Frictionless Pulley: m1 = M2 * a/g Steel Ball Bearing: d = v*t + (1/2)*a*t^2

[shimizua]

There are actually 2 questions that i have

Homework Statement

First is
a frictionless pulley with zero mass is attached to the ceiling, in a gravity field of 9.80 m/s2. Mass M2=0.250 kg is being accelerated downward with a=1.40m/s2. calculate the mass m1.
Second is
A small steel ball bearing with a mass of 24.0g is on a short compressed spring. when aimed vertically released, the spring sends the bearing to a height of 1.27m. calculate the horizontal distance the ball would travel if the same spring were aimed 35.0 deg from the horizontal

Homework Equations

so not so much wanting the answer just the equations on how to do these so then i can figure it out myself. thanks

The Attempt at a Solution

 

[Kurdt]

For the first problem a free body diagram will help you enormously.

For the second problem you can find the initial velocity of the bearing from the info given and then use that with the kinematic equations to find the horizontal distance traveled if it was fired at an angle.

 

[baba89]

First question: The equation for a frictionless pulley is m1 = M2 * a/g. In this case, M2 is given as 0.250 kg and a is given as 1.40 m/s2. Therefore, m1 = 0.250 kg * (1.40 m/s2/ 9.80 m/s2) = 0.0357 kg. This is the mass of the object attached to the other side of the pulley.

Second question: The equation for a projectile in motion is d = v*t + (1/2)*a*t^2. In this case, the ball bearing is being launched vertically, so the initial velocity (v) is 0. The final distance (d) is given as 1.27 m and the acceleration (a) is due to gravity, which is -9.80 m/s2. Therefore, we can rearrange the equation to solve for time (t): t = √(2d/a) = √(2*1.27 m/9.80 m/s2) = 0.508 s.

Now, to find the horizontal distance the ball would travel, we can use the same equation with a horizontal initial velocity (vx) and solve for distance (dx). The angle of 35 degrees indicates that the horizontal velocity is vx = v*cos(35) = 0.866*v. Plugging this into the equation, we get dx = vx*t = 0.866*v*0.508 s = 0.439*v meters. We do not have enough information to calculate the initial velocity (v), but this equation shows us that the horizontal distance is dependent on the initial velocity and time.