Question

The block shown in (Figure 1) has mass m = 7.0 kg and lies on a fixed smooth frictionless plane tilted at an angle θ = 24.5 ∘ to the horizontal.

Determine the acceleration of the block as it slides down the plane.
Express your answer to three significant figures and include the appropriate units.

Answer 1

To find the acceleration of the block, the gravitational force component along the plane is used. Since the plane is frictionless, the net force equals this component. Calculating this for the given mass and angle, the block's acceleration is approximately 3.98 m/s².

Step-by-step explanation:

To determine the acceleration of a block sliding down an incline, we use the equation for the component of the gravitational force acting along the incline:

F = m * g * sin(θ)

Here, m is the mass of the block, g is the acceleration due to gravity (9.81 m/s²), and θ is the angle of the incline. As there is no friction, the net force on the block is equal to the component of the gravitational force along the incline. To find the acceleration a, we use Newton's second law:

F = m * a

Therefore, the acceleration a is given by:

a = F / m = (m * g * sin(θ)) / m

Substituting the values, we get:

a = (7.0 kg * 9.81 m/s² * sin(24.5°)) / 7.0 kg = 9.81 m/s² * sin(24.5°)

After calculating, the acceleration a ≈ 3.98 m/s² (rounded to three significant figures).