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Delvig [45]
3 years ago
8

You weigh 620 N. What would you weigh if the Earth were three times as massive as it is and its radius were four times its prese

nt value? Answer in units of N
Physics
1 answer:
Klio2033 [76]3 years ago
4 0

Answer:

if

Explanation:

weight is the force of gravity on a mass; the force of gravity is

F = G M m/r^2

F is grav force

G is the newtonian gravitational constant = 6.67 x 10^-11 Nm^2/kg^2

M=mass of the earth

m=mass of the object

r= radius of the earth

if the mass of the earth increases by a factor of 6, this will tend to increase the grav force by a factor of 6

if the radius increases by a factor of 5, this will change the grav force by a factor of 1/5^2 = 1/25

the total effect is 6/25 = 0.24; therefore, your weight would be 0.24 * 620N = 149N

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Either 175 N or 157 N depending upon how the value of 48° was measured from.    
You didn't mention if the angle of 48° is from the lug wrench itself, or if it's from the normal to the lug wrench. So I'll solve for both cases and you'll need to select the desired answer.    
Since we need a torque of 55 N·m to loosen the nut and our lug wrench is 0.47 m long, that means that we need 55 N·m / 0.47 m = 117 N of usefully applied force in order to loosen the nut. This figure will be used for both possible angles.    
Ideally, the force will have a 0° degree difference from the normal and 100% of the force will be usefully applied. Any value greater than 0° will have the exerted force reduced by the cosine of the angle from the normal. Hence the term "cosine loss".     
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U = F*cos(48)  
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So solving for F and calculating gives:  
U = F*cos(48)  
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If the 48° is from the lug wrench itself, that means that the force is 90° - 48° = 42° from the normal. So doing the calculation again (this time from where we started plugging in values) we get  
U/cos(42) = F  
117/0.743144825 = F  
157.4390294 = F    
Or 157 Newtons is required for this case.
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