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guapka [62]
4 years ago
14

The mass of the Earth is 5.98 × 1024 kg . A 11 kg bowling ball initially at rest is dropped from a height of 2.63 m. The acceler

ation of gravity is 9.8 m/s 2 . What is the speed of the Earth coming up to meet the ball just before the ball hits the ground? Answer in units of m/s.
Physics
1 answer:
jekas [21]4 years ago
3 0

Answer:

v = 7.18_m/s

Explanation:

Velocity of the earth towards the ball is = velocity of the ball moving towards earth

For object in free fall, we have

Where

v = final velocity

u = initial velocity

g = acceleration due to gravity

t = time

S = height of ball above ground

v^2 = u^2 - 2×g×(-S)

= 0 + 2×9.8×2.63 = 51.55_m^2/s^2

Velocity of the ball just before it hits the ground is

v = 7.18_m/s

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3 years ago
A spring is 6.0cm long when it is not stretched, and 10cm long when a 7.0N force is applied. What force is needed to make it 20c
Artist 52 [7]

Answer:

Approximately 25\; {\rm N} (assuming that this spring is ideal.)

Explanation:

The displacement of a spring is the new length of the spring relative to the original length.

For example:

  • When the 6.0\; {\rm cm}-spring in this question is stretched to 10\; {\rm cm}, the displacement is x = (10\; {\rm cm} - 6.0\; {\rm cm}).
  • Likewise, if this spring is stretched to 20\; {\rm cm}, the displacement would be (20\; {\rm cm} - 6\; {\rm cm}).

If this spring is ideal, the force on the spring would be proportional to the displacement of the spring. In other words, if a force of F_{\text{a}} displaces this spring by x_{\text{a}}, while a force of F_{\text{b}} displaces this spring by x_{\text{b}}, then:

\displaystyle \frac{F_{\text{a}}}{x_{\text{a}}} = \frac{F_{\text{b}}}{x_{\text{b}}}.

In this question, it is given that a force of F_{\text{a}} = 7.0 \; {\rm N} would stretch this spring by x_{\text{a}} = (10\; {\rm cm} - 6.0\; {\rm cm}). Thus, the force F_{\text{b}} required to stretch this spring by x_{\text{a}} = (20\; {\rm cm} - 6.0\; {\rm cm}) would satisfy:

\displaystyle \frac{7.0\; {\rm N}}{10\; {\rm cm} - 6.0\; {\rm cm}}= \frac{F_{\text{b}}}{20\; {\rm cm} - 6.0\; {\rm cm}}.

Rearrange and solve for F_{\text{b}}:

\begin{aligned} F_{\text{b}} &= \frac{7.0\; {\rm N}}{10\; {\rm cm} - 6.0\; {\rm cm}} \, (20\; {\rm cm} - 6.0\; {\rm cm}) \\ &\approx 25\; {\rm N}\end{aligned}.

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2 years ago
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7 0
3 years ago
The formula v = √2.5r models the maximum safe speed, v, in miles per hour, at which a car can travel on a curved road with radiu
mel-nik [20]

Answer:

The maximum safe speed of the car is 30.82 m/s.

Explanation:

It is given that,

The formula that models the maximum safe speed, v, in miles per hour, at which a car can travel on a curved road with radius of curvature r r, is in feet is given by :

v=\sqrt{2.5\ r}.........(1)

A highway crew measures the radius of curvature at an exit ramp on a highway as 380 feet, r = 380 feet

Put the value of r in equation (1) as :

v=\sqrt{2.5\ \times 380}

v = 30.82 m/s

So, the maximum safe speed of the car is 30.82 m/s. Hence, this is the required solution.

4 0
3 years ago
A civil engineer must design a wheelchair-accessible ramp next to a set of steps leading up to a building. The height from the g
Westkost [7]

Answer:

A) B = 24 ft

B) H = 24.08 ft

C) M.A = 12.04

D) P = 13.7 lb

Explanation:

A)

Minimum allowable length of base of ramp can be found as follows:

Slope = H/B

where,

Slope = 1/12

H = Height of Ramp = 2 ft

B = Length of Base of Ramp = ?

Therefore,

1/12 = 2 ft/B

B = 2 ft * 12

<u>B = 24 ft</u>

B)

The length of the slope of ramp can be found by using pythagora's theorem:

L = √H² + B²

where,

H = Perpendicular = height = 2 ft

B = Base = Length of Base of Ramp = 24 ft

L = Hypotenuse = Length of Slope of Ramp = ?

Therefore,

H = √[(2 ft)² + (24 ft)²]

<u>H = 24.08 ft</u>

D)

The mechanical advantage of an inclined plane is given by the following formula:

M.A = L/H

M.A = 24.08 ft/2 ft

<u>M.A = 12.04</u>

D)

Another general formula for Mechanical Advantage is:

M.A = W/P

where,

W = Ideal Load = 165 lb

P = Ideal Effort Force = ?

Therefore,

12.04 = 165 lb/P

P = 165 lb/12.04

<u>P = 13.7 lb</u>

7 0
3 years ago
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