AP Physics 1 8.3.B Buoyant Force

[Maximum number: 8]

In Scenario 1, a swimmer holds a block of mass m at rest in a tank of freshwater with density $\rho_{1}$ , as shown in Figure 1. The block is released from rest and accelerates upward with an initial acceleration $a_{1}$ . All frictional forces are negligible.

Figure 1

In Scenario 2, the swimmer holds the same block at rest in a tank of salt water with density $\rho_{2}$ , where $\rho_{2}>\rho_{1}$ . The swimmer again releases the block from rest, and the block accelerates upward with initial acceleration $a_{2}$ . All frictional forces are negligible.

(a)

Indicate whether $a_{1}$ is greater than, less than, or equal to $a_{2}$ by writing one of the following in your answer booklet.

- $a_{1}>a_{2}$

- $a_{1}<a_{2}$

- $a_{1}=a_{2}$ Justify your answer in terms of ALL forces exerted on the block in each scenario. Use qualitative reasoning beyond referencing equations.

[ 3 ]

A	For indicating $a_{1}<a_{2}$	Point A1
	For a justification that indicates that the blocks have the same weight or mass	Point A2
	For a justification that indicates that the salt water exerts a larger buoyant force than the freshwater exerts (or the freshwater exerts a smaller buoyant force than the saltwater exerts)	Point A3
	Example Response There are identical downward forces (mg) on the block in both liquids. Each submerged block also has an upward buoyant force. Because the buoyant force is proportional to the density of the fluid, the block in salt water has a larger buoyant force exerted on it. Therefore, the block in salt water has a larger net force and so has a larger acceleration.

(b)

Consider the general case where a block of mass m and volume V is completely submerged in a fluid of density $\rho$ .

Starting with Newton's second law, derive an expression for the initial upward acceleration a of the block when the block is released from rest. Express your answer in terms of $m, V, \rho$ , and physical constants, as appropriate. Begin your derivation by writing a fundamental physics principle or an equation from the reference information.

[ 3 ]

B	For a multistep derivation that includes Newton's second law	Point B1
	For indicating $\rho V g$ is the buoyant force	Point B2
	For a correct expression for the initial upward acceleration a, consistent with the indicated expression for buoyant force Scoring Note: A correct, isolated, final expression for a earns points B2 and B3.	Point B3
	Example Response $\begin{aligned} & \Sigma F=m_{\mathrm{sys}} a_{\mathrm{sys}} & F_{B}-m g=m a & \rho V g-m g=m a & a=\frac{\rho V g}{m}-g \end{aligned}$

(c)

Indicate whether the expression for the acceleration a you derived in part B is or is not consistent with the claim made in part A. Briefly justify your answer by referencing your derivation in part B.

[ 2 ]

C	For attempting to address the functional dependence between a and $\rho$ in the equation derived in part B Scoring Note: It is not necessary to use the functional dependence correctly to earn this point. The response only needs to use functional dependence language such as proportional, inversely proportional, related, numerator, and denominator, to relate a and $\rho$ .	Point C1
	For correctly using functional dependence to evaluate the relationship between a and $\rho$ consistent with the expression derived in part B and the claim made in part A	Point C2
	Example Response The expression for the acceleration a is consistent with part A. In part A, I said the acceleration would be larger in salt water because the density is greater. In my expression, the acceleration increases with increasing density because of the $\frac{\rho V g}{m}$ term.

AP Physics 1: Algebra-Based 8.3 B Describe the Buoyant Force Exerted on an Object Interacting with a Fluid Questions

Exam points

AP Physics 1: Algebra-Based 8.3 B Describe the Buoyant Force Exerted on an Object Interacting with a Fluid Questions question 1

Question (a)

Question (b)

Question (c)