By definition we have that the energy at the top of the ramp is equal to the energy at the bottom of the ramp. This is due to the principle of energy conservation.
We have then:
The energy at the top is only potential energy:
Where,
- <em>m: mass
</em>
- <em>g: acceleration of gravity
</em>
- <em>h: vertical height of the ramp
</em>
The energy when it falls is transformed into kinetic energy and therefore:
Where,
- <em>v: object speed.
</em>
Therefore we have:
Answer:
The potential energy is transformed into kinetic energy.
If two variables are inversely proportional, then when one increases, the other decreases, and vice versa. If a variable, y, is inversely proportional to a variable, x, then y = k/x, where k is the proportionality constant.
The motorbike reaches 100 km/h in 3.5 seconds
Explanation:
The motion of the motorbike is a uniformly accelerated motion (= constant acceleration), therefore we can use the following suvat equation:
where
v is the final velocity
u is the initial velocity
a is the acceleration
t is the time
For the motorbike in this problem,
u = 0 (it starts from rest)
is the final velocity
is the acceleration
Solving for t, we find the time it takes for the bike to reach that velocity:
Learn more about accelerated motion:
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a.
The work done by a constant force along a rectilinear motion when the force and the displacement vector are not colinear is given by:
where F is the magnitude of the force, theta is the angle between them and d is the distance.
The problen gives the following data:
The magnitude of the force 750 N.
The angle between the force and the displacement which is 25°
The distance, 26 m.
Plugging this in the formula we have:
Therefore the work done is 17673 J.
b)
The power is given by:
the problem states that the time it takes is 6 s. Then:
Therefore the power is 2945.5 W
Answer: Add an incline or grade to the road track.
Explanation:
Refer to the figure shown below.
When a vehicle travels on a level road in a circular path of radius r, a centrifugal force, F, tends to make the vehicle skid away from the center of the circular path.
The magnitude of the force is
F = mv²/r
where
m = mass of the vehicle
v = linear (tangential) velocity to the circular path.
The force that resists the skidding of the vehicle is provided by tractional frictional force at the tires, of magnitude
μN = μW = μmg
where
μ = dynamic coefficient of friction.
At high speeds, the frictional force will not overcome the centrifugal force, and the vehicle will skid.
When an incline of θ degrees is added to the road track, the frictional force is augmented by the component of the weight of the vehicle along the incline.
Therefore the force that opposes the centrifugal force becomes
μN + Wsinθ = W(sinθ + μ cosθ).
