The world\'s lightest bird is the bee hummingbird; its mass is 1.6 g (less than

Question

The world's lightest bird is the bee hummingbird; its mass is 1.6 g (less than that of a penny). As shown in (Figure 1) , we design a perch for this bird that is supported by a magnetic force. The perch is 16 cm long, has a mass of 7.6 g , and contains a wire carrying a current I=4.0A. The perch is oriented at right angles to a uniform magnetic field that is just strong enough to support the perch and a bee hummingbird. What are the direction and magnitude of the magnetic field? (Solve part A down below in terms of mass)

SET UP The magnetic field must generate an upward force on the perch equal to the combined weight of the perch and bird.

SOLVE To find the direction of the magnetic field, we use the right-hand rule in reverse. The magnetic field must be perpendicular to the plane containing the magnetic force F B and I (that is, the plane of the page). We point our thumb in the direction of F B and imagine rotating the current arrow in the direction our fingers curl until it is perpendicular to the plane of the page. We find that it points into the paper, so that is the direction of B .

To find the magnitude of the magnetic field, we apply Newton's second law to the vertical (y) force components. The total mass is

M=mbird+mperch=1.6g+7.6g=9.2g=9.2×103kg

The equilibrium condition, Fy=0, gives

FBMg=0,IlB=Mg,

B=MgIl=(9.2×103kg)(9.8m/s2)(4.0A)(0.160m)=0.14T

Part A - Practice Problem:

How massive a bird could this perch support if the current were increased to I=4.6A?

Express your answer to two significant figures and include appropriate units.

m=____________________

Explanation / Answer

If mass is changed

Mg=iBl

M=(iBl)/g

Putting all values

We got

M=10.5 gram

Mass of bird=10.5-7.6=2.9g

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