VIPSolutionsgive answer in 2 step with explanation at the end of each step and final answer at the end:Problem 6: (17% of Assignment Value) y A bowling ball m = 2.6 kg is dropped from a height h. It falls a distance, d, before encountering a large tube r eo) =2.6 m which is connected by two bolts. Each bolt can individually sustain a force of £ = 10 N before failing. . Part (a) ‘Write an expression for the maximum distance, d, above the pipe from which the ball can be dropped so the bolts do not fail. — d=|(Fmg)r-(52)d Deductions 4% pe a a) 09) 0/00) ins 0 SS (Co eT EEE) rm, ar a ae) 0/8/0/0 0/6) w Cm or EOC IE) a er a) EE [errr EE — a TE Part (b) ‘What is the distance, in meters?
Question:
give answer in 2 step with explanation at the end of each step and final answer at the end:
Problem 6: (17% of Assignment Value) y
A bowling ball m = 2.6 kg is dropped from a height h. It falls a distance, d, before encountering a large tube r eo)
=2.6 m which is connected by two bolts. Each bolt can individually sustain a force of £ = 10 N before
failing.
.
Part (a)
‘Write an expression for the maximum distance, d, above the pipe from which the ball can be dropped so the bolts do not fail.
—
d=|(Fmg)r-(52)d Deductions 4%
pe
a a) 09) 0/00) ins
0 SS
(Co eT EEE) rm,
ar a ae) 0/8/0/0 0/6) w
Cm or EOC IE)
a er a) EE
[errr
EE — a TE
Part (b)
‘What is the distance, in meters?
This is AI generated Response.
Asked by: Rahul
Created at: 2025-11-20 03:06:56
Asked by: Rahul
Created at: 2025-11-20 03:06:56
Final Answer:
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Let's solve **Part (b)** step by step, using your given formula and the values from the problem.
---
## Step 1: Write Down the Known Values
From the problem:
- \( m = 2.6\, \text{kg} \)
- \( r = 2.6\, \text{m} \)
- Each bolt can hold \( F = 110\, \text{N} \)
- \( g = 9.8\, \text{m/s}^2 \) (acceleration due to gravity)
The formula from Part (a) is:
\[
d = \left(\frac{F}{mg}\right)r - \frac{5}{2}r
\]
**Explanation:**
This formula calculates the maximum drop height \( d \) so that the force on the bolts doesn't exceed their limit.
---
## Step 2: Substitute the Values and Calculate
Plug the known values into the formula:
\[
d = \left(\frac{110}{2.6 \times 9.8}\right) \times 2.6 - \frac{5}{2} \times 2.6
\]
Calculate each part:
- \( mg = 2.6 \times 9.8 = 25.48 \)
- \( \frac{F}{mg} = \frac{110}{25.48} \approx 4.317 \)
- \( \left(\frac{F}{mg}\right) r = 4.317 \times 2.6 \approx 11.224 \)
- \( \frac{5}{2} \times 2.6 = 2.5 \times 2.6 = 6.5 \)
Now, subtract:
\[
d = 11.224 - 6.5 = 4.724
\]
**Explanation:**
The calculations give the maximum height above the pipe from which the ball can be dropped so the bolts do not fail.
---
## **Final Answer**
\[
\boxed{d = 4.72\, \text{meters}}
\]
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