A cord is used to vertically lower an initially stationary block of mass M = 3.6 kg at a constant downward acceleration of g/7. When the block has fallen a distance d = 4.2 m, find (a) the work done by the cord's force on the block, (b) the work done by the gravitational force on the block, (c) the kinetic energy of the block, and (d) the speed of the block. (Note : Take the downward direction positive)
Answers
Answer:
a) W₁ = - 127 J, b) W₂ = 148.18 J, c) = 3.43 m/s and d)
= 3.43 m / s
Explanation:
The work is given the equation
W = F. d
Where the bold indicates vectors, we can also write this expression take the module of each element and the angle between them
W = F d cos θ
They give us displacement, let's use Newton's second law to find strength, like the block has an equal acceleration (a = g / 7). We take a positive sign down as indicated
W-T = m a
T = W -m a
T = mg -mg/7
T = mg 6/7
T = 3.6 9.8 6/7
T = 30.24 N
Now we can apply the work equation to our problem
a) the force of the cord is directed upwards, the displacement is downwards, so there is a 180º angle between the two
W₁ = F d cos θ
W₁ = 30.24 4.2 cos 180
W₁ = - 127 J
b) the force of gravity is directed downwards and the displacement is directed downwards, the angle between the two is zero (T = 0º)
W₂ = (mg) d cos 0º
W₂ = 3.6 9.8 4.2
W₂ = 148.18 J
c) kinetic energy
K = ½ m v²
Let's calculate speed with kinematics
² = vo² + 2 a y
v₀ = 0
a = g / 7
² = 2g / 7 y
= √ (2 9.8 4.2 / 7)
= 3.43 m/s
We calculate
K = ½ 3.6 3.43²
K = 21.18 J
d) the speed of the block and we calculate it in the previous part
= 3.43 m / s
Related Questions
Suppose that you run along three different paths from location A tolocation B. Along which path(s) would your distance traveled be different than your displacement (Question 2) please help
What electric field strength would store 12.5 JJ of energy in every 6.00 mm3mm3 of space?
A person pushing a stroller starts from rest, uniformly accelerating at a rate of 0.500 m/s2. What is the velocityof the stroller after it has traveled 6.32 m?
A 50.0-g hard-boiled egg moves on the end of a spring with force constant k = 25.0 N/m. It is released with an amplitude 0.300 m. A damping force F_x = -bv acts on the egg. After it oscillates for 5.00 s, the amplitude of the motion has decreased to 0.100 m.Calculate the magnitude of the damping coefficient b.Express the magnitude of the damping coefficient numerically in kilograms per second, to three significant figures.
Answers
Answer:
B- Velocity
Explanation:
This means gravity makes the Moon accelerate all the time, even though its speed remains constant.
Answers
Answer:
0.3659
Explanation:
The power (p) is given as:
P = AeσT⁴
where,
A =Area
e = transmittivity
σ = Stefan-boltzmann constant
T = Temperature
since both the bulbs radiate same power
P₁ = P₂
Where, 1 denotes the bulb 1
2 denotes the bulb 2
thus,
A₁e₁σT₁⁴ = A₂e₂σT₂⁴
Now e₁=e₂
⇒A₁T₁⁴ = A₂T₂⁴
or
substituting the values in the above question we get
or
=0.3659
Answers
Answer:
Knowing that these metals are infact good conductors of electricity we can infer that metals are able to hold and conduct certain temperatures. Another thing we can infer is that these good conductors can be used in connection to transferring energy or electricity.
a. Calculate in kPa the pressure in the hydraulic fluid induced by the applied pressure.
b. What is the magnitude of the force exerted on the load bearing piston by the hydraulic fluid?
Answers
Answer:
Explanation:
Pressure on the hydraulic system is expressed as;
Pressure = Force/Area
Given
Force on the fluid = 400N
Area = 0.001m²
Pressure in the fluid = 400/0.001
Pressure in the fluid = 400,000N/m²
1N/m² = 0.001kPa
400,000N/m² = x
x = 400,000 × 0.001
x = 400kPa
Hence the pressure in kPa is 400kPa
b) Using the formula;
Pa = Pb
Fa/Aa = Fb/Ab
Pa = Fb/Ab
Fb = PaAb
Fb = 400,000(0.2)
Fb = 80,000N
Hence the magnitude of the force exerted on the load bearing piston by the hydraulic fluid is 80,000N
Final answer:
In a hydraulic system, a force exerted creates a pressure that is transmitted equally throughout. The induced pressure in the hydraulic system is 400 kPa. By applying the same pressure across the larger piston (0.2 m2), a force of 80,000 N is generated on the load-bearing piston.
Explanation:
The subject of this question is the physics topic of hydraulic systems, specifically how forces and pressure interactions. Use Pascal's principle which states that a change in pressure at any point in an enclosed fluid under equilibrium will be transmitted equally to all parts of the fluid.
a. To find the pressure in kPa induced by the applied pressure, use the formula P=F/A, where P is pressure, F is force and A is area. With the force F = 400 N and area A = 0.001 m2, the induced pressure is P = 400 N / 0.001 m2 = 400,000 Pa or 400 kPa.
b. The force exerted on the load-bearing piston by the hydraulic fluid is calculated by rearranging the formula to F=PxA. So, F = 400kPa x 0.2m2 = 80,000 N. Therefore, the force exerted on the load-bearing piston by the hydraulic fluid is 80,000N.
Learn more about Hydraulic Systems here:
#SPJ3
Answers
Answer: the earth
Explanation: Earth exerts a gravitational pull on the moon 80 times stronger than the moon's pull on the Earth. Over a very long time, the moon's rotations created fiction with the Earth's tugging back, until the moon's orbit and rotational locked with Earth.
and that's why the earth pulls the moon
Final answer:
The Earth pulling on the moon and the moon pulling on the Earth exert the same amount of force on each other due to Newton's third law of motion.
Explanation:
In terms of force, the Earth pulling on the Moon and the Moon pulling on the Earth exert the same amount of force on each other. This is because of Newton's third law of motion, which states that for every action, there is an equal and opposite reaction. So, while the Earth's gravitational force pulls the Moon towards it, the Moon's gravitational force also pulls the Earth towards it with an equal amount of force.
Newton's third law of motion states that for every action, there is an equal and opposite reaction. In the context of the gravitational interaction between the Earth and the Moon, the forces they exert on each other are equal in magnitude and opposite in direction.
The Earth pulls on the Moon with a gravitational force, and, according to Newton's third law, the Moon simultaneously pulls on the Earth with an equal gravitational force. These forces are sometimes referred to as "action and reaction pairs." The force that the Earth exerts on the Moon is often called the gravitational attraction of the Earth on the Moon, and vice versa.
Learn more about gravitational force here:
#SPJ2
Answers
Answer:
Radius at liftoff 8.98 m
Explanation:
At the working altitude;
maximum radius = 24 m
air pressure = 0.030 atm
air temperature = 200 K
At liftoff;
temperature = 349 K
pressure = 1 atm
radius = ?
First, we assume balloon is spherical in nature,
and that the working gas obeys the gas laws.
from the radius, we can find the volume of the balloon at working atmosphere.
Volume of a sphere =
volume of balloon = x 3.142 x
= 57913.34 m^3
using the gas equation,
=
The subscript 1 indicates the properties of the gas at working altitude, and the subscript 2 indicates properties of the gas at liftoff.
imputing values, we have
=
0.03 x 57913.34 x 349 = 200V2
V2 = 606352.67/200 = 3031.76 m^3 this is the volume occupied by the gas in the balloon at liftoff.
from the formula volume of a sphere,
V = =
x 3.142 x
= 3031.76
4.19 = 3031.76
= 3031.76/4.19
radius r of the balloon on liftoff = = 8.98 m