A 15-kg block is on a frictionless ramp that is inclined at 20° above the horizontal. It is connected by a very light string over an ideal pulley at the top edge of the ramp to a hanging 19-kg block, as shown in the figure. The string pulls on the 15-kg block parallel to the surface of the ramp. Find the magnitude of the acceleration of the 19-kg block after the system is gently released? A) 4.0 m/s² B) 3.8 m/s² C) 4.2 m/s² D) 4.5 m/s²

Question

Quizplus · Accepted Answer

The first step is to draw a free-body diagram of each block.

For the 15-kg block, there are two forces: the weight (mg) straight down and the tension in the string (T) parallel to the ramp. Because the ramp is frictionless, there is no normal force.

For the 19-kg block, there is only one force: the weight (mg) straight down.

Next, we can analyze the forces to find the acceleration of the system. Because the string is ideal, the tension is the same for both blocks. Therefore, we can set up an equation for the forces in the vertical direction:

T - (19 kg)(9.8 m/s^2) = (19 kg)a

Solving for T, we get:

T = (19 kg)(9.8 m/s^2 + a)

Because the tension is also the force accelerating the 15-kg block, we can set up another equation for forces in the horizontal direction:

T = (15 kg)a

Substituting the first equation into the second, we get:

(19 kg)(9.8 m/s^2 + a) = (15 kg)a

Solving for a, we get:

a = 4.0 m/s^2

Therefore, the answer is A: 4.0 m/s^2.

A 15-Kg Block Is on a Frictionless Ramp That Is