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masya89 [10]
3 years ago
13

A roller coaster has a mass of 650 kg. It sits at the top of a hill with height 78 m. If it drops from this hill, how fast is it

going when it reaches the bottom? (Assume there is no air resistance or friction.)
Physics
1 answer:
Leto [7]3 years ago
5 0

Answer:

The roller coaster is going at 39.1 m/s when it reaches the bottom

Explanation:

We use conservation of mechanical energy to solve this problem. So, we need to estimate the potential energy of the cart at the top of the hill while it is sitting steady there. Such will give us the cart initial Total Energy (TE) since its kinetic energy at that moment is zero (the cart is not moving, just sitting at the top of the hill).

Its initial potential energy (Ui) is therefore: Ui=m*g*h=650 * 9.8 * 78=496860 J

Notice also that all units given are in the SI system, (including the acceleration of gravity g) and therefore the answer is in Joules.

As we said, this initial potential energy equals the Total Energy  (TE) of the roller coaster because its initial Kinetic Energy (Ki) is zero.

When we look at what happens the instant the cart reaches the bottom, at that point it has all kinetic energy and zero potential energy (h is zero at the bottom of the hill). Final Kinetic Energy is by definition: Kf =\frac{1}{2} m*v^2=\frac{1}{2}650*v^2=325 v^2

Therefore, the conservation of mechanical energy tells us that:

ET_i=ET_F\\U_i+K_i=U_F+K_F\\496860 J +0J=0J+325v^2

We can solve for the final velocity of the roller coaster in this equation by solving for it in the equation:

496860 J +0J=0J+325v^2\\\\496860J=325v^2\\v^2=\frac{496860}{325} =1528.8\\v=\sqrt{1528.8} = 39.1 \frac{m}{s}

The velocity should result with units of meters/second since all quantities were given in SI units.

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3) A driver in a 1000-kg car traveling at 24 m/s slams on the brakes and skids to a stop. If the coefticient of friction between
Natali5045456 [20]

Answer:

A) 37 m

Explanation:

The car is moving of uniformly accelerated motion, so the distance it covers can be calculated by using the following SUVAT equation:

v^2 -u^2 = 2ad (1)

where

v = 0 m/s is the final velocity of the car

u = 24 m/s is the initial velocity

a is the acceleration

d is the length of the skid

We need to find the acceleration first. We know that the force responsible for the (de)celeration is the force of friction, so:

F=ma=-\mu mg

where

m = 1000 kg is the mass of the car

\mu = 0.80 is the coefficient of friction

a is the deceleration of the car

g = 9.8 m/s^2 is the acceleration due to gravity

The negative sign is due to the fact that the force of friction is against the motion of the car, so the sign of the acceleration will be negative because the car is slowing down. From this equation, we find:

a=-\mu g

And we can substitute it into eq.(1) to find d:

v^2 -u^2 = 2(\-mu g) d\\d= \frac{v^2-u^2}{-2 \mu g}=\frac{0-(24 m/s)^2}{-2(0.80)(9.8 m/s^2)}=36.7 m \sim 37 m

7 0
3 years ago
Find the final velocity
Verizon [17]

Answer: v = 4.4 m/s

Explanation:

In the absence of friction, the total mechanical energy will be constant

KE₀ + PE₀ = KE₁ + PE₁

0 + mg(6) = ½mv₁² + mg(5)

½mv₁² = mg(6 - 5)

v = √(2g(1)) = 4.4 m/s

3 0
3 years ago
The cylinder valve is open and the gas is collected and atmospheric pressure
jok3333 [9.3K]

Less gas will be collected because some of the gases will escape from the open cylinder valve.

Cylinders used to store carbon dioxide will have thicker walls than those of butane because of higher pressures.

<h3>What are compressed gases?</h3>

Compressed gases are gases which are compressed under high pressure in gas cylinders.

Cylinder valves are used to reduce the pressure of the compressed gases and in the process, some of the gas molecules escape.

Since the cylinder valve is open and the gas is collected at atmospheric pressure, less gas will be collected because some of the gases will escape.

Since, the carbon dioxide not liquefy under pressure compared to butane, the cylinders used to store carbon dioxide will have thicker walls than those of butane.

Learn more about compressed gases at: brainly.com/question/518065

4 0
2 years ago
If it takes 100 N to get a 10 kg object to accelerate at 10m/s/s, how much force will it take to get a 20 kg object to accelerat
yan [13]

Answer: C) 200 N

Explanation:

The force F is defined as:

F=m.a

Where:

m=20 kg is the mass of the object

a=10 m/s^{2} is the acceleration

Then:

F=(20 kg)(10 m/s^{2})

Finally:

F=200 N

Hence, the correct option is C.

7 0
3 years ago
A 1 pound bucket rests on a table. What is the support force exerted on the bucket by the table? What is the support force when
katrin2010 [14]

This question involves the concepts of equilibrium and Newton's third law of motion.

The support force will be "1 pound" for the empty bucket and the support force will be "6 pounds" after pouring water into it.

  • According to the condition of equilibrium, the sum of forces acting on a stationary object must be zero. Hence, the support force of the table will be equal to the total mass of the bucket.
  • According to Newton's Third Law of Motion every action force has an equal but opposite reaction force. Hence, the support force will be a reaction force to the weight of the bucket.

Therefore, the support force in each case will be equal to the total mass of the bucket:

Case 1 (empty bucket):

<u>support force = 1 pound</u>

<u></u>

Case 1 (water poured):

support force = 1 pound + 5 pound

<u>support force = 6 pound</u>

<u></u>

Learn more about equilibrium here:

brainly.com/question/9076091

8 0
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