We appreciate your visit to A 3 0 kg mass is attached to a spring with a spring constant of tex k 185 text N m tex resting on a. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
the speed of the incoming mass before the collision is approximately 2.14 m/s.
your horizontal speed relative to the ground while in the air is approximately 7.8 m/s.
Problem 1:
Given:
Mass of stationary mass (m1) = 3.3 kg
Spring constant (k) = 185 N/m
Mass of incoming mass (m2) = 1.5 kg
Maximum spring compression (x) = 0.8 m
Find: Speed of the incoming mass (v1)
Solution:
Conservation of Momentum:
Before the collision, the total momentum is the momentum of the incoming mass:
p_before = m2 * v1
After the collision, the total momentum is the sum of the momenta of both masses:
p_after = (m1 + m2) * v_combined
Since the collision is perfectly elastic, the total momentum is conserved:
p_before = p_after
m2 * v1 = (m1 + m2) * v_combined
Maximum compression and kinetic energy:
At the point of maximum compression, the combined mass (m1 + m2) comes to a momentary stop (v_combined = 0). The initial kinetic energy of the combined mass is converted to the potential energy stored in the compressed spring:
1/2 * k * x^2 = 1/2 * (m1 + m2) * v1^2
Solve for v1:
Substitute the given values and rearrange:
v1^2 = (k * x^2) / (m1 + m2)
v1 = sqrt((k * x^2) / (m1 + m2))
v1 = sqrt((185 N/m * (0.8 m)^2) / (3.3 kg + 1.5 kg))
v1 ≈ 2.14 m/s
Therefore, the speed of the incoming mass before the collision is approximately 2.14 m/s.
Problem 2:
Given:
Mass of sled (M1) = 200 kg
Speed of sled (v1) = 4.6 m/s
Mass of you (M2) = 90 kg
Your initial speed relative to sled (v2) = 3.2 m/s
Find: Your horizontal speed relative to the ground (v_final) while in the air
Solution:
Relative Velocity:
Your initial horizontal velocity relative to the ground is the sum of your velocity relative to the sled and the sled's velocity:
v_final = v1 + v2
v_final = 4.6 m/s + 3.2 m/s
v_final = 7.8 m/s
Therefore, your horizontal speed relative to the ground while in the air is approximately 7.8 m/s.
The probable question can be: A3.3 kg mass is attached to a spring of spring constant k = 183 N/m resting on a horizontal frictionless surface. The other end of the spring is fixed to a wall. A 1.5 kg mass is thrown toward the 3.3 kg mass and collides with it in a perfectly elastic collision. The maximum compression of the spring is a 80. cm. Find the speed of the incoming mass. Number m/s During the Iditarod race in Alaska, your sled gets detached from your sled dogs. The sled (M = 200 kg) moves at 4.6 m/s, headed for thin loe. You (m= 90 kg) jump backward off the sled with a speed of 3.2 m/s with respect to the sled. What is your horizontal spoed with respect to the ground while you are in the air? Number m/s
Thanks for taking the time to read A 3 0 kg mass is attached to a spring with a spring constant of tex k 185 text N m tex resting on a. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
