The formulas used to analyze the horizontal and vertical motion of projectiles launched at an angle invlove and use of which fun
1 answer:
Answer:
Explanation:
The formula to analyze motion in the vertical (or y) dimension is
which says that the motion in the y-dimension is equal to the magnitude of the A vector times the sin of the angle.
The formula to analyze motion in the horizontal (or x) dimension is
which says that the motion in the x-dimension is equal t the mignitude of the A vector times the cosine of the angle.
Many times this is used to find the upwards velocity and the horizontal velocity when an overall velocity is given with an angle of inclination.
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a) 4 forces
b) 186 N
c) 246 N
Explanation:
a)
Let's count the forces acting on the bicylist:
1) Weight (): this is the gravitational force exerted on the bicyclist by the Earth, which pulls the bicyclist towards the Earth's centre; so, this force acts downward (m = mass of the bicyclist, g = acceleration due to gravity)
2) Normal reaction (N): this is the reaction force exerted by the road on the bicyclist. This force acts vertically upward, and it balances the weight, so its magnitude is equal to the weight of the bicyclist, and its direction is opposite
3) Applied force (): this is the force exerted by the bicylicist to push the bike forward. Its direction is forward
4) Air drag (): this is the force exerted by the air on the bicyclist and resisting the motion of the bike; its direction is opposite to the motion of the bike, so it is in the backward direction
So, we have 4 forces in total.
b)
Here we can find the net force on the bicyclist by using Newton's second law of motion, which states that the net force acting on a body is equal to the product between the mass of the body and its acceleration:
where
is the net force
m is the mass of the body
a is its acceleration
In this problem we have:
m = 60 kg is the mass of the bicyclist
is its acceleration
Substituting, we find the net force on the bicyclist:
c)
We can write the net force acting on the bicyclist in the horizontal direction as the resultant of the two forces acting along this direction, so:
where:
is the net force
is the applied force (forward)
is the air drag (backward)
In this problem we have:
is the net force (found in part b)
is the magnitude of the air drag
Solving for , we find the force produced by the bicyclist while pedaling: