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2 years ago

9

A steel playground slide is 5.25 m long and is raised 2.75 m on one end. A 45.0 kg child slides down from the top starting at re

st. The final speed of the child at the bottom is 6.81 m/s. Find the average force of friction between the child and the slide.

1 answer:

Temka [501]2 years ago

8 0

Answer:

$F=32.24N$

Explanation:

From the question we are told that:

Height $h= 2.75 m$

Length $l = 5.25 m$

Mass $m=45kg$

Final speed $v_f=6.81$

Generally the equation for Potential Energy P.E is mathematically given by

$P.E=mgh$

Therefore

Initial potential energy

$P.E_1=45*9.8*2.75 \\\\P.E_1= 1212.75 J$

Generally the equation for Kinetic Energy K.E is mathematically given by

$K.E=0.5mv^2$

Therefore

Final kinetic energy

$K.E_2= 1/2*45*6.81*6.81 \\\\K.E_2= 1043.46J$

Generally the equation for Work_done is mathematically given by

$W=P.E_1-K.E_2\\\\W=169.3$

Therefore

$F=\frac{W}{d}\\\\F=\frac{169.3}{5.25}$

$F=32.24N$

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A stone is catapulted at time t = 0, with an initial velocity of magnitude 19.9 m/s and at an angle of 39.9° above the horizonta

larisa [96]

Answer:

Part a)

$x = 15.76 m$

Part b)

$y = 7.94 m$

Part c)

$x = 26.16 m$

Part d)

$y = 7.49 m$

Part e)

$x = 83.23 m$

Part f)

$y = -75.6 m$

Explanation:

As we know that catapult is projected with speed 19.9 m/s

so here we have

$v_x = 19.9 cos39.9$

$v_x = 15.3 m/s$

similarly we have

$v_y = 19.9 sin39.9$

$v_y = 12.76 m/s$

Part a)

Horizontal displacement in 1.03 s

$x = v_x t$

$x = (15.3)(1.03)$

$x = 15.76 m$

Part b)

Vertical direction we have

$y = v_y t - \frac{1]{2}gt^2$

$y = (12.76)(1.03) - 4.9(1.03)^2$

$y = 7.94 m$

Part c)

Horizontal displacement in 1.71 s

$x = v_x t$

$x = (15.3)(1.71)$

$x = 26.16 m$

Part d)

Vertical direction we have

$y = v_y t - \frac{1]{2}gt^2$

$y = (12.76)(1.71) - 4.9(1.71)^2$

$y = 7.49 m$

Part e)

Horizontal displacement in 5.44 s

$x = v_x t$

$x = (15.3)(5.44)$

$x = 83.23 m$

Part f)

Vertical direction we have

$y = v_y t - \frac{1]{2}gt^2$

$y = (12.76)(5.44) - 4.9(5.44)^2$

$y = -75.6 m$

6 0

3 years ago

A gymnast of mass 62.0 kg hangs from a vertical rope attached to the ceiling. You can ignore the weight of the rope and assume t

MrRissso [65]

Answer:

a) T = 608.22 N

b) T = 608.22 N

c) T = 682.62 N

d) T = 533.82 N

Explanation:

Given that the mass of gymnast is m = 62.0 kg

Acceleration due to gravity is g = 9.81 m/s²

Thus; The weight of the gymnast is acting downwards and tension in the string acting upwards.

So;

To calculate the tension T in the rope if the gymnast hangs motionless on the rope; we have;

T = mg

= (62.0 kg)(9.81 m/s²)

= 608.22 N

When the gymnast climbs the rope at a constant rate tension in the string is

= (62.0 kg)(9.81 m/s²)

= 608.22 N

When the gymnast climbs up the rope with an upward acceleration of magnitude

a = 1.2 m/s²

the tension in the string is T - mg = ma (Since acceleration a is upwards)

T = ma + mg

= m (a + g )

= (62.0 kg)(9.81 m/s² + 1.2 m/s²)

= (62.0 kg) (11.01 m/s²)

= 682.62 N

When the gymnast climbs up the rope with an downward acceleration of magnitude

a = 1.2 m/s² the tension in the string is mg - T = ma (Since acceleration a is downwards)

T = mg - ma

= m (g - a )

= (62.0 kg)(9.81 m/s² - 1.2 m/s²)

= (62.0 kg)(8.61 m/s²)

= 533.82 N

5 0

2 years ago

the hydrometer with the density of liquid to be 800 kg metre per square is the volume of the submerged part of the hydrometer is

julia-pushkina [17]

Answer:

Mass = 0.04 Kg

Explanation:

Given the following data;

Density = 800 kg/m³

Volume = 5 * 10^{-5} m³

To find the mass of the object;

Density can be defined as mass all over the volume of an object.

Simply stated, density is mass per unit volume of an object.

Mathematically, density is given by the formula;

$Density = \frac {mass}{volume}$

Making mass the subject of formula, we have;

$Mass = density * volume$

Substituting the values into the formula, we have;

$Mass = 800 * 5 * 10^{-5}$

Mass = 0.04 Kg

8 0

3 years ago

How many meters are there in 4.80 ly ?

Masja [62]

Since each light year is approximately 9 trillion kilometres, 4.80 light years is 43.2 trillion kilometres, or 43,200,000,000,000,000 metres

6 0

3 years ago

Hi i need answers for this. Thank you!! this is also really important and is due tomorrow at 9am!!

Allushta [10]

Answer:

You're four sentences should include about how the roller coaster has the most potential energy at the top of the track, and the opposing energy, "kinetic" has the most kinetic energy when going down the hill.

Explanation:

Kinetic - In-Motion.

Potential - Gathering Energy to go into Motion.

( I'll try to answer questions to clear up confusion. )

7 0

3 years ago