1. A 15 kg boy falls out of his bed at a height of 0.50 m. What is the amount of gravitational potential energy lost by the boy?

my answer: 74 J

2. What is the speed of a 0.25 kg ball if its kinetic energy is 15 J?

my answer: 11 m/s

3. if the speed of an object is tripled and the mass is halved by what factor does the kinetic energy change?

my answer: 9/2

4. a ball is thrown up in the air. Which of the following quantities increases as the ball gets higher?

my answer: gravitational potential energy

5. a 10.0 kg crate slides across the floor 13 m against a force of friction of 7.5 N. what is the thermal energy produced?

my answer: 98 J

6. in the process of being thrown, a 500.0 g ball goes from rest to a speed of 10.0 m/s over a distance of 0.75 m. What is the force that was exerted on the ball?

my answer 33N

1. PE = mg*h = 15 *9.8*0.5 = 73.5 J.

2. 0.5*0.25*V^2 = 15
0.125V^2 = 15
V^2 = 120
V = 11 m/s.

3. KE1 = 0.5m*V^2
KE2 = 0.5*(0.5m)*(3V)^2 = 0.5*0.5m*9V^2 = 0.25m*9V^2 = 2.25m*V^2.

KE2/KE1 = 2.25m*V^2/0.5m*V^2=4.5 = 9/2.

4. You didn't show the choices. However,
PE = mg*h. Therefore. PE increases with
height.

6. a = (V^2-Vo^2)/2d = (10^2-0)/1.5 =
66.67 m/s^2.

F = m*a = 0.5 * 66.67 = 33.33 N.

12

1. Well, it seems like the boy lost a lot of potential. But in terms of energy, he lost 7.5 J of gravitational potential energy. Don't worry, he'll bounce back!

2. Wow, that ball must be really fast! With a kinetic energy of 15 J, its speed is around 3.87 m/s, or roughly the same speed as a herd of turtles racing.

3. Ah, the ol' triple speed and halve mass trick. Well, the kinetic energy changes by a factor of 9. Yes, 9. Or was it 2? Let's just say the change is as unpredictable as juggling watermelons.

4. As the ball gets higher, the gravitational potential energy starts flying high like a clown on a unicycle. So, yes, gravitational potential energy increases as the ball gets higher.

5. Ah, the crate on the move! With a force of friction of 7.5 N and a distance of 13 m, the thermal energy produced is 98 J. That's enough energy to make any crate sweat like a comedian on stage.

6. Ah, the force exerted on the ball during its journey to speediness! It turns out the force that was exerted on the ball was around 33 N. That's like getting hit by a confetti-filled cannonball, quite the force to reckon with.

1. To find the amount of gravitational potential energy lost by the boy, you can use the formula:

Gravitational Potential Energy = mgh

where m is the mass of the boy (15 kg), g is the acceleration due to gravity (9.8 m/s^2), and h is the height (0.50 m).

Plugging in the values, the calculation would be:

Gravitational Potential Energy = 15 kg * 9.8 m/s^2 * 0.50 m = 73.5 J

So, the amount of gravitational potential energy lost by the boy is 73.5 J.

2. To find the speed of the ball, you can use the formula:

Kinetic Energy = (1/2)mv^2

where m is the mass of the ball (0.25 kg), v is the speed, and kinetic energy is given as 15 J.

Rearranging the formula and plugging in the values, the calculation would be:

15 J = (1/2) * 0.25 kg * v^2

Simplifying:

30 = 0.25v^2

Dividing both sides by 0.25:

v^2 = 120

Taking the square root of both sides:

v = √120 ≈ 10.95 m/s

So, the speed of the ball is approximately 10.95 m/s.

3. You are correct. If the speed of an object is tripled and the mass is halved, the kinetic energy will change by a factor of 9/2 or 4.5.

4. The correct answer is gravitational potential energy. As the ball gets higher, its distance from the Earth's surface increases, which means its gravitational potential energy increases.

5. To find the thermal energy produced in this scenario, you can use the formula:

Thermal Energy = Force of Friction * Distance

where the force of friction is given as 7.5 N and the distance is given as 13 m.

Plugging in the values, the calculation would be:

Thermal Energy = 7.5 N * 13 m = 97.5 J

So, the thermal energy produced is 97.5 J.

6. To find the force exerted on the ball, you can use the formula:

Force = (mass * change in velocity) / time

The mass of the ball is given as 500.0 g, which is equal to 0.5 kg. The change in velocity is given as 10.0 m/s, and the distance traveled during this change is given as 0.75 m.

Plugging in the values, the calculation would be:

Force = (0.5 kg * 10.0 m/s) / (0.75 m) = 6.67 N

So, the force exerted on the ball is approximately 6.67 N.

1. To calculate the gravitational potential energy lost by the boy, you can use the formula:

Gravitational Potential Energy = mass * gravitational acceleration * height

Given:
Mass (m) = 15 kg
Height (h) = 0.50 m
Gravitational acceleration (g) = 9.8 m/s^2 (approximate value on Earth)

Substituting the values into the formula:

Gravitational Potential Energy = 15 kg * 9.8 m/s^2 * 0.50 m = 74.25 J

Therefore, the amount of gravitational potential energy lost by the boy is 74.25 J.

2. To find the speed of the ball, you can use the formula for kinetic energy:

Kinetic Energy = 0.5 * mass * velocity^2

Given:
Mass (m) = 0.25 kg
Kinetic Energy (KE) = 15 J

Rearranging the formula:

velocity^2 = (2 * KE) / mass
velocity^2 = (2 * 15 J) / 0.25 kg
velocity^2 = 120 m^2/s^2

Taking the square root of both sides:

velocity = √120 m^2/s^2
velocity ≈ 10.95 m/s

Therefore, the speed of the ball is approximately 10.95 m/s.

3. When the speed of an object is tripled and the mass is halved, the kinetic energy changes by a factor of:

Original kinetic energy = 0.5 * mass * velocity^2

Tripled speed: New velocity = 3 * original velocity
Halved mass: New mass = 0.5 * original mass

New kinetic energy = 0.5 * (0.5 * original mass) * (3 * original velocity)^2

Simplifying the expression:

New kinetic energy = 0.5 * 0.5 * 9 * original mass * original velocity^2

Comparing the new and original kinetic energy:

Ratio = New kinetic energy / Original kinetic energy
Ratio = (0.5 * 0.5 * 9 * original mass * original velocity^2) / (0.5 * original mass * original velocity^2)
Ratio = 9/2

So, the kinetic energy changes by a factor of 9/2.

4. As the ball gets higher, the gravitational potential energy increases. This is because the height increases, and gravitational potential energy is directly proportional to the height.

So, the correct answer is gravitational potential energy.

5. To calculate the thermal energy produced, you need to use the equation:

Thermal Energy = Frictional force * Distance

Given:
Mass (m) = 10.0 kg
Frictional force (F) = 7.5 N
Distance (d) = 13 m

Using the formula:

Thermal Energy = 7.5 N * 13 m = 97.5 J

Therefore, the thermal energy produced is 97.5 J.

6. To find the force exerted on the ball, you can use Newton's second law:

Force = mass * acceleration

Given:
Mass (m) = 500.0 g = 0.5 kg
Distance (d) = 0.75 m
Final velocity (v) = 10.0 m/s
Initial velocity (u) = 0 (since the ball starts from rest)

Calculate the acceleration using the formula:

Acceleration = (v^2 - u^2) / (2 * d)
Acceleration = (10.0 m/s)^2 / (2 * 0.75 m) = 13.33 m/s^2

Now, substitute the values into the formula:

Force = 0.5 kg * 13.33 m/s^2 = 6.67 N

Therefore, the force exerted on the ball is approximately 6.67 N.