1. A 2.5 kg mass at rest on a horizontal surface is acted upon by an applied horizontal force of 150 N. A frictional force of 100 N acts on the mass. How much work is done on the mass after 5 m?
I got 250 J but I'm not sure if that's correct.
2. A mass of 10 kg, initially at rest on a horizontal frictionless surface, is acted upon by a horizontal force of 25 N. What is the speed of the mass after it has moved 5.0 m?
I got 5 m/s for this but apparently that's incorrect.
3. a) A jet engine applies a force of 300 N horizontally to the right against a 50 kg rocket. The force of air friction 200 N. If the rocket is thrust horizontally 2.0 m, the kinetic energy gained by the rocket is:
I'm not sure how to find the answer for this one.
3. b) A jet engine applies a force of 300 N horizontally to the right against a 50 kg rocket. The force of air friction 200 N. If the rocket is thrust horizontally 2.0 m, the velocity of the rocket is:
Not sure how to answer this one either.
How should I solve these to get the correct answers? Help with any of them would be great!
1. yes ... 250 J is correct
2. kinetic energy = work ... 1/2 * m * v^2 = f * d
... find the work , then solve for the velocity
... 5 m/s seems correct ... maybe a significant figure issue?
3. similar to #2
... work on the rocket is "net force" multiplied by distance
Let's go through each question one by one:
1. To find the work done on the mass, we need to calculate the net force acting on it and multiply it by the distance traveled. The net force is the difference between the applied force and the frictional force:
Net force = Applied force - Frictional force
= 150 N - 100 N
= 50 N
Now we can calculate the work done:
Work done = Net force * Distance
= 50 N * 5 m
= 250 J
Your answer of 250 J is correct for question 1.
2. To find the speed of the mass, we need to use the work-energy theorem. The theorem states that the work done on an object is equal to the change in its kinetic energy. In this case, since the surface is frictionless, all the work done will go into changing the kinetic energy of the mass:
Work done = Change in kinetic energy
The work done is given by the applied force multiplied by the distance traveled:
Work done = Applied force * Distance
= 25 N * 5.0 m
= 125 J
Now we equate this to the change in kinetic energy:
Change in kinetic energy = 125 J
The change in kinetic energy can be calculated using the formula:
Change in kinetic energy = (final velocity)^2 - (initial velocity)^2
Since the mass is initially at rest, the initial velocity is 0. We can rearrange the equation to solve for the final velocity:
Change in kinetic energy = (final velocity)^2 - 0^2
125 J = (final velocity)^2
(final velocity)^2 = 125 J
Taking the square root of both sides:
final velocity = √(125 J) ≈ 11.2 m/s
So the correct answer for question 2 is approximately 11.2 m/s, not 5 m/s.
3a. To find the kinetic energy gained by the rocket, we need to calculate the net force and multiply it by the distance traveled. The net force is the difference between the thrust force and the force of air friction:
Net force = Thrust force - Force of air friction
= 300 N - 200 N
= 100 N
Now we can calculate the work done:
Work done = Net force * Distance
= 100 N * 2.0 m
= 200 J
The work done is equal to the kinetic energy gained by the rocket. So the correct answer for question 3a is 200 J.
3b. To find the velocity of the rocket, we can use the work-energy theorem:
Work done = Change in kinetic energy
The work done is given by the thrust force multiplied by the distance traveled:
Work done = Thrust force * Distance
= 300 N * 2.0 m
= 600 J
Now we equate this to the change in kinetic energy:
Change in kinetic energy = 600 J
The change in kinetic energy can be calculated using the formula:
Change in kinetic energy = 0.5 * mass * (final velocity)^2
Since the rocket has a mass of 50 kg, we can rearrange the equation to solve for the final velocity:
0.5 * 50 kg * (final velocity)^2 = 600 J
(final velocity)^2 = 600 J / (0.5 * 50 kg)
(final velocity)^2 = 24 m^2/s^2
final velocity = √(24 m^2/s^2) ≈ 4.9 m/s
So the correct answer for question 3b is approximately 4.9 m/s.
1. To calculate the work done on an object, you need to know the applied force, the displacement, and the angle between the direction of the applied force and the direction of displacement. In this case, the force and displacement are both horizontal, so the angle between them is 0 degrees.
The formula for work done is:
Work = Force * Displacement * cos(theta)
Given:
Applied force (F) = 150 N
Frictional force (f) = 100 N
Mass (m) = 2.5 kg
Displacement (d) = 5 m
To find the net force, subtract the frictional force from the applied force:
Net force = F - f
Next, calculate the acceleration of the mass using Newton's second law:
Acceleration (a) = Net force / Mass
Now, use the equation of motion to find the velocity (v) of the mass at the end of the displacement:
v^2 = u^2 + 2ad
Since the mass is initially at rest, the initial velocity (u) is 0.
v^2 = 2ad
v = sqrt(2ad)
Finally, calculate the work done using the equation:
Work = Force * Displacement * cos(theta)
Since cos(0) = 1, the cosine term can be omitted.
Plug in the numbers and calculate the work done:
Work = Net force * Displacement
2. The speed of an object after it has moved a certain distance can be found using the kinematic equation:
v^2 = u^2 + 2ad
Given:
Force (F) = 25 N
Mass (m) = 10 kg
Distance (d) = 5.0 m
To find the acceleration (a), use Newton's second law:
a = F / m
Since the initial velocity (u) is zero, the equation becomes:
v^2 = 0^2 + 2ad
v^2 = 2ad
Solve for v by taking the square root of both sides:
v = sqrt(2ad)
3a. To calculate the kinetic energy gained by an object, use the equation:
Kinetic energy (KE) = 1/2 * mass * velocity^2
Given:
Force (F) = 300 N
Frictional force (f) = 200 N
Mass (m) = 50 kg
Distance (d) = 2.0 m
First, calculate the acceleration (a) using Newton's second law:
a = (F - f) / m
Next, calculate the final velocity (v) after the given distance:
v^2 = u^2 + 2ad
Since the initial velocity (u) is zero, the equation becomes:
v^2 = 0^2 + 2ad
v^2 = 2ad
Finally, calculate the kinetic energy using the equation:
KE = 1/2 * m * v^2
3b. To find the velocity of the rocket after being thrust horizontally, you can use the same equation as in part 3a:
v^2 = u^2 + 2ad
Given:
Force (F) = 300 N
Frictional force (f) = 200 N
Mass (m) = 50 kg
Distance (d) = 2.0 m
First, calculate the acceleration (a) using Newton's second law:
a = (F - f) / m
Next, calculate the final velocity (v) after the given distance:
v^2 = u^2 + 2ad
Since the initial velocity (u) is zero, the equation becomes:
v^2 = 0^2 + 2ad
v^2 = 2ad
Solve for v by taking the square root of both sides:
v = sqrt(2ad)
I hope this helps you solve the problems and get the correct answers!