26c Dynamics Review B

1. Sirius B is a white dwarf star, in orbit around Sirius, with a mass of 2.0 x 1030 kg (approximately the mass of the Sun), and a radius of 2.4 x 107 m (approximately one-thirtieth of the radius of the Sun).
a. What is the force on a 1.0 kg mass on the surface of Sirius B? [2.3 x 105 N]
b. What is the acceleration due to gravity on the surface of Sirius B? [2.3 x 105 m/s2]

2. A 1000 kg communications satellite in synchronous orbit 42 400 km from the Earth’s centre gas a period of 24 h. Placed in orbit above the equator, and moving in the same direction as the Earth is turning, it stays above the same point on Earth at all times. This makes it useful for the reception and retransmission of telephone, radio, and TV signals.
a. Calculate the force of gravity acting on the satellite. [222 N]
b. What is the gravitational field strength at this altitude? [0.222 N/kg]

3. An 1100 kg car accelerates from rest at 3.4 m/s2.
a. What is the unbalanced force acting on it? [3.7 x 103 N]
b. If the horizontal force exerted on the wheels by the road is 5600 N, what force must be resisti ng the motion of the car? [1.9 x 103 N]

4. A block if wood of mass 6.0 kg slides along a skating rink at 12.5 m/s [W]. The block slides onto a rough section of ice that exerts a 30 N force of friction on the block of wood. Calculate:
a. the acceleration of the block of wood. [5.0 m/s2 [E]]
b. the time it takes the block of wood to stop [2.5 m/s]
c. how far the block slides after friction begins to act on it. [15.6 m]

5. A force of 36 N gives a mass m1 an acceleration of 4.0 m/s2. The same force gives a mass m2 an acceleration of 12 m/s2. What acceleration will this force give to m1 and m2 if the two masses are fastened together. [3.0 m/s2]

6. A fully loaded Saturn V rocket has a mass of 2.92 x 106 kg. Its engines have a thrust of 3.34 x 107 N.
a. What is the downward force of gravity on the rocket at blast-off?
[2.86 x 107 N]
b. What is the unbalanced force on the rocket at blast-off? [4.8 x 106 N [up]]
c. What is the acceleration of the rocket as it leaves the launching platform? [1.6 m/s2]
d. As the rocket travels upwards, the engine thrust remains constant, but the mass of the rocket decreases. Why?
e. Does the acceleration of the rocket increase, decrease, or remain the same as the engines continue to fire?

7. Determine the acceleration of the blocks and the tension in each rope. Assume the surface is frictionless. [1.0 m/s2, left rope is 1 N, right rope 3 N]

8. A racing car has a mass of 1500 kg, is accelerating at 5.0 m/s2, is experiencing a lift force of 600 N up (due to its streamlined shape) and ground effects of 1000 N down (due to air-dams and spoilers). Find the driving force needed to keep the car going given that  = 1.0 for the car. [2.26 x 104 N]

9. Try question 7 again, but add in a force of friction. Assume  = 0.10.
[0.02 m/s2; 1 N, 3 N]

10. Determine the minimum coefficient of static friction that will keep the top box moving along with the bottom box. Assume that the applied force is only applied to the bottom box. Assume the coefficient of kinetic friction between the bottom box and the counter is 0.25. [S = 0.36]