Answer:
0.04225 Nm
Explanation:
N = Force applied = 5 N
= Coefficient of static friction = 0.65
d = Diameter of knob = 1.3 cm
r = Radius of knob = ![\frac{d}{2}=\frac{1.3}{2}=0.65\ cm](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7B2%7D%3D%5Cfrac%7B1.3%7D%7B2%7D%3D0.65%5C%20cm)
Force is given by
![F=N\mu\\\Rightarrow F=5\times 0.65\\\Rightarrow F=3.25\ N](https://tex.z-dn.net/?f=F%3DN%5Cmu%5C%5C%5CRightarrow%20F%3D5%5Ctimes%200.65%5C%5C%5CRightarrow%20F%3D3.25%5C%20N)
When we multiply force and radius we get torque
Torque on thumb
![\tau_t=F\times r\\\Rightarrow \tau_t=3.25\times 0.0065\\\Rightarrow \tau_t=0.021125\ Nm](https://tex.z-dn.net/?f=%5Ctau_t%3DF%5Ctimes%20r%5C%5C%5CRightarrow%20%5Ctau_t%3D3.25%5Ctimes%200.0065%5C%5C%5CRightarrow%20%5Ctau_t%3D0.021125%5C%20Nm)
Torque on forefinger
![\tau_f=F\times r\\\Rightarrow \tau_f=3.25\times 0.0065\\\Rightarrow \tau_f=0.021125\ Nm](https://tex.z-dn.net/?f=%5Ctau_f%3DF%5Ctimes%20r%5C%5C%5CRightarrow%20%5Ctau_f%3D3.25%5Ctimes%200.0065%5C%5C%5CRightarrow%20%5Ctau_f%3D0.021125%5C%20Nm)
The total torque is given by
![\tau=\tau_t+\tau_f\\\Rightarrow \tau=0.021125+0.021125\\\Rightarrow \tau=0.04225\ Nm](https://tex.z-dn.net/?f=%5Ctau%3D%5Ctau_t%2B%5Ctau_f%5C%5C%5CRightarrow%20%5Ctau%3D0.021125%2B0.021125%5C%5C%5CRightarrow%20%5Ctau%3D0.04225%5C%20Nm)
The most torque that exerted on the knob is 0.04225 Nm
The speed of the two boats are 7 miles per hour and 24 miles per hour.
Explanation:
Let the speed of the first boat be x miles per hour and second boat be x+17 miles per hour.
As they move at right angle to each other, this problem can be solved using Pythagoras theorem.
The two boats will form a right angle with hypotenuse 25 miles after one hour.
Applying the theorem we get,
![x^{2} +(x+17)^{2}=25^{2}](https://tex.z-dn.net/?f=%20x%5E%7B2%7D%20%2B%28x%2B17%29%5E%7B2%7D%3D25%5E%7B2%7D%20%20%20)
![2x^{2} +34x + 289=625](https://tex.z-dn.net/?f=%202x%5E%7B2%7D%20%2B34x%20%2B%20289%3D625%20)
![2x^{2} +34x - 336=0](https://tex.z-dn.net/?f=%202x%5E%7B2%7D%20%2B34x%20-%20336%3D0%20)
![(x+24)(x-7)=0](https://tex.z-dn.net/?f=%20%28x%2B24%29%28x-7%29%3D0%20)
∴ x= -24 and 7
As speed cannot be negative,
We get speed of first boat = 7 miles per hour and
Speed of second boat = 7+17 = 24 miles per hour.
Answer:
![Desired\ effect=1312.5\ W](https://tex.z-dn.net/?f=Desired%5C%20effect%3D1312.5%5C%20W)
The net effect on the laboratory is cooling of the space.
Explanation:
Given:
power used by the air conditioner, ![P_i=750\ W](https://tex.z-dn.net/?f=P_i%3D750%5C%20W)
coefficient of performance, ![COP=1.75](https://tex.z-dn.net/?f=COP%3D1.75)
We know that:
![\rm COP=\frac{desired\ effect}{Power\ consumed}](https://tex.z-dn.net/?f=%5Crm%20COP%3D%5Cfrac%7Bdesired%5C%20effect%7D%7BPower%5C%20consumed%7D)
<u>Therefore the cooling power capacity:</u>
![\rm Desired\ effect=COP\times power\ consumend](https://tex.z-dn.net/?f=%5Crm%20Desired%5C%20effect%3DCOP%5Ctimes%20power%5C%20consumend)
![Desired\ effect=1.75\times750](https://tex.z-dn.net/?f=Desired%5C%20effect%3D1.75%5Ctimes750)
![Desired\ effect=1312.5\ W](https://tex.z-dn.net/?f=Desired%5C%20effect%3D1312.5%5C%20W)
The net effect on the laboratory is cooling of the space.