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Butoxors [25]
3 years ago
11

A force of 960 newtons stretches a spring 4 meters. A mass of 60 kilograms is attached to the end of the spring and is initially

released from the equilibrium position with an upward velocity of 6 m/s. Find the equation of motion.
Physics
1 answer:
Drupady [299]3 years ago
4 0

Answer:

x(t) = - 6 cos 2t

Explanation:

Force of spring = - kx

k= spring constant

x= distance traveled by compressing

But force = mass × acceleration

==> Force = m × d²x/dt²

===> md²x/dt² = -kx

==> md²x/dt² + kx=0   ------------------------(1)

Now Again, by Hook's law

Force = -kx

==> 960=-k × 400

==> -k =960 /4 =240 N/m

ignoring -ve sign k= 240 N/m

Put given data in eq (1)

We get

60d²x/dt² + 240x=0

==> d²x/dt² + 4x=0

General solution for this differential eq is;

x(t) = A cos 2t + B sin 2t   ------------------------(2)

Now initially

position of mass spring

at time = 0 sec

x (0) = 0 m

initial velocity v= = dx/dt=  6m/s

from (2) we have;

dx/dt= -2Asin 2t +2B cost 2t = v(t) --- (3)

put t =0 and dx/dt = v(0) = -6 we get;

-2A sin 2(0)+2Bcos(0) =-6

==> 2B = -6

B= -3

Putting B = 3 in eq (2) and ignoring first term (because it is not possible to find value of A with given initial conditions) - we get

x(t) = - 6 cos 2t

==>  

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Which of the following statements is/are true?Check all that apply.a. A conservative force permits a two-way conversion between
Eddi Din [679]

Answer:

a). A conservative force permits a two-way conversion between kinetic and potential energies.

TRUE

Because there is no energy loss in presence of conservative forces so energy conversion in two ways are possible.

b). A potential energy function can be specified for a conservative force.

TRUE

negative gradient of potential energy is equal to conservative force

F = -\frac{dU}{dr}

c). A non-conservative force permits a two-way conversion between kinetic and potential energies.

FALSE

here energy is lost against non-conservative forces

d). The work done by a conservative force depends on the path taken.

FALSE

work done by conservative force is independent of path

e). The work done by a non-conservative force depends on the path taken.

TRUE

work done by non conservative forces depends on path.

f). A potential energy function can be specified for a non-conservative force.

FALSE

It is not defined for non conservative forces

3 0
3 years ago
The voltage supplied to a circuit is 17 V and the current running through is 10 A. What is the power generated?
Lelu [443]

Answer:

170 W

Explanation:

Applying

P = VI.................... Equation 1

Where P = Power generated in watt, V = Voltage supplied to the circuit, I = Current running through the circuit.

From the question,

Given: V = 17 V, I = 10 A

Substitute these values into equation 1

P = (17×10)

P = 170 Watt.

Hence the power generated is 170 W.

The right option is A. 170 W

3 0
2 years ago
5. An object has a momentum of 4,000 kg-m/s and a mass of 115 kg. It crashes into another object that has a mass of 100 kg, and
marishachu [46]

Answer:

D. 18.60

Explanation:

By the law of conservation, the momentum is neither loss nor gained but instead transfered. When they crash into each other, and stick, they combine to create a total mass of 215 kg. Since the momentum is transfered, the two objects, combined, have a total momentum of 4000 kg-m/s. We know that momentum equals mass times velocity. You then divide 4000 by 215 and get approximately 18.6 m/s

4 0
3 years ago
PLEASE HELP WILL MAKE BRAINIEST (GIVING AWAY 20 POINTS)
Bond [772]

1) The most potential energy is at position A

2) The most kinetic energy is at position C

Explanation:

1)

The gravitational potential energy is the energy possessed by an object due to its position in a gravitational field, and it is given by the equation

PE=mgh

where

m is the mass of the object

g is the acceleration of gravity

h is the height of the object relative to the ground

From the equation, we see that the potential energy is directly proportional to the heigth of the object: therefore, the roller coaster in this problem will have the most potential energy at its highest postion, so at position A.

2)

The total mechanical energy of the roller coaster at any point along the track is given by

E=PE+KE

where

PE is the potential energy

KE is the kinetic energy

Assuming there is no friction, the mechanical energy E is constant. This means that when PE increases, KE decreases, and when PE increases, KE decreases.

Therefore, the cart will have maximum kinetic energy when the potential energy is at minimum: and since the potential energy is directly proportional to the height of the track, this will occur at the lowest position, so at position C.

Learn more about kinetic and potential energy:

brainly.com/question/6536722

brainly.com/question/1198647

brainly.com/question/10770261

#LearnwithBrainly

5 0
3 years ago
What conversion takes place in a generator?
Andrew [12]

Answer:

B. An electric current into a magnetic field

Explanation:

The generation of electrical power requires relative motion between a magnetic field and a conductor. In a generator, mechanical energy is converted into electrical energy. The electricity produced by most generators is in the form of alternating current.

5 0
3 years ago
Read 2 more answers
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