An experimental rail car with a rocket mounted on it is free to slide on a rail that is so slippery it can be considered to be frictionless. The force that the rocket exerts on the car is given by: F(x)= Ax2N, 0396m where x is the position along the rail and A = 18.5. The mass of the rail car is 6390 kg. The rail car starts from rest. (a) What are the units of A? (b) What is the total work done on the rail car by the rocket in the first 448 m of travel? (answer: 4.98 x 107 J) (c) What is the speed of the rail car after the first 448 m of travel? (answer: 125 m/s)

An experimental rail car with a rocket mounted on it is free to slide on a rail that is so slippery it can be considered to be frictionless. The force that the rocket exerts on the car is given by: F(x)= Ax2N, 0396m where x is the position along the rail and A = 18.5. The mass of the rail car is 6390 kg. The rail car starts from rest. (a) What are the units of A? (b) What is the total work done on the rail car by the rocket in the first 448 m of travel? (answer: 4.98 x 107 J) (c) What is the speed of the rail car after the first 448 m of travel? (answer: 125 m/s)

Related questions

Q: A 4.0 kg toy car can move along an x axis. The figure gives Fx of the force acting on the car, which…

Q: A 1,959-kg car starts from rest at the top of a driveway 7.26 m long that is sloped at an angle of…

A: Given data: The mass, m=1959 kg The distance is d = 7.26 m The angle is θ=21° The force is F=2338 N…

Q: A box is released from rest at the top of a flat rough slope of length 20 metres that is inclined at…

Q: A 3 kg object moves along an x axis according to x (t) = 9 + 8 t + 7 t 2 +9 t 3, with x in meters…

Q: An electron is a subatomic particle (m = 9.11 x 10-31 kg) that is subject to electric forces. An…

A: First, we need to calculate the acceleration of the electron. We can use the equation of motion: v2…

Q: An electron is a subatomic particle (m = 9.11 x 10*31 kg) that is subject to electric forces. An…

Q: A 3.0 kg toy car can move along an x axis. The figure gives Fx of the force acting on the car, which…

Q: A car accident occurs when a car slides into another car at the base of a hill. Car A was…

Q: A 75-kg snowboarder has an initial velocity of 5 m/s and slides down a 92-m-long straight incline…

Q: A parachutist whose mass is 65 kg drops from a helicopter hovering 2500 m above the ground and falls…

A: Given Data:Mass of the person Height of the helicopter The proportionality constant when the…

Q: A parachutist whose mass is 80 kg drops from a helicopter hovering 1500 m above the ground and falls…

Q: Two boxes are placed on an inclined plane at angle a to the horizontal. The masses of the two boxes…

A: Consider the following diagram. It shows various forces on two boxess. On box 1, the forces are:…

Q: At a given instant A has the motion shown in (Figure 1). Figure 3 ft -1.5 ft- VA=3 ft/s -X A=6 ft/s²…

A: The disk doesn't slip. So that

Q: A woman pushes an initially stationary 11.3 kg gift up a 15.90 ramp a distance of 7.21 m. If she…

Q: The force acting on an object is given by F, = (6x - 10) N, where x is in meters. (a) Choose the…

Q: 2. An air track is set to be perfectly level on a lab table, and the glider (total mass 120 grams)…

Q: A 1,652-kg car starts from rest at the top of a driveway 7.03 m long that is sloped at an angle of…

Q: A horizontal force of magnitude F = 57.5 N pushes on a block of mass m = 4.7 kg. The block is on a…

A: The given situation can be represented as

Q: A parachutist whose mass is 85 kg drops from a helicopter hovering 2000 m above the ground and falls…

A: The objective of the question is to find out the total time taken by the parachutist to reach the…

Q: Chapter 05, Problem 010 GO A 0.180 kg particle moves along an x axis according to x(t) = - 14.0 +…

Q: 1 2 The figure shows an overhead view of a 0.029 kg lemon half and two of the three horizontal…

Q: A mass m is suspended from a massless spring of natural length 90 cm with the spring constant k = 10…

A: Given: The spring constant is 10 N/m. The natural length of the spring is 90 cm. The extension in…

Q: An electron is a subatomic particle (m = 9.11 x 10-31 kg) that is subject to electric forces. An…

Q: A small boat is crossing a lake on a windy day. During some interval of time, the boat undergoes the…

A: ∆r⇀ = 3.19 i⏜ + 2.89 j ⏜F→ = 261 i⏜ - 125 j⏜

Q: A theme park is planning out a new free-fall ride. The drop is almost perfectly frictionless, with a…

A: Given:- The height of the theme park is planning a new free-fall ride h = 190 m. The initial…

Q: The football's initial velocity comp ir resistance and any other noncon

A: The initial height of football, x-component of an initial velocity,…

Q: What is the coefficient of friction between the tires and the surface?

A: Giiven: m= 2500 kg Initial velocity =vi=14.0 m/s Final velocity= 0 m/s accelerartion due to…

Q: A small block slides down a frictionless track whose shape is described by y = (x^2) /d for x0.The…

Q: A block of mass m = 0.5 kg is kicked so that it slides up a ramp inclined at an angle θ = 30°. At…

Q: A bowling ball weighing 60.0 N initially moves at a speed of 4.20 m/s. How long must a force of 47.5…

Q: An electron is a subatomic particle (m = 9.11 x 10-31 kg) that is subject to electric forces. An…

Q: A 125 kg body sits at rest until 3 forces act up the body: F1 = 24.5 N @ 0o, F2 = 38.0 N @ 160o,…

Question

An experimental rail car with a rocket mounted on it is free to slide on a rail that is so slippery it can be considered to be frictionless. The force that the rocket exerts on the car is given by:

F(x)= Ax²N, 0<x<127m

1.38x10⁵ N, 127<x<396m

0, x>396m

where x is the position along the rail and A = 18.5. The mass of the rail car is 6390 kg. The rail car starts from rest.

(a) What are the units of A?

(b) What is the total work done on the rail car by the rocket in the first 448 m of travel? (answer: 4.98 x 107 J)

(d) Show that the rate of change of kinetic energy (K) of an object at a particular moment is given by dK/dt = Fv, where F is the net force exerted on the object at that particular moment and v is the speed of the object at that particular moment.

(e) Calculate the rate of change of the rail car’s kinetic energy at x = 123 m. (answer: 1.68 x 107 J/s)

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step 5

Step by step

Solved in 5 steps with 4 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

Two forces F, = -8.40i + 4.30j and F, = 7.50i + 5.30j are acting on an object with a mass of m = 7.80 kg. The forces are measured in newtons, i and j are the unit vectors. What is the magnitude of the object's acceleration? Submit Answer Tries 0/10
A force in the +x-direction with magnitude F(x) = 18.0 N - (0.530 N/m)x is applied to a 8.30 kg box that is sitting on the horizontal, frictionless surface of a frozen lake. F(x) is the only horizontal force on the box.
A particle moves in the horizontal xy plane. A variable force acts on the particle with expression (in newtons) given by F =(4.10y+3.10)ȷ^, where y is in meters. Assume that even the particle's trajectory is a straight line from the position (in meters) r0=2.80ı^ +2.30ȷ^ to the position (in meters) rf=2.80ı^ +6.30ȷ^. Calculate the work done by this trajectory force and its de in joules, with three digits answers. ** only numbers in the answer **
G=25
Tarzan, who weighs 777 N, swings from a cliff at the end of a 16.5 m vine that hangs from a high tree limb and initially makes an angle of 21.9° with the vertical. Assume that an x axis points horizontally away from the cliff edge and a y axis extends upward. Immediately after Tarzan steps off the cliff, the tension in the vine is 721 N. Just then, what are (a) the force from the vine on Tarzan in unit-vector notation, and (b) the net force acting on Tarzan in unit-vector notation? What are (c) the magnitude and (d) the direction (measured counterclockwise from the positive x-axis) of the net force acting on Tarzan? What are (e) the magnitude and (f) the direction of Tarzan's acceleration just then?
Imagine a skydiver with a mass of m jumping out of an airplane at an altitude of h. As the skydiver descends, they experience two forces: air resistance and gravity. The force of air resistance varies with time and is described by the following function, where t is the time in seconds since t e skydiver has jumped: vec 2 (F)(t) = (0.5t)ha (x) + (0.11 +0.3t)hat(y) a) Create a air free body diagrar for the skydiver at t = 2 seconds. b) - What is the net for e acting on the skydiver at t = 2 seconds? c) What i the magnitude of the acceleration of the skydiver at t = 2 seconds? Imagine a skydiver with a mass of m jumping out of an airplane at an altitude of h. As the skydiver descends, they experience two forces: air resistance and gravity. The force of air resistance varies with time and is described by the following function, where t is the time in seconds since the skydiver has jumped: Fair (t) = (0.5t)2 + (0.12 + 0.3t)ŷ a) Create a free-body diagram for the skydiver at t = 2 seconds.…
A ball with mass 0.75 kg is thrown upward with initial velocity 25 m/s from the roof of a building 20 m high. Assume there is a force due to |v| air resistance of magnitude directed opposite to the velocity, where 30 the velocity v is measured in m/s. NOTE: Use g=9.8 m/s² as the acceleration due to gravity. Round your answers to 2 decimal places. a) Find the maximum height above the ground that the ball reaches. Height: 51.89 m Time: 5.81 X b) Find the time that the ball hits the ground. seconds X c) Use a graphing utility to plot the graphs of velocity and position versus time. Edit
A parachutist whose mass is 90 kg drops from a helicopter hovering 1500 m above the ground and falls toward the ground under the influence of gravity. Assume that the force due to air resistance is proportional to the velocity of the parachutist, with the proportionality constant b₁ = 20 N-sec/m when the chute is closed and b₂ = 100 N-sec/m when the chute is open. If the chute does not open until the velocity of the parachutist reaches 35 m/sec, after how many seconds will the parachutist reach the ground? Assume that the acceleration due to gravity is 9.81 m/sec². The parachutist will reach the ground after (Round to two decimal places as needed.) seconds.
An electron is a subatomic particle (m = 9.11 x 10-31 kg) that is subject to electric forces. An electron moving in the +x direction accelerates from an initial velocity of +6.88 x 105 m/s to a final velocity of 2.30 x 106 m/s while traveling a distance of 0.0685 m. The electron's acceleration is due to two electric forces parallel to the x axis: F₁ = 7.84 x 10-17 N, and F2, which points in the -x direction. Find the magnitudes of (a) the net force acting on the electron and (b) the electric force F2. F₂ F₁ VO (a) Number i ! Units N (b) Number Units N eTextbook and Media -> C Σ > F2 F₁ וום 1 0> Assistance Used
An constant applied force of 40.1 N lifts an 2.50 kg mass straight up, resulting in a final speed of 3.6 m/s. What distance did the mass move if it was initially at rest?
A mysterious force acts on all particles along a particular line and always points towards a particular point P on the line. The magnitude of the force on a particle increases as the cube of the distance from that point, that is, F∝ r3, if the distance from the P to the position of the particle is r. It has been determined that the constant of proportionality is 0.23 N/m3, i.e. the magnitude of the force on a particle can be written as 0.23r3, when the particle is at a distance r from the force center. Find the magnitude of the potential energy, in joules, of a particle subjected to this force when the particle is at a distance 0.21 m from point P assuming the potential energy to be zero when the particle is at P. PE= ?
A bowling ball weighing 54.0 N initially moves at a speed of 5.60 m/s. How long must a force of 36.0 N be applied to the ball to stop it?