Static Equilibrium

There must be equal amounts of mass on both sides of the center of mass (or center of gravity) of a system.

• True
• False

If an object remains at rest, then the sum of both the external torques and the external forces on the object must be zero.

• True
• False

A croquet mallet balances when suspended from its center of mass, as shown in the left part of the figure. If you cut the mallet into two pieces at its center of mass, as shown in the right part of the figure, how do the masses of the two pieces compare? 

• The piece with the head of the mallet has the greater mass.
• The piece with the head of the mallet has the smaller mass.
• The masses are equal.

A mobile is shown in the figure. The horizontal supports have negligible mass. Assume that all the numbers given in the figure are accurate to two significant figures. What mass M is required to balance the mobile?

• 36 g
• 90 g
• 18 g
• 60 g

Tags

NGSS.HS-PS2-1

A uniform rod weighs 40 N and is 1.0 m long. It is hinged to a wall at the left end, and held in a horizontal position at the right end by a vertical string of negligible weight, as shown in the figure. What is the magnitude of the torque due to the string about a horizontal axis that passes through the hinge and is perpendicular to the rod? The hinge is very small with negligible friction.

• 5.0 N ∙ m
• 20 N ∙ m
• 10 N ∙ m
• 40 N ∙ m

To determine the location of the center of mass (or center of gravity) of a car, the car is driven over a scale on a horizontal floor. When the front wheels are over the scale, the weight recorded by the scale is 5800 N, and when the rear wheels are over the scale, the scale reads 6500 N. The distance between the front and rear wheels is measured to be 3.20 m. How far behind the front wheels is the center of mass located?

• 1.69 m
• 0.845 m
• 1.72 m
• 1.50 m

A uniform 40-N board supports two children weighing 500 N and 350 N.  If the support is at the center of the board and the 500-N child is 1.5 m from its center, how far is the 350-N child from the center?

• 1.5 m
• 2.7 m
• 2.1 m
• 1.1 m

Tags

NGSS.MS-PS2-2

NGSS.MS-PS2-4

An irregularly shaped object that is 10 m long is placed with each end on a scale. If the scale on the right reads 96 N while the scale on the left reads 71 N, how far from the left end is the center of gravity of this object?

• 7.4 m
• 4.3 m
• 5.7
• 14 m

A 15-kg child is sitting on a playground teeter-totter, 1.5 m from the pivot. What is the minimum distance, on the other side of the pivot, such that a 220-N force will make the child lift off the ground?

• 9.8 m
• 1.0 m
• 1.5 m
• 0.10 m

Tags

NGSS.MS-PS2-2

A 15-kg child is sitting on a playground teeter-totter, 1.5 m from the pivot. What is the magnitude of the minimum force, applied 0.30 m on the other side of the pivot, that is needed to make the child lift off the ground?

• 66 N
• 740 N
• 23 N
• 44 N

Tags

NGSS.MS-PS2-2