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Ray Of Light [21]
3 years ago
13

A single, nonconstant force acts in the + x ‑direction on an object of mass M that is constrained to move along the x ‑axis. As

a result, the object's position as a function of time is x ( t ) = P + Q t + R t 3 How much work W is done by this force from t = 0 s to final time T ? Express the answer in terms of P , Q , R , M , and T .
Physics
1 answer:
klasskru [66]3 years ago
6 0

Answer:

3MQRT^2+\frac{9}{2}MR^2T^4

Explanation:

In order to find the work done by the force, we use the work-energy theorem, which states that the work done by a force on an object is equal to the change in kinetic energy of the object. Mathematically:

W=K_f-K_i = \frac{1}{2}mv^2-\frac{1}{2}mu^2 (1)

where

W is the work done

m is the mass of the object

v is the final speed of the object

u is the initial speed

In this problem, we have:

m = M is the mass of the object

The position of the object at time t is

x(t)=P+Qt+Rt^3

We can find its speed at time t by calculating the derivative of the position:

v(t)=x'(t)=Q+3Rt^2

Therefore:

- The speed at time t = 0 is

u=v(0)=Q

- The speed at time t = T is

v=v(T)=Q+3RT^2

Substituting into eq.(1), we find the work done:

W=\frac{1}{2}M(Q+3RT^2)^2-\frac{1}{2}MQ^2=\\=\frac{1}{2}MQ^2+3QRT^2+\frac{9}{2}MR^2T^4-\frac{1}{2}MQ^2=\\=3MQRT^2+\frac{9}{2}MR^2T^4

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It’s a chemical change
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A jumbo jet weighing 65,000 kg Is accelerating at 3 m/s^2 while its jet engines are putting out 200000 N of thrust.
sveticcg [70]

Answer:

Fa = 5000 [N]

Explanation:

To solve this problem we must use Newton's second law, which tells us that the sum of forces on a body is equal to the product of mass by acceleration.

Let's assume that the movement of the plane is to the right, any movement or force to the right will be marked with a positive sign, while any force or movement to the left, will be taken as negative.

The force of the turbine drives the plane to the right, therefore it is positive, the acceleration is constant and keeps the movement to the right, therefore it is positive, the wind drag force tries to prevent the movement of the plane to the left therefore it is negative, with this analysis we deduce the following equation.

ΣF = m*a

where:

ΣF = sum of forces [N] (units of Newtons)

m = mass = 65000 [kg]

a = acceleration = 3 [m/s²]

Fa = force exerted by the air [N]

200000 - Fa = 65000*3

Fa = 200000 - (3*65000)

Fa = 5000 [N]

8 0
3 years ago
Teachers are interested in knowing what study techniques their students are utilizing. The researchers randomly select every 10t
uranmaximum [27]

Answer:

Simple Random Sample (SRS)

Explanation:

5 0
3 years ago
Andy Petite pitches a 0.8 kg baseball with a velocity of 67 m/s. Josh Hamilton
kodGreya [7K]

The Impulse delivered to the baseball is 89 kgm/s.

To solve the problem above, we use the formula of impulse.

⇒ Formula:

  • I = m(v-u)................. Equation 1

Where:

  • I = Impulse delivered to the baseball
  • m = mass of the baseball
  • v = Final velocity of the baseball
  • u = initial speed of the baseball

From the question,

⇒ Given:

  • m = 0.8 kg
  • u = 67 m/s
  • v = -44 m/s

⇒ Substitute these values into equation 1

  • I = 0.8(-44-67)
  • I = 0.8(-111)
  • I = -88.8
  • I ≈ -89 kgm/s

Note: The negative tells that the impulse is in the same direction as the final velocity and therefore can be ignored.

Hence, The Impulse delivered to the baseball is 89 kgm/s.

Learn more about impulse here: brainly.com/question/7973509

7 0
2 years ago
A slender rod is 90.0 cm long and has mass 0.120 kg. A small 0.0200 kg sphere is welded to one end of the rod, and a small 0.070
likoan [24]

Given Information:

length of slender rod = L = 90 cm = 0.90 m

mass of slender rod = m = 0.120 kg

mass of sphere welded to one end = m₁ = 0.0200 kg

mass of sphere welded to another end = m₂ = 0.0700 kg (typing error in the question it must be 0.0500 kg as given at the end of the question)

Required Information:

Linear speed of the 0.0500 kg sphere = v = ?

Answer:

Linear speed of the 0.0500 kg sphere = 1.55 m/s

Explanation:

The velocity of the sphere can by calculated using

ΔKE = ½Iω²

Where I is the moment of inertia of the whole setup ω is the speed and ΔKE is the change in kinetic energy

The moment of inertia of a rigid rod about center is given by

I = (1/12)mL²

The moment of inertia due to m₁ and m₂ is

I = (m₁+m₂)(L/2)²

L/2 means that the spheres are welded at both ends of slender rod whose length is L.

The overall moment of inertia becomes

I = (1/12)mL² + (m₁+m₂)(L/2)²

I = (1/12)0.120*(0.90)² + (0.0200+0.0500)(0.90/2)²

I = 0.0081 + 0.01417

I = 0.02227 kg.m²

The change in the potential energy is given by

ΔPE = m₁gh₁ + m₂gh₂

Where h₁ and h₂ are half of the length of slender rod

L/2 = 0.90/2 = 0.45 m

ΔPE = 0.0200*9.8*0.45 + 0.0500*9.8*-0.45

The negative sign is due to the fact that that m₂ is heavy and it would fall and the other sphere m₁ is lighter and it would will rise.

ΔPE = -0.1323 J

This potential energy is then converted into kinetic energy therefore,

ΔKE = ½Iω²

0.1323 = ½(0.02227)ω²

ω² = (2*0.1323)/0.02227

ω = √(2*0.1323)/0.02227

ω = 3.45 rad/s

The linear speed is

v = (L/2)ω

v = (0.90/2)*3.45

v = 1.55 m/s

Therefore, the linear speed of the 0.0500 kg sphere as its passes through its lowest point is 1.55 m/s.

8 0
3 years ago
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