Two blocks made of different materials, connected by a thin cord, slide down a plane ramp inclined at an angle $ \theta $ to the horizontal. If the coefficients of friction are $ \mu_A = 0.2 $ and $ \mu_B = 0.3 $ and if $ m_A = m_B = 5.0 $ $ \text{kg} $, determine: • Nerd Notes

AP Physics

Unit 2 - Linear Forces

Advanced

Mathematical

FRQ

Two blocks made of different materials, connected by a thin cord, slide down a plane ramp inclined at an angle $\theta = 32^\circ$ above the horizontal. If the coefficients of friction are $\mu_A = 0.2$ and $\mu_B = 0.3$ and if $m_A = m_B = 5.0$ $\text{kg}$ , determine:

Answer Feedback from Phy

Verfied Answer

Verfied Explanation 0 likes

Part (a): Acceleration of the blocks

Step	Derivation/Formula	Reasoning
1	$F_{g_x} = m g \sin \theta$	Calculate the component of gravitational force along the incline for one block.
2	$F_{f_A} = \mu_A m_A g \cos \theta$	Calculate the frictional force for block A. Frictional force is the product of the friction coefficient, mass, gravitational acceleration, and the cosine of the incline angle.
3	$F_{f_B} = \mu_B m_B g \cos \theta$	Calculate the frictional force for block B using its coefficient of friction.
4	$F_{\text{net}} = 2 F_{g_x} – F_{f_A} – F_{f_B}$	Net force is the sum of both gravitational components minus the frictional forces for both blocks.
5	$F_{\text{net}} = 2 (m g \sin \theta) – (\mu_A m g \cos \theta$ $+ \mu_B m g \cos \theta)$	Substitute the expressions for gravitational and frictional forces into the net force equation.
6	$F_{\text{net}} = 2 \cdot 5 \cdot 9.8 \sin(32) – (0.2 \cdot 5 \cdot 9.8 \cos(32)$ $+ 0.3 \cdot 5 \cdot 9.8 \cos(32))$	Substitute known values: $m = 5 \ \text{kg}, \ g = 9.8 \ \text{m/s}^2, \ \theta = 32^\circ$ .
7	$F_{\text{net}} = 52.012 – 8.3 – 12.5 =$ $31.2 \ \text{N}$	Calculate the net force acting on both blocks by subtracting the calculated frictional forces from the gravitational force component.
8	$a = \frac{F_{\text{net}}}{2m} = \frac{31.2}{2 \times 5}$	Use Newton’s second law $F = ma$ to solve for acceleration.
9	$\boxed{3.1 \ \text{m/s}^2}$	Calculate the acceleration of the blocks.

Part (b): Tension in the cord

Step	Derivation/Formula	Reasoning
1	$T = m_A g \sin \theta – F_{f_A} – m_A a$	Consider block A. The tension is the net force after subtracting the force needed for acceleration and friction.
2	$T = 5 \cdot 9.8 \sin(32) – (0.2 \cdot 5 \cdot 9.8 \cos(32)) – 5 \cdot 3.1$	Substitute known values for mass, gravitational acceleration, incline angle, friction coefficient, and acceleration.
3	$T = 26 – 8.3 – 15.6 = 2.1 \ \text{N}$	Calculate the tension in the cord between the blocks.
4	$\boxed{2.1 \ \text{N}}$	Express the tension in the cord as the final answer.

Need Help? Ask Phy To Explain

Just ask: "Help me solve this problem."

Just Drag and Drop!

Quick Actions ?

Topics in this question

Inclines, Linear Forces, Multi-Body Systems

Everything you need to master Physics — for free.

Meet Phy. The world's most advanced personal AI tutor.

Learning supercharged. 1000+ Physics problems + AI help.

7 AP Physics 1 units condensed into 8 short articles.

Proven tip, tricks, and hacks to help you score that coveted five.

Learn Physics, from scratch at your own pace.

Guaranteed performance boost in scores and understanding.

5 weeks for a 5. Expedited progress. Stellar Results.

1-to-1 lessons covering AP Physics from start to end.

Other 1-to-1 and group programs to accelerate Physics mastery.

AP Physics

Unit 2 - Linear Forces

Advanced

Mathematical

FRQ

You're a Pro Member

Supercharge UBQ

Part (a): Acceleration of the blocks

Part (b): Tension in the cord

Need Help? Ask Phy To Explain

Topics in this question

Join 1-to-1 Elite Tutoring

See how Others Did on this question | Coming Soon

Related Questions

5 More similar questions to the one you just solved

Discussion Threads

Leave a Reply Cancel reply

How to UBQ

1. UBQ Credits

2. Auto Track Stats

3. Point System

Phy helps customize your learning experience.

4. Question Explantions

Phy gives feedback.

4. Feedback