Question

Consider a free-rolling ramp with stairs as shown. A little boy, weighing 35 kg, is trying to climb the stairs starting at the bottom to reach the top and look at what's on the other side of the ramp. The rolling ramp itself is about 300 kg. The length of the ramp is L = 3 m and the height difference between the top and the bottom stairs is H = 2.1 m. Everything is at rest initially and then, the boy dashes off and reaches the top at a ruthless pace of 3 m/s (in the direction of ascent, in the frame of the ramp). Write all the known information and unknown variables you need to find (add to the list here if/when you find new unknowns later), distinguishing between relative and absolute values [2 pt] Find the velocity of the rolling ramp when the boy reaches the top [4 pt] How much energy does the boy have to generate to reach the top at 3 m/s, starting from zero? [2 pt] If the boy had a constant acceleration while ascending the steps, how much time did it take him to reach the top from the bottom? [2 pt]

          Consider a free-rolling ramp with stairs as shown. A little boy, weighing 35 kg, is trying to climb the stairs starting at the bottom to reach the top and look at what's on the other side of the ramp. The rolling ramp itself is about 300 kg. The length of the ramp is L = 3 m and the height difference between the top and the bottom stairs is H = 2.1 m. Everything is at rest initially and then, the boy dashes off and reaches the top at a ruthless pace of 3 m/s (in the direction of ascent, in the frame of the ramp).

Write all the known information and unknown variables you need to find (add to the list here if/when you find new unknowns later), distinguishing between relative and absolute values [2 pt]

Find the velocity of the rolling ramp when the boy reaches the top [4 pt]

How much energy does the boy have to generate to reach the top at 3 m/s, starting from zero? [2 pt]

If the boy had a constant acceleration while ascending the steps, how much time did it take him to reach the top from the bottom? [2 pt]

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consider a free rolling ramp with stairs as shown a little boy weighing 35 kg is trying to climb the stairs starting at the bottom to reach the top and look at whats on the other side of the 61173

Added by Andrea D.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Melissa Munoz

07/02/2025

Step 1

Knowns: - Mass of the boy, $m_b = 35 \text{ kg}$ - Mass of the ramp, $m_r = 300 \text{ kg}$ - Length of the ramp, $L = 3 \text{ m}$ - Height difference, $H = 2.1 \text{ m}$ - Initial state: Everything is at rest, so initial velocity of the boy relative to the Show more…

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Consider a free-rolling ramp with stairs as shown. A little boy, weighing 35 kg, is trying to climb the stairs starting at the bottom to reach the top and look at what's on the other side of the ramp. The rolling ramp itself is about 300 kg. The length of the ramp is L = 3 m and the height difference between the top and the bottom stairs is H = 2.1 m. Everything is at rest initially and then, the boy dashes off and reaches the top at a ruthless pace of 3 m/s (in the direction of ascent, in the frame of the ramp). Write all the known information and unknown variables you need to find (add to the list here if/when you find new unknowns later), distinguishing between relative and absolute values [2 pt] Find the velocity of the rolling ramp when the boy reaches the top [4 pt] How much energy does the boy have to generate to reach the top at 3 m/s, starting from zero? [2 pt] If the boy had a constant acceleration while ascending the steps, how much time did it take him to reach the top from the bottom? [2 pt]

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Transcript

00:01 In a warehouse, a wagon with a mass of 250 kilograms must be transported over a ramp.

00:09 The height of the ramp is 1 .5 meters and the slope angle is 5 degrees.

00:14 The rolling friction coefficient of the wheels is 0 .5.

00:21 We can neglect the moment of inertia of the wheel.

00:25 Question 8, you want to calculate the frictional force which acts on the wagon during rolling on the ramp.

00:34 Let's draw illustration.

00:36 I'm going to exaggerate the angle of the wheel.

00:38 Ramp so our ramp at the end is at a height of 1 .5 meters and here we have an angle of 5 degrees so when our wagon is being pushed up the ramp it is being weighted down by gravity and what's opposing the upwards motion is a downwards force of friction and its force of friction is related as usual to the normal force let's place our corner system and client and let's sum the forces along y in order to find the normal force.

01:41 So the sums of the forces along y must be equal to zero, which means that our normal force is equal to m g coast theta.

01:55 And from here we can calculate our friction force, which is given by our coefficient of friction times the normal force.

02:22 So we obtain mu and g cost data.

02:28 And just to elaborate on the variables here, um, i'll label the height as 1 .5 meters the angle ramp is 5 degrees and hence the length of our ramp can be found as untrigger will have the pythagorean theorem the hypotenuse will be given by 1 .5 over sign data which is 17 .21 meters and next we want to find or let's label we have the mass which is 250 kilograms and the coefficient of friction which is 0 .0.

03:38 0 .05.

03:41 The rolling friction, so kinetic friction.

03:45 And putting all these variables, we obtain a friction force of 122, putting 0 .03.

04:00 Mows assume that the wagon is at the top of the ramp and starts to roll down from rest.

04:05 We want to determine the velocity at the end of the ramp.

04:09 So here we're going to look at our kinematic expressions...

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