Question 1

A 2.00-kg mass is located at (4.00 m)  +(-1.00 m)  . A 1.00-kg mass is located at (1.00 m)  + (2.00 m)  . Where must a 3.00-kg mass be located so that the center of mass of the system is located at (-1.00 m)  + (1.00 m)  ?

Accepted Answer

The answer of A 2.00-kg mass is located at (4.00...

Question 2

A 1000-kg helicopter hovers over a forest fire and starts to squirt water downward with a speed of 10 m/s at a rate of 40 kg/s. What is the initial upward acceleration on the helicopter when it first starts to release the water?

Accepted Answer

The answer of A 1000-kg helicopter hovers over a forest...

Question 3

A toy rocket with a mass of 300 g takes off in a vertical direction under the influence of gravity. It burns fuel at the rate of 25 g/s. The exhaust speed of the gases is 80 m/s. What is the speed of the rocket at the end of 10 seconds?

Accepted Answer

The rocket equation (Tsiolkovsky's equation) is used to calculate the speed: v = v_exhaust * ln(m_initial/m_final) - g*t. Initial mass = 300 g, final mass = 300 g - 25 g/s * 10 s = 50 g. v = 80 m/s * ln(300/50) - 9.8 m/s² * 10 s = 145 m/s.

Question 4

A rocket with a mass of 2.0 × 10⁶ kg is designed to take off from the surface of the earth by burning fuel and ejecting it with an exhaust speed of 3500 m/s. What is the minimum rate at which the fuel should be consumed in order to attain liftoff?

Accepted Answer

The thrust must equal the gravitational force for liftoff. Thrust = exhaust speed × fuel consumption rate. Gravitational force = mass × gravity. Solving 3500 × rate = 2.0 × 10^6 × 9.8 gives rate = 5.6 × 10^3 kg/s.

Question 5

A 320-g air track cart is traveling at 1.25 m/s and a 270-g cart traveling in the opposite direction at 1.33 m/s. What is the speed of the center of mass of the two carts?

Accepted Answer

The speed of the center of mass is given by:$$v_{cm}=\frac{m_1v_1+m_2v_2}{m_1+m_2}$$where $m_1$ and $v_1$ are the mass and velocity of the first cart, and $m_2$ and $v_2$ are the mass and velocity of the second cart.Plugging in the given values, we get:$$v_{cm}=\frac{(0.320	ext{ kg})(1.25	ext{ m/s})+(0.270	ext{ kg})(-1.33	ext{ m/s})}{0.320	ext{ kg}+0.270	ext{ kg}}=0.0693	ext{ m/s}$$Therefore, the speed of the center of mass of the two carts is 0.0693 m/s.

Quiz 9: Linear Momentum

A 2.00-kg mass is located at (4.00 m) +(-1.00 m) . A 1.00-kg mass is located at (1.00 m) + (2.00 m) . Where must a 3.00-kg mass be located so that the center of mass of the system is located at (-1.00 m) + (1.00 m) ?

A 1000-kg helicopter hovers over a forest fire and starts to squirt water downward with a speed of 10 m/s at a rate of 40 kg/s. What is the initial upward acceleration on the helicopter when it first starts to release the water?

A toy rocket with a mass of 300 g takes off in a vertical direction under the influence of gravity. It burns fuel at the rate of 25 g/s. The exhaust speed of the gases is 80 m/s. What is the speed of the rocket at the end of 10 seconds?

A rocket with a mass of 2.0 × 106 kg is designed to take off from the surface of the earth by burning fuel and ejecting it with an exhaust speed of 3500 m/s. What is the minimum rate at which the fuel should be consumed in order to attain liftoff?

A 320-g air track cart is traveling at 1.25 m/s and a 270-g cart traveling in the opposite direction at 1.33 m/s. What is the speed of the center of mass of the two carts?

A rocket with a mass of 2.0 × 10⁶ kg is designed to take off from the surface of the earth by burning fuel and ejecting it with an exhaust speed of 3500 m/s. What is the minimum rate at which the fuel should be consumed in order to attain liftoff?