A baseball of mass m1 = 0.32 kg is thrown at a concrete block m2 = 6.25 kg. The block has a coefficient of static friction of μs = 0.71 between it and the floor. The ball is in contact with the block for t = 0.195 s while it collides elastically.

What is the minimum velocity the ball must have to make the block move?

force to move block=mu*m2*g

force*time=massball(2v)

v=force*time/2*massball=
= mu*m2*g*t/2m1

Well, you know what they say, "When in doubt, add a little humor!" So, here we go:

The minimum velocity the ball must have to make the block move depends on whether the block is in the mood to dance. You see, if the block is feeling particularly lazy and doesn't want to budge, it will demand a higher velocity from the ball. On the other hand, if it's feeling a little more adventurous, it might be willing to move with a lower velocity.

In this case, the coefficient of static friction becomes the judge, jury, and dance instructor for the block. With a coefficient of static friction of 0.71, the block is a bit of a drama queen and requires some persuasion to start dancing. So, you'll need to do some calculations to find the minimum velocity.

Take the kinetic friction equation and use it to determine the force of friction acting on the block: F_friction = μs * F_normal. The normal force (F_normal) is equal to the weight of the block, which is m2 * g, where g is the acceleration due to gravity.

Next, you'll want to find the impulse experienced by the block during the collision with the ball. Impulse is the change in momentum, which is equal to the mass of the ball (m1) times the change in velocity (Δv). Here, you can use the fact that the collision is elastic, so the change in velocity of the ball is twice the velocity of the block.

Now, the impulse experienced by the block is equal to the force of friction multiplied by the time of the collision. So, you can set up the equation: J = F_friction * t = Δp = 2 * m1 * Δv.

Plug in the values, solve for Δv, and voila! You'll have the minimum velocity the ball must have to make the block move. Just remember to have some patience and gently nudge the ball to warm up the block. Dance lessons are no joke, my friend!

To find the minimum velocity the ball must have to make the block move, we need to consider the forces acting on the block during the collision.

1. First, let's calculate the force of static friction between the block and the floor using the coefficient of static friction (μs) and the weight (mass x gravity).

Frictional force (Ff) = μs * Normal force

The normal force (Fn) is equal to the weight of the block:
Fn = m2 * gravity

The weight (W) is calculated as:
W = m2 * gravity

2. Next, let's calculate the impulse imparted to the block during the collision.

Impulse (J) = Change in momentum (m2 * Δv)

Since the ball and block collide elastically, the change in velocity (Δv) of the block is given by the negative of the change in velocity of the ball:
Δv = -2 * (velocity of the ball)

So, the impulse imparted to the block is:
J = m2 * (-2 * velocity of the ball)

3. The impulse is also equal to the average force (F) multiplied by the time of collision (t):
J = F * t

Using this equation, we can solve for the force (F):
F = J / t

4. Finally, the force required to overcome static friction and set the block in motion is equal to the force of static friction (Ff) calculated earlier.

Now we can set up an equation to solve for the minimum velocity of the ball:

F = Ff

J / t = μs * m2 * g

Plug in the values and solve for the velocity of the ball:

(-2 * velocity of the ball) / t = μs * m2 * g

velocity of the ball = - (μs * m2 * g * t) / 2

Substituting the given values:
velocity of the ball = - (0.71 * 6.25 * 9.8 * 0.195) / 2

Calculating the minimum velocity of the ball will give you the answer.

To determine the minimum velocity required to make the block move, we need to analyze the forces acting on the system and apply Newton's laws of motion.

Let's start by identifying the relevant forces:

1. Weight: The weight of the baseball and the concrete block can be calculated using the equation W = m * g, where m is the mass and g is the acceleration due to gravity (approximately 9.8 m/s^2). The weight acts vertically downward on each object.

2. Normal force: Since the block is on a flat surface and not moving vertically, the normal force exerted by the floor will be equal in magnitude and opposite in direction to the weight of the block. The normal force acts vertically upward.

3. Friction force: The friction force between the block and the floor opposes the motion of the block. It can be calculated using the equation f = μ * N, where μ is the coefficient of static friction and N is the normal force.

Now let's analyze the dynamics of the collision between the baseball and the block:

1. Impulse: During the collision, an impulse is applied to the block due to the force exerted by the baseball. This impulse is given by the equation J = Δp, where J is the impulse and Δp is the change in momentum. Since the collision is elastic, the momentum after the collision will be equal in magnitude but opposite in direction to the momentum before the collision.

2. Momentum conservation: We can use the principle of momentum conservation to relate the ball's initial momentum to the block's final momentum. Before the collision, the ball has momentum p = m * v, where m is the mass of the ball and v is its velocity.

After the collision, the ball rebounds in the opposite direction with the same speed, so its final momentum is -m * v. The block, initially at rest, gains momentum equal to the ball's initial momentum, so its final momentum is m * v.

Now, let's calculate the minimum velocity for the ball to make the block move:

1. Determine the normal force: Since the block is not moving vertically, the normal force is equal in magnitude to the weight of the block, which can be calculated as N = m2 * g.

2. Calculate the friction force: Using the formula f = μs * N, we can find the maximum static friction force between the block and the floor.

3. Apply Newton's second law: The net force acting on the block in the horizontal direction will be the friction force, which is equal in magnitude and opposite in direction to the force exerted by the ball. Since the net force F_net = ma, we can write the equation ΣF = F_ball - f = m2 * a, where a is the acceleration of the block.

4. Calculate the acceleration: Rearranging the equation, we have a = (F_ball - f) / m2.

5. Apply momentum conservation: The ball gains momentum equal to its initial momentum, so we can write m * v = m * (-v) + m2 * v_final, where v_final is the final velocity of the block.

6. Solve for minimum ball velocity: Rearranging the previous equation, we can isolate v by moving terms around, obtaining v = (m2 * v_final) / (m + m2).

By substituting this value of v into the equation for acceleration from step 4, we can obtain the minimum velocity the ball must have to make the block move.