**Problem Statement:**Position vector of a particle of mass \( m = 5 \, \text{kg} \) is given by \[ \mathbf{r}(t) = 3t^3 \mathbf{i} + 5t \mathbf{j} - 7t^2 \mathbf{k} \]. What is its linear momentum at \( t = 2 \, \text{s} \)?**Options:** - \( \mathbf{G} = 180\mathbf{i} + 0\mathbf{j} - 140\mathbf{k} \, \text{kg} \cdot \text{m/s} \)- \( \mathbf{G} = 36\mathbf{i} + 5\mathbf{j} - 28\mathbf{k} \, \text{kg} \cdot \text{m/s} \)- \( \mathbf{G} = 0\mathbf{i} + 0\mathbf{j} + 0\mathbf{k} \, \text{kg} \cdot \text{m/s} \)- \( \mathbf{G} = 180\mathbf{i} + 25\mathbf{j} - 140\mathbf{k} \, \text{kg} \cdot \text{m/s} \)**Explanation:**To find the linear momentum \( \mathbf{G} \) of the particle, we need to follow these steps:1. **Find the velocity vector \( \mathbf{v}(t) \) by differentiating the position vector \( \mathbf{r}(t) \) with respect to time \( t \)**: \[ \mathbf{v}(t) = \frac{d\mathbf{r}(t)}{dt} = \frac{d}{dt} \left( 3t^3 \mathbf{i} + 5t \mathbf{j} - 7t^2 \mathbf{k} \right) \] Differentiating each term: \[ \mathbf{v}(t) = 9t^2 \mathbf{i} + 5 \mathbf{j} - 14t \mathbf{k} \]2. **Evaluate the velocity vector at \( t = 2 \, \text{s} \)**: \[ \mathbf{v}(2) =

Given data: m = 5 kg position vector, r(t) = 3t3i +5j - 7t2k time, t= 2s

Position vector of a particle of mass m = 5 kg is given by r(t) = 3t³i+5j - 7t²k. What is its linear momentum at t = 2 s? G = 180i+0j 140k kg.m/s G = 36i + 5j - 28k kg.m/s + 0k kg.m/s G = 180i + 25j - 140k kg.m/s OG=0i+0j

Position vector of a particle of mass m = 5 kg is given by r(t) = 3t³i+5j - 7t²k. What is its linear momentum at t = 2 s? G = 180i+0j 140k kg.m/s G = 36i + 5j - 28k kg.m/s + 0k kg.m/s G = 180i + 25j - 140k kg.m/s OG=0i+0j

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

See similar textbooks

Related questions

Q: There are two springs attached to a mass with an unknown weight. The springs have a stiffness of k =…

A: Given that , μ=50N/mxo=5m h=4m

Q: a) Determine the z component of the angular momentum HP of particle A about point P using scalar…

Q: Two objects are connected by a light string passing over a light, frictionless pulley as shown in…

A: Given Data, m1 = 7 Kg m2 = 3 Kg Height, h =2.6 m To find :- a) Speed of mass, m2 just as mass m1…

Q: Figure mOA 2m 1.5m 6 m/s 3m 2m o 15 m 2 m 1m 1 of 1 > ▾ Part A Determine the x, y, z components of…

A: To find: The x, y, and z components of angular momentum. Given: The mass of the particle is m=4.4…

Q: Consider a satellite around Earth in an elliptic orbit. At a point in its orbit, the radius (in km)…

Q: Two objects are connected by a light string passing over a light, frictionless pulley as shown in…

A: Mass of m1 block = 5.20 kgMass of m2 block = 3.0 kgHeight of m1 block from table, h = 2.60 m The…

Q: A barbell consists of two small balls, each with mass, m at the ends of a very low mass rod of…

Q: A 0.45 kg tetherball is attached to a pole and rotating in a horizontal circle of radius r₁ = 1.4 m…

Q: Determine kinetic energy of a 10 lb mass moving at a velocity of 5 ft/sec. Provide your answer in Ib…

Q: A 100-kg box is towed to move horizontally from rest by a constant force P=200 N. The kinetic…

A: Given:m=100 KgP=200 Nμk=0.1θ=30 deg

Q: A block of mass m₁ = 20.4 kg is on a frictionless table to the left of a second block of mass m₂ =…

A: Given: Mass of the block on the left side, m1=20.4kg Mass of the block on the right side, m2=21.7kg…

Q: A dog runs at 0.85 m/s of velocity towards a cat which stays at rest. The dog accidently collides…

Q: AW disk = 5 lb disk is travelling around in a circle of radius r₁ with an initial tangential…

A: The weight of the disk, Wdisk = 5 lbThe tangential velocity of the disk, vB1 = 5 ft/sThe velocity of…

Q: Since you are studying mechanics, you decide to consider what Isaac Newton learned by sitting under…

Q: A happy kangaroo leaps vertically upward at a time t = 0. At time t = 0.50 s the kangaroo is at a…

Q: 1. A chain of blocks is moving upward at 3 m/s. The tension in the cable connected to the top of the…

A: Given data with suitable variable is shown below. v=3 m/sT0=800 N It is required to determine the…

Q: A body has an initial linear momentum of (30i – 50j) kgm/s. A force of (6i + 10j) N is applied to…

Q: Mechanics question 2: Figure 1.2 shows a ball of mass m =3 kg, which is released from rest at point…

A: Weight of the ball, W = 481 Nmass of the ball, m = W/g = 49.031 kgBC = 1000 cm = 10 mThe vertical…

Q: A mass of 3 kg has the position vector (5i + 2j) m and a linear velocity of (30i – 50j) m/s. What is…

Question

**Problem Statement:**

Position vector of a particle of mass \( m = 5 \, \text{kg} \) is given by
\[ \mathbf{r}(t) = 3t^3 \mathbf{i} + 5t \mathbf{j} - 7t^2 \mathbf{k} \].
What is its linear momentum at \( t = 2 \, \text{s} \)?

**Options:**

- \( \mathbf{G} = 180\mathbf{i} + 0\mathbf{j} - 140\mathbf{k} \, \text{kg} \cdot \text{m/s} \)
- \( \mathbf{G} = 36\mathbf{i} + 5\mathbf{j} - 28\mathbf{k} \, \text{kg} \cdot \text{m/s} \)
- \( \mathbf{G} = 0\mathbf{i} + 0\mathbf{j} + 0\mathbf{k} \, \text{kg} \cdot \text{m/s} \)
- \( \mathbf{G} = 180\mathbf{i} + 25\mathbf{j} - 140\mathbf{k} \, \text{kg} \cdot \text{m/s} \)

**Explanation:**

To find the linear momentum \( \mathbf{G} \) of the particle, we need to follow these steps:

1. **Find the velocity vector \( \mathbf{v}(t) \) by differentiating the position vector \( \mathbf{r}(t) \) with respect to time \( t \)**:
\[ \mathbf{v}(t) = \frac{d\mathbf{r}(t)}{dt} = \frac{d}{dt} \left( 3t^3 \mathbf{i} + 5t \mathbf{j} - 7t^2 \mathbf{k} \right) \]

Differentiating each term:
\[ \mathbf{v}(t) = 9t^2 \mathbf{i} + 5 \mathbf{j} - 14t \mathbf{k} \]

2. **Evaluate the velocity vector at \( t = 2 \, \text{s} \)**:
\[ \mathbf{v}(2) =

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

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.

Similar questions

F A block of mass of 2kg is being pushed by of force F = 10 N at an angle of 0 = 30° to the horizontal. If the block starts from rest, what is its speed after it has travelled 5 meters Without friction, v = m/s With μk m/s - With Uk m/s 0.25, v= What if it starts with an initial speed of 5 m/s Without friction, v = m/s = BY UBC Engineering 0.25, v=
Which of the following is the most ideally constructed momentum-impulse diagram for the system of golf ball and golf club?
Figure 4 shows a trolley of mass 6.12 kg passing through point A with a velocity of 6 m/s. It slides down a rail to point C. From A to C, 250 J of energy is lost due to friction. What is the equation used to find the velocity of the trolley at point C ?
A 2 kg object is located relative to an axis that passes through the origin by the following position vector. r = -5î+ 2) + 7k The velocity vector that describes the object's motion at that time is given as v=î-3ĵ-5k Calculate the angular momentum vector for the object.
h L/2 L/4 MR Ms A horizontal rod of length L and mass MR = 2.6 kg is used to hang a sign on a wall. The right end of the rod is attached to the wall by a hinge. A wire having tension T runs from the center of the rod to a place on the wall a distance h above the hinge as shown. The wire makes an angle 0 = 25° with the rod. The sign has mass Ms = 0.867 kg and hangs distance L/4 from the end of the rod. The system is in equilibrium. What is the tension T in the wire that runs between the wall and the rod? T = 60.35 N %3! T = 42.22 N %3D T = 14.08 N O T = 90.54 N T = 30.19 N %3! What is Fy, the vertical component of the force that the hinge exerts on the right end of the rod? A positive answer indicates an upward force and a negative answer indicates a downward force. Hint: Balance torques about an axis through the center of the rod. O Fy = -4.25 N Fy = 4.25 N Fy = -8.51 N Fy = -6.38 N Fy = 8.51 N
2. Which of the following momentum equations about B is CORRECT for the system of the golf ball and the golf club?