Question

An 8 kg block is placed at the top of a plane inclined by 30 degrees with a coefficient of kinetic friction of 0.1. What is the block's acceleration down the ramp?

A) 5-√3/2 m/s^2
B) 5-√5/2 m/s^2
C) 10-√3/2 m/s^2
D) 10-√5/2 m/s^2

Answer 1

Option (A), To find the block's acceleration down the ramp, calculate the net force acting on the block by resolving the force of gravity and subtracting the force of friction. Then, use Newton's second law to find the acceleration. The block's acceleration down the ramp is approximately 5 - √3/2 m/s^2.

Step-by-step explanation:

To find the block's acceleration down the ramp, we need to calculate the net force acting on the block.

1. First, resolve the force of gravity into components parallel and perpendicular to the ramp. The perpendicular component is mg * cos(30°) and the parallel component is mg * sin(30°).
2. The force of friction can be calculated as the product of the coefficient of kinetic friction and the perpendicular force of gravity: f_k = μ_k * (mg * cos(30°)).
3. The net force down the ramp is the difference between the parallel component of the force of gravity and the force of friction: F_net = mg * sin(30°) - f_k.
4. Finally, use Newton's second law (F = m * a) to find the acceleration down the ramp: a = F_net / m.

Using the given values, the block's acceleration down the ramp is approximately 5 - √3/2 m/s^2, which corresponds to answer choice A.