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NeTakaya
3 years ago
11

A solid ball of inertia m rolls without slipping down a ramp that makes an angle θ with the horizontal.

Physics
1 answer:
LekaFEV [45]3 years ago
8 0

Answer:

Part a)

f = \frac{2}{7}mgsin\theta

Part b)

\mu = \frac{2}{7} gtan\theta

Explanation:

Part a)

Force equation on the inclined plane is given as

mgsin\theta - f = ma

now for torque equation of the ball

fR = \frac{2}{5}mR^2 ( \frac{a}{R})

f = \frac{2}{5}ma

now from above two equations

mg sin\theta - \frac{2}{5}ma = ma

mg sin\theta = \frac{7}{5} ma

a = \frac{5}{7} gsin\theta

so frictional force is given as

f = \frac{2}{5}ma

f = \frac{2}{5}m(\frac{5}{7}gsin\theta)

f = \frac{2}{7}mgsin\theta

Part b)

Also we know that in the normal direction of the motion we have

F_n = mgcos\theta

so we have

f = \mu F_n

\frac{2}{7} mg sin\theta = \mu (mg cos\theta)

now we have

\mu = \frac{2}{7} gtan\theta

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A stone is dropped from the edge of a roof, and hits the ground with a velocity of -180 feet per second. How high (in feet) is t
Neko [114]

Answer:

d = 506.25 ft

Explanation:

As we know by kinematics that

v_f^2 - v_i^2 = 2 a d

here we know that initially the stone is dropped from rest from the edge of the roof

so here initial speed will be zero

now we have

v_i = 0

also the acceleration of the stone is due to gravity which is given as

g = 32 ft/s^2

now we have

v_f = 180 ft/s

so from above equation

180^2 - 0 = 2(32)d

d = 506.25 ft

6 0
3 years ago
if the forces acting upon an object are balanced, then an object must a) be moving. b) be accelerating. c) be beginning to slow
Dennis_Churaev [7]

The correct answer to the question is : D) Be moving at a constant velocity.

EXPLANATION:

As per Newton's first laws of motion, every body continues to be  at state of rest or of uniform motion in a straight line unless and until it is compelled by some external unbalanced forces acting on it.

Hence, it is the unbalanced force which changes the state of rest or motion of a body. Balanced force is responsible for keeping the body to be either in static equilibrium or in dynamic equilibrium.

As per the options given in the question, the last one is true for an object under balanced forces.


4 0
3 years ago
astronauts in space cannot weigh themselves by standing on a bathroom scale. Instead, they determine their mass by oscillating o
devlian [24]

Answer:

The right answer is:

(a) 63.83 kg

(b) 0.725 m/s

Explanation:

The given query seems to be incomplete. Below is the attachment of the full question is attached.

The given values are:

T = 3 sec

k = 280 N/m

(a)

The mass of the string will be:

⇒ T=2 \pi\sqrt{\frac{m}{k} }

or,

⇒ m=\frac{k T^2}{4 \pi^2}

On substituting the values, we get

⇒     =\frac{280\times (3)^2}{4 \pi^2}

⇒     =\frac{280\times 9}{4\times (3.14)^2}

⇒     =68.83 \ kg

(b)

The speed of the string will be:

⇒  \frac{1}{2}k(0.4)^2=\frac{1}{2}k(0.2)^2+\frac{1}{2}mv^2

then,

⇒             v=\sqrt{\frac{k((0.4)^2-(0.2)^2)}{m} }

On substituting the values, we get

⇒                =\sqrt{\frac{280\times ((0.4)^2-(0.2)^2)}{63.83} }

⇒                =\sqrt{\frac{280(0.16-0.04)}{63.83} }

⇒                =\sqrt{\frac{280\times 0.12}{63.83} }

⇒                =0.725 \ m/s

4 0
3 years ago
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Mice21 [21]

Answer:

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Explanation:

The complete question is presented in the attached image to this solution.

v(t) = 61 - 61e⁻⁰•²⁶ᵗ

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We just substitute 43 m/s into the equation for the velocity of the diver and solve for t.

43 = 61 - 61e⁻⁰•²⁶ᵗ

- 61e⁻⁰•²⁶ᵗ = 43 - 61 = -18

e⁻⁰•²⁶ᵗ = (18/61) = 0.2951

In e⁻⁰•²⁶ᵗ = In 0.2951 = -1.2205

-0.26t = -1.2205

t = (1.2205/0.26) = 4.694 s = 4.7 s to the nearest tenth.

Hope this Helps!!!

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