Question

If someone could answer these questions it would be greatly appreciated:

1. What is the MKS unit for energy?

2. What is the energy required to raise a 3kg mass 15m?

3. What is the minimum power required to move a 200kg elevator 5m between floors in 3 seconds

4. What is the kinetic energy of a 6kg bowling ball traveling 2 meters per second

5. How much current should a 60 watt light bulb draw from a 120V outlet

6. A 10 kg mass is accerlerated for 10s using a 1 hp motor. what is the resulting velocity.

7. A 10 amp current is flowing through a 20 ohm resistor. How much power is being dissipated by the resistor.

8. How much power is required to propel a 60kg cart up a 30 degree incline at a speed of 10 meters per second

9. How much energy has been used by a 1000 watt room heater when it has run for 1 hour.

10. The heating element of a car cigarette lighter is intended to provide 20 watts of power. If the lighter is operating off the 12 V car battery, how much current is flowing in the circuit?

11. The vector forces (2 Newton in the i direction + 3 Newton in the j direction) and  (1 Newton in the j direction + 5 Newton in the k direction) are applied to the same point. what is the magnitude of the total force applied to this point?

12. A 90 kg man stands on the end of a 2m long diving board. what is the maximum moment applied to any point on the diving board?

13. How much torque is required to raise a 10 kg bucket using a 0.2 m diameter winch?

14. The wheel base (distance between the front and rear wheels) of a 2000 kg car is 3m. If the center of mass of the car lies 1 meter behind the front wheels, what is the load on the front wheels?

17. the integral from 0 to 1 of (t+t^2)dt

Thanks in advance

Answer 1

1) Joules or J

2) E = m g h = 3*9.81*15=441.45 J

3) P = m g h/t = 200*9.81*5/3= 3270 W

4) KE = 1/2 mv^2 = 0.5*6*2^2 =12 J

5) P = I V

I = P/V = 60/120 = 0.5 A

6) 1 hp = 745.7 W

P= E/t

1/2 mv^2 = P t

0.5*10*v^2 = 745.7*10

v =sqrt(2*745.7)= 38.6 m/s

7) P = I^2 R = 10^2 *20 = 2000 W

8) P = F v

F = m g sin theta

P = 60*9.81*sin(30 degrees)*10= 2943 W

9) E = P t = 1000*(1*60*60)= 3.6E6 J

10) P = I V
I = po/V = 20/12 = 1.67 A

11)
sum = 2 i + 4 j + 5 k

mag = sqrt(2^2 + 4^2 + 5^2)= 6.7 N

12) moment = F d = m g d = 90*9.81*2=1765.8 Nm

13) torque = m g r = 10*9.81*0.1 = 9.81 Nm

14) torque about back wheels must equal zero

2000*2 - F*3 = 0

F = 4000/3=1333 N

17) integral of t + t^2 = t^2/2 + t^3/3 from 0 to 1 = 1/2 + 1/3 = 3/6 + 2/6 = 5/6