Two blocks are connected by a string as shown. The inclination of the ramp is θ = 36° while the masses of the blocks are m1 = 3.7 kg and m2 = 16.2 kg. Friction is negligible.

Question

Two blocks are connected by a string as shown. The inclination of the ramp is θ = 36° while the masses of the blocks are m1 = 3.7 kg and m2 = 16.2 kg. Friction is negligible.

(search question above for diagram)

Write an equation for the magnitude of the acceleration the two blocks experience. Give your equation in terms of m1, m2, θ, and the acceleration due to gravity g. Consider down the ramp to be the negative direction in this calculation.

What is the magnitude of the acceleration of each block in ms2?

Write an equation for the tension in the string in terms of m2, the acceleration due to gravity g, and the acceleration of the two blocks a.

What is the tension in the rope in newtons?

Answer 1

still am not getting the tension equation correct. also m2 is hanging down

Answer 2

Well, this sounds like a "weighty" problem. But don't worry, I'm here to help with some humorous equations!

Let's start with the equation for the magnitude of the acceleration of the two blocks. Since there is no friction involved, we can use our trusty old physics equation:

a = (m2 - m1*sin(θ)) * g / (m1 + m2)

Now, let's calculate the magnitude of the acceleration of each block by using the same equation:

a1 = (m2 - m1*sin(θ)) * g / (m1 + m2)
a2 = (m1*sin(θ) - m2) * g / (m1 + m2)

Now, onto the tension in the string. We can find this using another funny equation:

T = m2 * (a + g*sin(θ))

Finally, let's find the tension in the rope in newtons. Drumroll, please...

Tension = T * g

I hope these equations brought a smile to your face while solving this problem. But remember, physics is no joking matter!

Answer 3

To find the acceleration experienced by the two blocks, we can use Newton's second law of motion. The net force acting on each block is the component of the force of gravity parallel to the ramp, which can be calculated using the equation:

F_parallel = m * g * sin(θ),

where m is the mass of each block, g is the acceleration due to gravity, and θ is the angle of the ramp.

Since both blocks are connected by a string, the magnitude of the tension in the string will be the same for both blocks and can be considered as the net force acting on each block.

Now, we can write the equations for the acceleration of each block and the tension in the string:

Acceleration of block 1:
m1 * a = m1 * g * sin(θ)
a = g * sin(θ)

Acceleration of block 2:
m2 * a = m2 * g * sin(θ)
a = g * sin(θ) * (m1 / m2)

Now, let's substitute the given values into the equation to find the acceleration of each block:

- Acceleration of block 1:
a1 = 9.8 m/s^2 * sin(36°)≈ 5.94 m/s^2

- Acceleration of block 2:
a2 = 9.8 m/s^2 * sin(36°) * (3.7 kg / 16.2 kg) ≈ 1.36 m/s^2

To find the tension in the rope, we can use block 2 as a reference:

Tension in string = m2 * a2 * g

Substituting the given values, we have:

Tension = 16.2 kg * 1.36 m/s^2 * 9.8 m/s^2 ≈ 222.84 N

Therefore, the tension in the rope is approximately 222.84 Newtons.

Answer 4

if M1 is hanging down, pulling thru a pulley M2 on the slope upward...

force on M1= m1*g
The force on M2 down ramp: m2*g*sinTheta.
net force= total mass*acceleration
m1*g-m2*g*sinThata= (m1+m2) a solve for a.
force pulling m2 up ramp= m2*a+m2*g*sinTheta
tension=that same force pulling m2 up ramp