mg*R
Using these two definitions, we have: (2/5)*m*R²*α = μ*mg*R
So the magnitude of the angular acceleration would be: α = (5/2R)*μ*g = 67.28 rad/s².
2. The force definition is F = m*a, when a is the linear acceleration.
F = -μ*mg.
Then -μ*mg = m*a. Solving the equation for a we have: a = -μ*g = -3.04 m/s².
3. To get the time when the ball star to rolling we need to use angular and linear velocity equation.
- ωf = ω0 + α*t ; we assume that initial angular velocity is 0.
- vf = v0 - a*t; v0 is the initial linear velocity
The relation to pure rolling is: v = ω*R. Rewriting this equation in terms of time v0 - a*t = α*t*R, so t = v0/(α*R+a) = 0.76 s.
4. Using the distance equation: xf = x0 + v0*t - 0.5*a*t² = 5.28 m.
5. vf = v0 - a*t = 5.78 m/s.
Have a nice day!
