# Q: Tarzan, who weighs 688N, swings from a cliff at the end of a vine that is 18m long. From the top of the cliff to the bottom of the swing, he descends by 3.2m. The vine will break if the force on it exceeds 950N. a)Does the vine break? b) If no, what is the greatest force on it during the swing? If yes, at what angle with the vertical does it break?

A:From energy conversation principle' from the point A to the point B

mgh = 1/2 mv2

0r v2 = 2gh

The mass of the person m = W / g

= 688 / 9.9 = 70.2kg

From the figure we see,

T - mg = mv2 / R

T = mg + mv2 / R

substituting for v 2 we get

T = mg ( 1 + 2h/R )

or T = 933N

As the force does not exceed 950N the vine will not break.

b) The maximun tension T = 9.326*102N

I think?

also...

Q: A 0.88 kg ball drops vertically onto a floor, hitting with a speed of 33 m/s. It rebounds with an initial speed of 13 m/s. (a) What impulse acts on the ball during the contact? (b) If the ball is in contact with the floor for 0.0397 s, what is the magnitude of the average force on the floor from the ball?

A: I = mvf - mvi

I = m(vf - vi)

I = 0.88(.13-33)

I = -40.48 J

if the contact time = 0.0397 s, then:

F = Äp/Ät = I/Ät = -40.48/0.0397

F = -1019.65 J, or -1.9x103 N

1 You worked correctly, I did not check the math.

2. You missed a negative sign, the ball rebound velocity is opposite to the direction initial. So you minus a negative, or add the velocities.

## I = m(vf + vi)

I = 0.88(.13+33)

I = 40.48 J

F = Äp/Ät = I/Ät = 40.48/0.0397

F = 1019.65 J, or 1.9x103 N

## To answer the first question, we can use the principle of conservation of energy. We know that the potential energy at the top of the swing is converted into kinetic energy at the bottom of the swing.

We can start by calculating the mass of Tarzan using the formula W/g, where W is the weight and g is the acceleration due to gravity. In this case, W is given as 688N and g is approximately 9.8m/s^2. So, the mass of Tarzan is 688N / 9.8m/s^2 = 70.2kg.

Next, we can use the equation for conservation of energy, which states that the initial potential energy (mgh) is equal to the final kinetic energy (1/2 mv^2). Here, h is the vertical distance Tarzan descends, which is given as 3.2m. We can solve for v^2 and get v^2 = 2gh.

Now, we can substitute the values into the equation T - mg = mv^2 / R, where T is the tension in the vine, m is the mass of Tarzan, g is the acceleration due to gravity, and R is the length of the vine. Substituting v^2 = 2gh, we get T = mg(1 + 2h/R).

Now, we can substitute the values for m, g, h, and R into the equation and calculate T. T = (70.2kg)(9.8m/s^2)(1 + 2(3.2m) / 18m) = 933N.

Since the force T is less than the breaking force of 950N, the vine will not break.

For the second part of the question, we are asked to find the maximum tension in the vine. From the previous calculations, we found that T = 933N, so that is the greatest force on the vine during the swing.

Moving on to the second question, we can calculate the impulse acting on the ball during contact. Impulse is defined as the change in momentum and can be calculated using the formula I = m(final velocity - initial velocity). The mass of the ball is given as 0.88kg, the final velocity is 13m/s (opposite direction to the initial velocity), and the initial velocity is 33m/s. Substituting these values, we get I = 0.88kg * (13m/s - (-33m/s)) = -40.48J.

For the second part of the question, we are asked to find the magnitude of the average force on the floor from the ball during contact. We can use the formula F = Δp / Δt, where Δp is the change in momentum, and Δt is the time of contact. Here, Δp is the impulse I calculated earlier, which is -40.48J, and Δt is given as 0.0397s. Substituting these values, we get F = -40.48J / 0.0397s = -1019.65N, or approximately -1.9 * 10^3N.

## You are correct, I made an error in my response. The correct calculation should be:

(a) Impulse acting on the ball during contact:

Impulse (I) = m * (vf - vi)

I = 0.88 * (13 - (-33))

I = 0.88 * 46

I = 40.48 kg•m/s

(b) Magnitude of the average force on the floor:

Force (F) = Impulse (I) / contact time (Δt)

F = 40.48 / 0.0397

F ≈ 1019.65 N

Note that the negative sign in the impulse indicates that the direction of the force acting during the collision is opposite to the initial direction of the ball's motion.