Question

A spring is compressed and a mass is placed in front of it. The spring is released, sending the mass up a frictionless ramp. The mass slides up the ramp, then across a rough horizontal surface until friction brings it to rest. Values: m = 2.50 kg, k = 2.00 N/m, x = 0.550 m, h = 8.50 m, Î¼k = 0.425. a) Find the velocity of the mass just after release, before it starts up the ramp. (5 points) b) Find the velocity of the mass at the top of the ramp, just before it reaches the rough surface. (7 points) c) Find the horizontal distance, d, where the mass is brought to rest by friction. (5 points) d) What is the amount of energy dissipated by friction? (3 points)

          A spring is compressed and a mass is placed in front of it. The spring is released, sending the mass up a frictionless ramp. The mass slides up the ramp, then across a rough horizontal surface until friction brings it to rest.

Values: m = 2.50 kg, k = 2.00 N/m, x = 0.550 m, h = 8.50 m, Î¼k = 0.425.

a) Find the velocity of the mass just after release, before it starts up the ramp. (5 points)
b) Find the velocity of the mass at the top of the ramp, just before it reaches the rough surface. (7 points)
c) Find the horizontal distance, d, where the mass is brought to rest by friction. (5 points)
d) What is the amount of energy dissipated by friction? (3 points)

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Added by Maria L.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Prachi Joshi

03/20/2022

Step 1

Given: - Mass, m = 2.50 kg - Spring constant, k = 2.00 N/m - Compression of the spring, x = 0.550 m Using the formula for potential energy stored in the spring: \[ \frac{1}{2} k x^2 = \frac{1}{2} m v^2 \] Substitute the given values: \[ \frac{1}{2} \times 2.00 Show more…

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A spring is compressed and a mass is placed in front of it. The spring is released, sending the mass up a frictionless ramp. The mass slides up the ramp, then across a rough horizontal surface until friction brings it to rest. Values: m = 2.50 kg, k = 2.00 N/m, x = 0.550 m, h = 8.50 m, Î¼k = 0.425. a) Find the velocity of the mass just after release, before it starts up the ramp. (5 points) b) Find the velocity of the mass at the top of the ramp, just before it reaches the rough surface. (7 points) c) Find the horizontal distance, d, where the mass is brought to rest by friction. (5 points) d) What is the amount of energy dissipated by friction? (3 points)

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Transcript

0:00 Hello everyone.

00:01 So here in this question it is given that there is a spring and spring constant is given as two multiplied by 10 to the part three.

00:14 Value of x is given as 0 .55 meters.

00:21 Mass of the block is 2 .5 kg.

00:26 We have to calculate the velocity just after leaving the spring after compressing it.

00:34 So we can use energy conservation here that half kx square is equals to half m v square.

00:42 So from here we can say that v is equals to x under root k divided by m.

00:50 So as we know value of x is 0 .55 under root, value of k is 2 multiplied by 10 to be power 3 and value of m is 2 .4.

01:02 So we can write it as 0 .55 under root 2 multiplied by, if we will remove decimal from here, it will add on here.

01:17 So we can write it as 400.

01:20 So on solving this, velocity will come out to be 15 .84 meter per second.

01:29 So this is the velocity.

01:31 Now in the next question, it is asked that if at the end when velocity will be zero, what will be the distance? it will travel.

01:41 What will be the distance? it will travel if it is a friction surface.

01:45 If it is via rough surface.

01:47 So we can say that half mv1 square will convert it into mgh plus mu mgm...

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