A 34.0 kg block accelerates along a frictionless ramp that is inclined at 35 degrees.

Determine the acceleration of the block.

force down plane: mg*sinTheta

acceleration=forcedownplane/mass

To determine the acceleration of the block, we need to use Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and acceleration.

In this case, we can break down the forces acting on the block into two components: the force due to gravity and the perpendicular force. The force due to gravity can be separated into two components as well: the component parallel to the ramp (Fg_parallel) and the component perpendicular to the ramp (Fg_perpendicular).

The perpendicular component of the gravitational force is given by Fg_perpendicular = mg * cos(theta), where m is the mass of the block and theta is the angle of the ramp (35 degrees in this case). The parallel component of the gravitational force is given by Fg_parallel = mg * sin(theta).

Since the ramp is frictionless, the only force parallel to the ramp is the component of the gravitational force. Therefore, the net force acting on the object is equal to Fg_parallel.

Using Newton's second law, we can write the equation as follows:

F_net = m * a
Fg_parallel = m * a

Substituting the components of the gravitational force, we have:

mg * sin(theta) = m * a

Now we can solve for the acceleration (a):

a = g * sin(theta)

Where g is the acceleration due to gravity, which is approximately 9.8 m/s^2. Substituting the given values:

a = 9.8 m/s^2 * sin(35 degrees) ≈ 5.63 m/s^2

Therefore, the acceleration of the block is approximately 5.63 m/s^2.