Acceleration Needed to Keep Block From Falling

In summary, to find the acceleration needed for a person to keep a block from falling when it is 20% more massive than the person, use the equation m_1a = -1.2m_1g and solve for a, resulting in an acceleration of 11.76 m/s^2. It is important to leave unknown quantities as variables in equations to avoid errors in calculations.

Homework Statement

a block 20% moe massive than yo uhangs from a rope. the other end of hte rpe goes over a massless frictionless pulley and dangles freely, with what acceleration must you climb th rope to keep the block from falling.

possible w = mg
f = ma
p = mv

The Attempt at a Solution

mass of the body = 1 kg (easy to work with)
mass of block = 1.2 kg

the block falls w/ -g

if i want to keep the block from falling i haev to counter the block falling at

g * mass of block = 11.76 m/s^2 * kg
i feel like the answer is wrong because of units...

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bump =P

You have the (almost) correct answer, but I would suggest you change your process a bit.

You're looking for the acceleration of 'you' so that the block does not move. So, you're main goal is:

$$\Sigma F = ma = 0$$

We can use $$m_1$$ for the person, and $$m_2$$ for the block. And we know
$$m_2 = 1.2 m_1$$
and the weight of the block is $$m_2 g$$

The equation will look like:
$$m_1a + m_2g = 0$$
$$m_1a = -m_2g$$

Substituting for $$m_2$$ we get:
$$m_1a = -1.2 m_1 g$$
divide by $$m_1$$ to get
$$a = -1.2g$$
Then solve using -9.8 for g
$$a = 11.76 m/s^2$$

Even though it may seem more complicated, it is generally easier and cleaner just to leave unknown quantities as the variables, i.e. don't substitute some random amount such as the 1 you used for m.

ah that makes sense how you got the units to end up correct, i like how you set it up, thanks!

You're welcome!

1. What is the acceleration needed to keep a block from falling?

The acceleration needed to keep a block from falling depends on the mass of the block and the force of gravity. The equation for calculating acceleration is a = F/m, where a is the acceleration, F is the force, and m is the mass. Therefore, the acceleration needed to keep a block from falling will vary depending on the specific variables in the scenario.

2. How does the height of the block affect the acceleration needed to keep it from falling?

The height of the block does not directly affect the acceleration needed to keep it from falling. However, the higher the block is from the ground, the longer the distance it will fall and therefore the greater the acceleration it will experience due to gravity. This means that the acceleration needed to keep the block from falling will need to be greater in order to counteract the force of gravity and prevent the block from falling.

3. What other factors can affect the acceleration needed to keep a block from falling?

Besides the mass and force of gravity, other factors that can affect the acceleration needed to keep a block from falling include air resistance, the incline of the surface the block is on, and any additional forces acting on the block (such as friction or external forces).

4. Can the acceleration needed to keep a block from falling ever be negative?

No, the acceleration needed to keep a block from falling cannot be negative. Acceleration is a vector quantity, meaning it has both magnitude and direction. In order for the block to not fall, the acceleration must be in the opposite direction of the force of gravity. This means that the acceleration needed to keep the block from falling will always be positive, in the direction opposite of the force of gravity.

5. How is the acceleration needed to keep a block from falling related to Newton's Laws of Motion?

The acceleration needed to keep a block from falling is related to Newton's Laws of Motion, specifically the second law which states that force is equal to mass times acceleration (F=ma). This means that in order to counteract the force of gravity and keep the block from falling, there must be an equal and opposite force acting on the block, resulting in a specific acceleration. This also relates to the third law, which states that for every action, there is an equal and opposite reaction. In this case, the action is the force of gravity pulling the block down, and the reaction is the force needed to keep the block from falling.

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