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A steel ball rolls with a constant velocity on a tabletop 0.950 m high it rolls off and hit the ground 0.352 m from the edge of

sp2606 [1]

Answer:

0.799 m/s if air resistance is negligible.

Explanation:

For how long is the ball in the air?

Acceleration is constant. The change in the ball's height $\Delta h$ depends on the square of the time:

$\displaystyle \Delta h = \frac{1}{2} \;g\cdot t^{2} + v_0\cdot t$ ,

where

$\Delta h$ is the change in the ball's height.
$g$ is the acceleration due to gravity.
$t$ is the time for which the ball is in the air.
$v_0$ is the initial vertical velocity of the ball.

The height of the ball decreases, so this value should be the opposite of the height of the table relative to the ground. $\Delta h = -0.950\;\text{m}$ .
Gravity pulls objects toward the earth, so $g$ is also negative. $g \approx -9.81\;\text{m}\cdot\text{s}^{-2}$ near the surface of the earth.
Assume that the table is flat. The vertical velocity of the ball will be zero until it falls off the edge. As a result, $v_0 = 0$ .

Solve for $t$ .

$\displaystyle \Delta h = \frac{1}{2} \;g\cdot t^{2} + v_0\cdot t$ ;

$\displaystyle -0.950 = \frac{1}{2} \times (-9.81) \cdot t^{2}$ ;

$\displaystyle t^{2} =\frac{-0.950}{1/2 \times (-9.81)}$ ;

$t \approx 0.440315\;\text{s}$ .

What's the initial horizontal velocity of the ball?

Horizontal displacement of the ball: $\Delta x = 0.352\;\text{m}$ ;
Time taken: $\Delta t = 0.440315\;\text{s}$

Assume that air resistance is negligible. Only gravity is acting on the ball when it falls from the tabletop. The horizontal velocity of the ball will not change while the ball is in the air. In other words, the ball will move away from the table at the same speed at which it rolls towards the edge.

$\begin{aligned}\text{Rolling Velocity}&=\text{Horizontal Velocity} \\&= \text{Average Horizontal Velocity}\\ &=\frac{\Delta x}{\Delta t}=\frac{0.352\;\text{m}}{0.440315\;\text{s}}=0.0799\;\text{m}\cdot\text{s}^{-1}\end{aligned}$ .

Both values from the question come with 3 significant figures. Keep more significant figures than that during the calculation and round the final result to the same number of significant figures.

3 0

2 years ago

Determine which heat transfers below are due to the process of conduction. I) You walk barefoot on the hot street and it burns y

Rudik [331]

I) You walk barefoot on the hot street and it burns your toes.

The road is in direct contact with your skin. Thermal energy from the road will transfer to the bottom of your feet, then to the rest of your body. This is an example of conduction.

II) When you get into a car with hot black leather in the middle of the summer and your skin starts to get burned.

Just like in the previous example, the hot leather is in direct contact with your skin (I guess if you're going to drive naked). Thermal energy from the leather will transfe to your skin, then to the rest of your body. This is also conduction.

III) A flame heats the air inside a hot air balloon and the balloon rises.

The flame heats air directly at the bottom of the balloon. The warm air expands and becomes less dense. This will rise and let the unheated, denser air in the balloon fall down toward the flame. This is an example of the convection cycle.

IV) A boy sits to the side of a campfire. He is 10 feet away, but still feels warm.

The campfire heats air directly nearby. The warm air expands and moves away from the fire in all directions, leaving behind unheated, denser air to be heated up. Some of the warm air reaches the boy. This is another example of convection.

The answer is A) 1 and 2.

3 0

3 years ago

Read 2 more answers

A horizontal aquifer is overlain by 73.5 ft of water-saturated clay with a porosity of 0.4. The solid density of the clay partic

mr_godi [17]

Answer:

Explanation:

solution is in the attachment below

5 0

3 years ago

A 250 - ω resistor is connected in series with a 4.80 - μf capacitor. the voltage across the capacitor is vc=(7.60v)⋅sin[(120rad

galben [10]

<span>553 ohms The Capacitive reactance of a capacitor is dependent upon the frequency. The lower the frequency, the higher the reactance, the higher the frequency, the lower the reactance. The equation is Xc = 1/(2*pi*f*C) where Xc = Reactance in ohms pi = 3.1415926535..... f = frequency in hertz. C = capacitance in farads. I'm assuming that the voltage and resistor mentioned in the question are for later parts that are not mentioned in this question. Reason is that they have no effect on the reactance, but would have an effect if a question about current draw is made in a later part. With that said, let's calculate the reactance. The 120 rad/s frequency is better known as 60 Hz. Substitute known values into the formula. Xc = 1/(2*pi* 60 * 0.00000480) Xc = 1/0.001809557 Xc = 552.6213302 Rounding to 3 significant figures gives 553 ohms.</span>

6 0

3 years ago

Read 2 more answers

Describe the difference between contact forces and field forces.

Salsk061 [2.6K]

Contact forces has to be touching for it to be an actual force. A field force does not have to be touching but it does have to be acting on particles at different positions in a space.

8 0

3 years ago