Referring to the image to the right, the mass of block 1 is m1 = 3.4 kg while the mass of block 2 is m2 = 8.6 kg. The coefficient of friction between m1 and the inclined surface is μ = 0.31. The inclined surface is at an angle θ = 31° above the horizontal. Part A) Write an equation for the magnitude of this system's acceleration. Use the variables from the problem statement together with g for acceleration from gravity in order to write your equation.

Part (b) Calculate the magnitude of the system's acceleration in m/s2.

a= 4.14 m/s²

Explanation

We calculate the weight component parallel to the displacement of the block:

We define the x-axis in the direction of the inclined plane , 25° to the horizontal.

W= m*g   : Total block weight

Wx= W*sen25°= m*g* sen25°

We apply Newton's second law :

∑F = m*a (Formula 1)

∑F : algebraic sum of the forces in Newton (N)

m : mass in kilograms (kg)

a : acceleration in meters over second square (m/s²)

Problem development

We apply the formula (1) to calculate the acceleration of the block:

∑Fx = m*a

Wx = m*a

m*g* sen25°  = m*a  : We divide by m on both sides of the equation

g* sen25° = a

a = g* sen25° = 9.8* sen25° = 4.14 m/s²

b

step-by-step explanation: a third of 24 is 8, 8 times 3 is 24 so 8 - 2 would be 6

in simple terms, the principle states that the buoyancy force on an object is equal to the weight of the fluid displaced by the object, or the density of the fluid multiplied by the submerged volume times the gravitational acceleration, g. this is also known as upthrust.