How Far and How Fast Does the 25 kg Block Move?

[cdirk11]

A 25 kg block on a table with a pulley attached, slides along a frictionless surface. It is connected by a massless string to a 5.9 kg block hanging straight down off the table. Find the horizontal distance the 25 kg block moves when the 5.9 kg block descends a distance of .102 m. Also find the acceleration of the 25 kg block.

 

[Pyrrhus]

You could use

Newton's 2nd Law

$$\sum^{n}_{i=1} \vec{F}_{i} = m \vec{a}$$

and

$$W = \Delta K$$

 

[M98Ranger]

To find the horizontal distance the 25 kg block moves, we can use the equation d = (m2/m1) * h, where d is the horizontal distance, m1 is the mass of the hanging block, m2 is the mass of the sliding block, and h is the vertical distance the hanging block descends. Plugging in the given values, we get d = (5.9 kg/25 kg) * 0.102 m = 0.024 m.

To find the acceleration of the 25 kg block, we can use the equation a = (m2*g)/(m1 + m2), where a is the acceleration, m1 is the mass of the hanging block, m2 is the mass of the sliding block, and g is the acceleration due to gravity. Plugging in the given values, we get a = (5.9 kg*9.8 m/s^2)/(25 kg + 5.9 kg) = 0.774 m/s^2.

Therefore, the 25 kg block will move a horizontal distance of 0.024 m and will experience an acceleration of 0.774 m/s^2. This is because the hanging block exerts a force on the sliding block through the string, causing it to accelerate horizontally. The motion of the pulley also plays a role in the acceleration of the sliding block.