Question

if the blocks are released from rest, which way does the 10 kg block slide, and what is its acceleration? Enter a positive value if 10 kg block accelerates up the rump, and a negative value otherwise.

Answer 1

Suppose that θ=35∘

First, you need to set up equations for both blocks.

Let m1 be 10kg and m2 be 5kg and for our computations suppose right is positive and up is positive

For m1 the solution is:
Sigma Fx = ma 
T - m1gsin35 = m1a where T = tension 

For m2 
m2g - T = m2a 

Add the two equations together 

m1a + m2a = T-m1gsin35 + m2g - T 
a(m1 + m2) = m2g - m1gsin35 
a= (5*9.8 - 10*9.8*sin35)/(10 + 5) 
a= -0.48m/s/s 

Answer 2

The acceleration of the block is about 0.48 m/s² downward.

$\texttt{ }$

Further explanation

Newton's second law of motion states that the resultant force applied to an object is directly proportional to the mass and acceleration of the object.

$\boxed {F = ma }$

F = Force ( Newton )

m = Object's Mass ( kg )

a = Acceleration ( m )

Let us now tackle the problem !

$\texttt{ }$

Complete Question:

The ramp in the figure is frictionless. Suppose that  θ = 35°. If the blocks are released from rest, which way does the 10 kg block slide, and what is its acceleration? Enter a positive value if 10 kg block accelerates up the ramp, and a negative value otherwise. Express your answer to two significant figures and include the appropriate units.

Given:

mass of first block = m₁ = 10 kg

mass of second block = m₂ = 5 kg

angle of the slope = θ = 35°

Asked:

acceleration of first block = a = ?

Solution:

We will use Newton's Law of Motion to solve this problem as follows:

$\Sigma F = ( m_1 + m_2 )a$

$w_2 - w_1\sin \theta = ( m_1 + m_2 )a$

$m_2g - m_1g\sin \theta = ( m_1 + m_2 )a$

$\boxed{a = (\frac{ m_2 - m_1 \sin \theta } { m_1 + m_2 }) g}$

$a = (\frac{ 5 - 10 \sin 35^o } { 10 + 5 }) 9.8}$

$a \approx -0.48 \texttt{ m/s}^2$

$\texttt{ }$

Conclusion:

The 10 kg block slides 0.48 m/s² downward.

$\texttt{ }$

Learn more

• Impacts of Gravity : brainly.com/question/5330244
• Effect of Earth’s Gravity on Objects : brainly.com/question/8844454
• The Acceleration Due To Gravity : brainly.com/question/4189441
• Newton's Law of Motion: brainly.com/question/10431582
• Example of Newton's Law: brainly.com/question/498822

$\texttt{ }$

Answer details

Grade: High School

Subject: Physics

Chapter: Dynamics