Question

1. A person pushes on a doorknob with a force of 5.00 N perpendicular to the surface of the door. The doorknob is located 0.800 m from the axis of the hinges of the door. The door begins to rotate with an angular acceleration of 2.00 rad/s². What is the moment of inertia of the door about hinges?

Select one:

a. 6.50 kg.m²

b. 2.50 kg.m²

c. 12.5 kg.m²

d. 2.00 kg.m²

2. A dumbbell has a connecting bar of negligible mass. Find the location of its center of mass (X_CM) if the end masses m₁ and m₂ are 5.0 kg and 10.0 Kg, respectively. m₁ is located at 0.20 m and m₂ is located at 0.90 m on the x-axis.

Select one:

a. 0.67 m

b. 0.55 m

c. 0.61 m

d. 0.30 m

3.A crane lifts the 16,000-kg steel hull of a sunken ship out of the water. Determine the tension in the crane’s cable when the hull is fully submerged in water. Density of water = 1000 kg/m³. Density of steel = 7800 kg/m³.

Select one:

a. 6.4 X 10⁵ N

b. 1.4 X 10³ N

c. 1.4 X 10⁵ N

d. 2.4 X 10⁵ N

4.Three loops are observed on a string fixed at both ends as it vibrates at a frequency of 180 Hz. The fundamental frequency of the string is

Select one:

a. 30 Hz

b. 20 Hz

c. 90 Hz

d. 60 Hz

5.A golfer drives a 0.046 kg ball from an elevated tee, giving the ball a horizontal speed of 40.0 m/s. If the during of contact is 1.00 X 10^–3 s, what is the magnitude of the average force exerted by the club on the ball during this time?

Select one:

a. 7800 N

b. 3800 N

c. 1840 N

d. 1200 N

6.An object of mass 2.00 kg starts at rest from the top of a smooth inclined plane (no friction) of height 20.0 m. What is the speed of the object as it reaches the bottom of the inclined plane?

Select one:

a. 15.6 m/s

b. 19.8 m/s

c. 12.4 m/s

d. 17.1 m/s

7.A man is holding an 8.00-kg vacuum cleaner at arm’s length, a distance of 0.550 m from the shoulder. What is the torque on the shoulder joint if the arm is horizontal?

Select one:

a. 14.5 N.m

b. 4.40 N.m

c. 0.242 N.m

d. 43.1 N.m

Answer 1

(1) Moment of force, T = 5.0 * 0.8 = 4.0 N*m

Suppose,

I = Moment of inertia of the door about the hinges.

= angular acceleration = 2.0 rad/s^2

Now -

T = I*

=> I = T / = 4.0 / 2.0 = 2.0 kg*m^2

Hence, option (d) is the correct answer.

(2) Center of mass = (m1*r1 + m2*r2) / (m1 + m2) = (5*0.2 + 10*0.9) / (5 + 10) = (1.0 + 9.0) / 15 = 0.67 m

Hence, option (a) is the correct answer.

(3) Volume of the steel hull, V = 16000 / 7800 m^3 = 2.05 m^3

So,

Tension in the crane's cable, T = m*g - V*1000*g

= 16000*9.8 - 2.05*1000*9.8

= 156800 - 20090 = 136710 N = 1.4 x 10^5 N

Hence, option (c) is the correct answer.

(4) Fundamental frequency = 180 / 3 = 60 Hz

Hence, option (d) is the correct answer.