A large crate sits on the floor of a warehouse. Paul and Bob apply constant horizontal forces to the crate. The force applied by
Paul has magnitude 48.0 N and direction 61.0∘ south of west. How much work does Paul’s force do during a displacement of the crate that is 12.0 m in the direction 22.0∘ east of north?
1 answer:
Answer:
-570.4 J
Explanation:
Parameters given:
Force = 48N, 61° SW
Displacement = 12m, 22.0 NE
Work done is given by:
W = F*d*cosθ
To find θ:
θ = 61 + 90 + 22 = 172°
=> W = 48 * 12 * cos172
W = - 570.4 J
Hence, the work to be done is - 570.4J.
This value is negative because the applied force is opposite the direction of the displacement.
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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: